Math Curriculum Map Kindergarten Domain Clusters Key Vocabulary Core Standard I/R/M ODE / TC Grade Level Specific Standard Quarter Taught Student Engagement/ Learning Activity / Special Resource / Web Link Counting and Cardinality Know number names and the count sequence. Number words, skip counting, even, odd, twos, fives, tens K.CC 1a I/R ODE Count to 100 by ones and by tens. 1,2,3,4 CD, manipulatives, 100s chart, internet4classrooms. com, calendar time Counting and Cardinality Know how to skip count. Number words, skip counting, even, odd, twos, fives, tens K.CC 1b I/R TC Skip count by 2s to 20, by 5s to 100. 1,2,3,4 CD, manipulatives, 100s chart, internet4classrooms. com, calendar time Counting and Cardinality Know how to count backwards from twenty. Number words, counting back K.CC 1c I/R TC Count back from 20 to 0. 1,2,3,4 CD, manipulatives, 100s chart, internet4classrooms. com, calendar time Counting and Cardinality Know number names and the count sequence. Number words, counting on K.CC 2 I/R ODE Count forward beginning from a given number within the known sequence (instead of having to begin at 1). 1,2,3,4 silent line up, adding on, calendar Counting and Cardinality Know number names and the count sequence. Number words, rhymes K.CC 3 I/R ODE Write numbers from 0 to 20. Represent a number of objects with a written numeral 0–20 (with 0 representing a count of no objects). 1,2,3,4 rhymes, journal pages, number worksheets, practice in shaving cream and others Counting and Cardinality Count to tell the number of objects. Number Words, one to one K.CC 4a I/R ODE Understand the relationship between numbers and quantities; connect counting to cardinality. a. When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object. 1,2,3,4 one to one counting, using various manipulatives to count (food) 1
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Math
Curriculum Map
Kindergarten
Domain Clusters Key Vocabulary
Co
re S
tan
dard
I/R
/M
OD
E / T
C
Grade Level
Specific Standard
Qu
art
er
Tau
gh
t Student
Engagement/
Learning
Activity / Special
Resource / Web
Link
Counting and
Cardinality
Know number names and the
count sequence.
Number words, skip
counting, even, odd,
twos, fives, tens
K.CC
1a
I/R ODE Count to 100 by ones and by tens. 1,2,3,4 CD, manipulatives,
100s chart,
internet4classrooms.
com, calendar time
Counting and
Cardinality
Know how to skip count. Number words, skip
counting, even, odd,
twos, fives, tens
K.CC
1b
I/R TC Skip count by 2s to 20, by 5s to 100. 1,2,3,4 CD, manipulatives,
100s chart,
internet4classrooms.
com, calendar time
Counting and
Cardinality
Know how to count backwards
from twenty.
Number words,
counting back
K.CC
1c
I/R TC Count back from 20 to 0. 1,2,3,4 CD, manipulatives,
100s chart,
internet4classrooms.
com, calendar time
Counting and
Cardinality
Know number names and the
count sequence.
Number words,
counting on
K.CC
2
I/R ODE Count forward beginning from a given number
within the known sequence (instead of having
to begin at 1).
1,2,3,4 silent line up, adding
on, calendar
Counting and
Cardinality
Know number names and the
count sequence.
Number words,
rhymes
K.CC
3
I/R ODE Write numbers from 0 to 20. Represent a
number of objects with a written numeral 0–20
(with 0 representing a count of no objects).
1,2,3,4 rhymes, journal
pages, number
worksheets, practice
in shaving cream and
others
Counting and
Cardinality
Count to tell the number of
objects.
Number Words, one
to one
K.CC
4a
I/R ODE Understand the relationship between numbers
and quantities; connect counting to cardinality.
a. When counting objects, say the number
names in the standard order, pairing each
object with one and only one number name
and each number name with one and only one
object.
1,2,3,4 one to one counting,
using various
manipulatives to
count (food)
1
Math
Curriculum Map
Kindergarten
Domain Clusters Key Vocabulary
Co
re S
tan
dard
I/R
/M
OD
E / T
C
Grade Level
Specific Standard
Qu
art
er
Tau
gh
t Student
Engagement/
Learning
Activity / Special
Resource / Web
Link
Counting and
Cardinality
Count to tell the number of
objects.
Number Words, one
to one
K.CC
4b
I/R ODE Understand the relationship between numbers
and quantities; connect counting to cardinality.
b. Understand that the last number name said
tells the number of objects counted. The
number of objects is the same regardless of
their arrangement or the order in which they
were counted.
1,2,3,4 one to one counting,
using various
manipulatives to
count (food)
Counting and
Cardinality
Count to tell the number of
objects.
Number Words, one
to one
K.CC
4c
I/R ODE Understand the relationship between numbers
and quantities; connect counting to cardinality.
c. Understand that each successive number
name refers to a quantity that is one larger.
1,2,3,4 one to one counting,
using various
manipulatives to
count (food)
Counting and
Cardinality
Count to tell the number of
objects.
Match K.CC
5
I/R ODE Count to answer “how many?” questions about
as many as 20 things arranged in a line, a
rectangular array, or a circle, or as many as 10
things in a scattered configuration; given a
number from 1–20, count out that many
objects.
1,2,3,4 Worksheets -
pictures with
numbers
Counting and
Cardinality
Compare numbers. Graph, more, less,
same as, equal to,
greater than, less
than
K.CC
6
I/R ODE Identify whether the number of objects in one
group is greater than, less than, or equal to the
number of objects in another group, e.g., by
using matching and counting strategies.
1,2,3,4 weather graph,
theme graphs
Counting and
Cardinality
Compare numbers. Graph, more, less,
same as, equal to,
greater than, less
than
K.CC
7
I/R ODE Compare two numbers between 1 and 10
presented as written numerals.
1,2,3,4 graphs - weather
2
Math
Curriculum Map
Kindergarten
Domain Clusters Key Vocabulary
Co
re S
tan
dard
I/R
/M
OD
E / T
C
Grade Level
Specific Standard
Qu
art
er
Tau
gh
t Student
Engagement/
Learning
Activity / Special
Resource / Web
Link
Observations
and Algebraic
Thinking
Understand addition as putting
together and adding to, and
understand subtraction as taking
apart and taking from.
Equation, plus sign,
minus sign, equal
sign, number
sentence
K.OA
1
I/R ODE Represent addition and subtraction with
objects, fingers, mental images, drawings1,
sounds (e.g., claps), acting out situations,
verbal explanations, expressions, or
equations.
1,2,3,4 calendar, various
worksheets, hands
on activities (food),
graphing
Observations
and Algebraic
Thinking
Understand addition as putting
together and adding to, and
understand subtraction as taking
apart and taking from.
Equation, plus sign,
minus sign, equal
sign, number
sentence
K.OA
2
I/R ODE Solve addition and subtraction word problems,
and add and subtract within 10, e.g., by using
objects or drawings to represent the problem.
1,2,3,4 calendar, various
worksheets, hands
on activities (food),
graphing
Observations
and Algebraic
Thinking
Understand addition as putting
together and adding to, and
understand subtraction as taking
apart and taking from.
Equation, plus sign,
minus sign, equal
sign, number
sentence, number
words
K.OA
3
I/R ODE Decompose numbers less than or equal to 10
into pairs in more than one way, e.g., by using
objects or drawings, and record each
decomposition by a drawing or equation (e.g.,
5 = 2 + 3 and 5 = 4 + 1).
1,2,3,4 number worksheets
(journal pages),
probability
Observations
and Algebraic
Thinking
Understand addition as putting
together and adding to, and
understand subtraction as taking
apart and taking from.
Tens, ones, number
words, place value
K.OA
4
I/R ODE For any number from 1 to 9, find the number
that makes 10 when added to the given
number, e.g., by using objects or drawings,
and record the answer with a drawing or
equation.
1,2,3,4 calendar, money,
straws
Observations
and Algebraic
Thinking
Understand addition as putting
together and adding to, and
understand subtraction as taking
apart and taking from.
Equation, plus sign,
minus sign, equal
sign, number
sentence
K.OA
5
I/R ODE Fluently add and subtract within 5. 1,2,3,4 worksheets, hands
on, calendar,
computer games
Observations
and Algebraic
Thinking
Recognize a pattern and
describe the pattern.
pattern, repeating,
AB, AABB, ABC,
etc.
K.OA
6a
I/R TC Describe orally the pattern of a given sequence. 1,2,3,4 unifix cubes, bears,
drawing, calendar, I
spy, motion patterns
Observations
and Algebraic
Thinking
Recognize a pattern and
describe the pattern.
pattern, repeating,
AB, AABB, ABC,
etc.
K.OA
6b
I/R TC Identify, create and extend a pattern 1,2,3,4 unifix cubes, bears,
drawing, calendar, I
spy, motion patterns
3
Math
Curriculum Map
Kindergarten
Domain Clusters Key Vocabulary
Co
re S
tan
dard
I/R
/M
OD
E / T
C
Grade Level
Specific Standard
Qu
art
er
Tau
gh
t Student
Engagement/
Learning
Activity / Special
Resource / Web
Link
Numbers and
Operations in
Base Ten
Work with numbers 11-19 to
gain foundations for place value.
ones, tens, place
value, add, subtract
K.NBT
1
I/R ODE Compose and decompose numbers from 11
to 19 into ten ones and some further ones,
e.g., by using objects or drawings, and record
each composition or decomposition by a
drawing or equation (such as 18 = 10 + 8);
understand that these numbers are composed
of ten ones and one, two, three, four, five, six,
seven, eight, or nine ones.
1,2,3,4 calendar straws,
money
Measurement
and Data
Describe and compare
measurable attributes.
length, width,
height, weight, unit,
circumfrence,
balance
K.MD
1
I/R ODE Describe measurable attributes of objects,
such as length or weight. Describe several
measurable attributes of a single object.
1,2,3,4 bears, pumpkins,
science table - gold
rocks, bats
Measurement
and Data
Describe and compare
measurable attributes.
more, less, equal,
taller, shorter
K.MD
2
I/R ODE Directly compare two objects with a
measurable attribute in common, to see which
object has “more of”/“less of” the attribute, and
describe the difference. For example, directly
compare the heights of two children and
describe one child as taller/shorter.
1,2,3,4 bears, scale, kids
with pumpkins
Measurement
and Data
Classify objects and count the
number of objects in each
category.
sorting, alike,
different, attribute,
same, shape, size,
number words, label
K.MD
3
I/R ODE Classify objects into given categories; count
the numbers of objects in each category and
sort the categories by count.
1,2,3,4 sorting bears,
shapes, graphs -
m&ms, bugs, fine
motor
Measurement
and Data
Work with time and money. clock, hour hand,
minute hand, to the
hour
K.MD
4
I/R TC Identify time to the hour. 1,2,3,4 journal pages, clock
worksheets, hands
on clock practice,
books
Measurement
and Data
Work with time and money. coin, penny, nickel,
dime, quarter,
cents, value
K.MD
5
I/R TC Identify and state value of penny, nickel, dime,
quarter.
1,2,3,4 calendar, piggy
banks, journal
worksheets, hands,
simon says
4
Math
Curriculum Map
Kindergarten
Domain Clusters Key Vocabulary
Co
re S
tan
dard
I/R
/M
OD
E / T
C
Grade Level
Specific Standard
Qu
art
er
Tau
gh
t Student
Engagement/
Learning
Activity / Special
Resource / Web
Link
Geometry Identify and describe shapes
(squares, circles, triangles,
rectangles, hexagons, cubes,
cones, cylinders, and spheres).
shape names, 3D
shapes, position
words
K.G 1 I/R ODE Describe objects in the environment using
names of shapes, and describe the relative
positions of these objects using terms such as
above , below , beside , in front of , behind , and
next to .
1,2,3,4 poems, worksheets,
x hunt, calendar,
shape hunt, animal
cookie activity,
geoboards
Geometry Identify and describe shapes
(squares, circles, triangles,
rectangles, hexagons, cubes,
cones, cylinders, and spheres).
shape names, 3D
shapes, position
words
K.G 2 I/R ODE Correctly name shapes regardless of their
orientations or overall size.
1,2,3,4 poems, worksheets,
x hunt, calendar,
shape hunt, animal
cookie activity,
geoboards
Geometry Identify and describe shapes
(squares, circles, triangles,
rectangles, hexagons, cubes,
cones, cylinders, and spheres).
3D, names, shapes K.G 3 I/R ODE Identify shapes as two-dimensional (lying in a
plane, “flat”) or three-dimensional (“solid”).
1,2,3,4 calendar
Geometry Analyze, compare, create, and
compose shapes.
3D, names, shapes K.G 4 I/R ODE Analyze and compare two- and three-
dimensional shapes, in different sizes and
orientations, using informal language to
describe their similarities, differences, parts
(e.g., number of sides and vertices/“corners”)
and other attributes (e.g., having sides of
equal length).
1,2,3,4 shape poems,
shapes with food
(licorice, pretzels)
Geometry Analyze, compare, create, and
compose shapes.
3D, names, shapes K.G 5 I/R ODE Model shapes in the world by building shapes
from components (e.g., sticks and clay balls)
and drawing shapes.
1,2,3,4 math journal, art
center, blocks,
calendar
Geometry Analyze, compare, create, and
compose shapes.
3D, names, shapes K.G 6 I/R ODE Compose simple shapes to form larger
shapes. For example, “Can you join these two
triangles with full sides touching to make a
rectangle?”
1,2,3,4 tangrams, block
shapes
5
Math Curriculum Map
Grade 1
Domain Clusters Key Vocabulary
Co
re S
tan
dard
I/R
/M
OD
E / T
C
Grade Level
Specific Standard
Qu
art
er
Tau
gh
t
Student
Engagement/
Learning Activity /
Special Resource /
Web Link
Operations and
Algebraic
Thinking
Represent and solve
problems involving addition
and subtraction.
symbol,equal, plus,
minus, sum ,
difference, together,
in all, how many
more, addition,
subtraction,
1.OA
1
I/R/M ODE Use addition and subtraction within
20 to solve word problems involving
situations of adding to, taking
from, putting together, taking apart,
and comparing, with unknowns in all
positions, e.g., by using objects,
drawings, and equations with a
symbol for the unknown number to
represent the problem.
1,2,3,4 Use of manipulatives and
mats, stories involving
putting together and taking
apart, math journals in
which to draw pictures and
number sentences to
represent stories, Smart
Board e-tools to represent
stories about combining
and taking apart.
Operations and
Algebraic
Thinking
Represent and solve
problems involving addition
and subtraction.
equal, sum, plus,
together, in all,
addends, symbol,
1.0A
2
R/M ODE Solve word problems that call for
addition of three whole numbers
whose sum is less than or equal to
20, e.g., by using objects, drawings,
and equations with a symbol for the
unknown number to
represent the problem.
2,3,4 Manipulatives such as
goldfish, candy corn,
m&m's, cubes, counters,
mats and journals to
represent word problems
that call for three addend
addition. Smartboard
pictures that can be
manipulated to represent
stories.
Operations and
Algebraic
Thinking
Understand and apply
properties of operations and
the relationship between
addition and subtraction.
Commutative
property, Associative
property, add,
subtract, plus,
minus, equal
1.OA
3
I/R/M ODE Apply properties of operations as
strategies to add and subtract.
Examples: If 8 + 3 = 11 is known,
then 3 + 8 = 11 is also known
(commutative property of addition).To
add 2 + 6 + 4, the second two
numbers can be added to make a
ten, so 2 + 6 + 4 = 2 + 10 = 12
(associative property of addition).
2,3,4 manipulatives, such as
linking cubes, counters,
journals,modeling,
practice.
1
Math Curriculum Map
Grade 1
Domain Clusters Key Vocabulary
Co
re S
tan
dard
I/R
/M
OD
E / T
C
Grade Level
Specific Standard
Qu
art
er
Tau
gh
t
Student
Engagement/
Learning Activity /
Special Resource /
Web Link
Operations and
Algebraic
Thinking
Understand and apply
properties of operations and
the relationship between
addition and subtraction.
addend, subtraction 1.OA
4
I/R ODE Understand subtraction as an
unknown-addend problem. For
example, subtract 10 – 8 by finding
the number that makes 10 when
added to 8.
2,3,4 manipulatives, journals,
modeling, guided practice
Operations and
Algebraic
Thinking
Add and subtract within 20. plus, minus, equal,
sum, difference,
counting on,
counting back
1.OA
5
I/R ODE Relate counting to addition and
subtraction (e.g., by counting on 2 to
add 2).
2,3,4 manipulatives, such as
linking cubes, counters,
journals,modeling, practice
Operations and
Algebraic
Thinking
Add and subtract within 20. Counting on, making
a ten, decomposing,
addition, subtraction,
equal, equivalent,
counting back
1.OA
6
I/R ODE Add and subtract within 20,
demonstrating fluency for addition
and subtraction within 10. Use
strategies such as counting on;
making ten (e.g., 8 + 6 = 8 + 2 + 4 =
10 + 4 = 14); decomposing a number
leading to a ten (e.g., 13 – 4 = 13 – 3
– 1 = 10 – 1 = 9); using the
relationship between addition and
subtraction (e.g., knowing that 8 + 4 =
12, one knows 12 – 8 = 4); and
creating equivalent but easier or
known sums (e.g., adding 6 + 7 by
creating the known equivalent 6 + 6 +
1 = 12 + 1 = 13).
3,4 manipulatives, particularly
linking cubes, number
lines, tens frames,
counters, e tools on the
Smart Board, Sites such
as
Illuminations.NCTM.org,
modeling, guided practice
Operations and
Algebraic
Thinking
Work with addition and
subtraction equations.
equal, plus, minus,
equation, addition,
subtraction, false,
true
1.OA
7
I/R ODE Understand the meaning of the equal
sign, and determine if equations
involving addition and subtraction are
true or false. For example, which of
the following equations are true and
which are false? 6 = 6, 7 = 8 – 1, 5 +
2 = 2 + 5, 4 + 1 = 5 + 2.
2,3,4 manipulatives, journals,
modeling, guided practice
2
Math Curriculum Map
Grade 1
Domain Clusters Key Vocabulary
Co
re S
tan
dard
I/R
/M
OD
E / T
C
Grade Level
Specific Standard
Qu
art
er
Tau
gh
t
Student
Engagement/
Learning Activity /
Special Resource /
Web Link
Operations and
Algebraic
Thinking
Work with addition and
subtraction equations.
addition, subtraction,
equation, true, false,
1.OA
8
I/R ODE Determine the unknown whole
number in an addition or subtraction
equation relating three whole
numbers. For example, determine the
unknown number that makes the
equation true in each of the equations
3,4 manipulaticves, journals,
modeling, guided practice
Operations and
Algebraic
Thinking
Identify, create and extend
patterns
pattern unit, extend,
grow
1.TC
9
R/M TC Create a patten unit. Identify and
label the pattern unit. Extend the unit
by making it again or growing a part
of the unit.
1, 2 manipulatives, particularly
pattern blocks, Smart
Board etools, modeling,
guided and independent
practice, journals.
Number and
Operations in
Base Ten
Extend the counting
sequence.
numeral 1.NB
T1
I/R ODE Count to 120, starting at any number
less than 120. In this range, read and
write numerals and represent a
number of objects with a written
numeral.
1,2,3,4 120 number chart, 1 inch
graph paper,blank
counting charts,modeling,
practice
3
Math Curriculum Map
Grade 1
Domain Clusters Key Vocabulary
Co
re S
tan
dard
I/R
/M
OD
E / T
C
Grade Level
Specific Standard
Qu
art
er
Tau
gh
t
Student
Engagement/
Learning Activity /
Special Resource /
Web Link
Number and
Operations in
Base Ten
Understand place value. digits, ones, tens,
bundle
1.
NBT
2
I/R ODE Understand that the two digits of a
two-digit number represent amounts
of tens and ones. Understand the
following as special cases:a. 10 can
be thought of as a bundle of ten ones
— called a “ten.”b. The numbers from
11 to 19 are composed of a ten and
one, two, three, four, five, six, seven,
eight, or nine ones.c. The numbers
10, 20, 30, 40, 50, 60, 70, 80, 90 refer
to one, two, three, four, five, six,
seven, eight, or nine tens (and 0
ones).
2,3,4 Manipulatives such as
linking cubes, straws or
other materials to bundle,
place value mats,
Smartboard teacher
resources,
Illumiinations.NCTM.org,
tenmarks.com,
ohiotreasurechest.org,
Internetforschool.com,
Funbrain.com.
Number and
Operations in
Base Ten
Understand place value. digit, tens, ones,
place value, equal,
greater than , less
than, fewer than
1.NB
T 3
I/R ODE Compare two two-digit numbers
based on meanings of the tens and
ones digits, recording the results of
comparisons with the symbols >, =,
and <.
2,3,4 Base ten blocks, linking
cubes, tens frames,
counting chart, teacher
modeling, practice
4
Math Curriculum Map
Grade 1
Domain Clusters Key Vocabulary
Co
re S
tan
dard
I/R
/M
OD
E / T
C
Grade Level
Specific Standard
Qu
art
er
Tau
gh
t
Student
Engagement/
Learning Activity /
Special Resource /
Web Link
Number and
Operations in
Base Ten
Use place Value
Understanding and
properties of operations to
add and subtract.
Place value, digits,
tens, ones, compose
1.NB
T4
I/R ODE Add within 100, including adding a
two-digit number and a one-digit
number, and adding a two-digit
number and a multiple of 10, using
concrete models or drawings and
strategies based on place value,
properties of operations, and/or the
relationship between addition and
subtraction; relate the strategy to a
written method and explain the
reasoning used. Understand that in
adding two-digit numbers, one adds
tens and tens, ones and ones; and
sometimes it is necessary to
compose a ten.
3,4 Manipulatives such as
linking cubes, straws or
other materials to bundle,
place value mats,
Smartboard teacher
resources,
Illumiinations.NCTM.org,
tenmarks.com,
ohiotreasurechest.org,
Internetforschool.com,
Funbrain.com.
Number and
Operations in
Base Ten
Use place Value
Understanding and
properties of operations to
add and subtract.
more, less 1.NB
T 5
I/R ODE Given a two-digit number, mentally
find 10 more or 10 less than the
number, without having to count;
explain the reasoning used.
3, 4 Number chart, teacher
modeling, practice
5
Math Curriculum Map
Grade 1
Domain Clusters Key Vocabulary
Co
re S
tan
dard
I/R
/M
OD
E / T
C
Grade Level
Specific Standard
Qu
art
er
Tau
gh
t
Student
Engagement/
Learning Activity /
Special Resource /
Web Link
Number and
Operations in
Base Ten
Use place Value
Understanding and
properties of operations to
add and subtract.
tens, plus, minus,
sum, difference,
subtract, add
1.NB
T 6
I/R ODE Subtract multiples of 10 in the
range 10-90 from multiples of 10
in the range 10-90 (positive or
zero differences), using concrete
models or drawings and
strategies based on place value,
properties of operations, and/or
the relationship between addition
and subtraction; relate the
strategy to a written method and
explain the reasoning used.
3,4 Manipulatives such as
linking cubes, straws or
other materials to bundle,
place value mats,
Smartboard teacher
resources,
Illumiinations.NCTM.org,
tenmarks.com,
ohiotreasurechest.org,
Internetforschool.com,
Funbrain.com.
Measurement
and Data
Measure lengths indirectly
and by interating length units
length, longer,
longest, compare
1.MD
1
I/R/M ODE Order three objects by length;
compare the lengths of two objects
indirectly by using a third object.
2,3,4 Objects of different
lengths, teacher modeling,
practice
Measurement
and Data
Measure lengths indirectly
and by interating length units.
Length unit, non
standard unit,
standard unit,
centimeter, meter,
inch, foot, yard
1.MD
1
I/R/M ODE Express the length of an object as a
whole number of length units, by
laying multiple copies of a shorter
object (the length unit) end to end;
understand that the length
measurement of an object is the
number of same-size length units that
span it with no gaps or overlaps. Limit
to contexts where the object being
measured is spanned by a whole
number of length units with no gaps
or overlaps.
3, 4 Objects of different
lengths, cubes, paperclips,
ruler, yardstick, centimeter
and meter stick,
Smartboard resources,
teacher modeling, practice
6
Math Curriculum Map
Grade 1
Domain Clusters Key Vocabulary
Co
re S
tan
dard
I/R
/M
OD
E / T
C
Grade Level
Specific Standard
Qu
art
er
Tau
gh
t
Student
Engagement/
Learning Activity /
Special Resource /
Web Link
Measurement
and Data
Tell and write time. second, minute,
hour, half hour,
analog, digital
1.MD
2
I/R ODE Tell and write time in hours and half-
hours using analog and digital clocks.
3,4 Judy teaching clocks,
analog and digital clocks,
Smartboard resources,
teacher modeling, practice
Measurement
and Data
Represent and Interpret
Data.
data, category 1.MD
3
I/R/M ODE Organize, represent, and interpret
data with up to three categories; ask
and answer questions about the total
number of data points, how many in
each category, and how many more
or less are in one category than in
another.
1,2,3,4 Smartboard tools, teacher
modeling, practice,
http://nlvm.usu.edu/en/nav/
vlibrary.html
Measurement
and Data
Identify and count coins penny, nickel, dime,
quarter, equal,
cents, dollar, equal
value, amount
1.MD
4
I/R/M TC Identify, name value, and determine
the value of a small collection of coins
(with a total value up to one dollar)
using 1 or 2 different type
coins, including pennies, nickels,
dimes and quarters. Identify different
combinations of coins with equal
values.
2,3,4 Coins, Smartboard
resources, teacher
modeling, teacher
resources,
Illumiinations.NCTM.org,
tenmarks.com,
ohiotreasurechest.org,
Internetforscho
Measurement
and Data
Identify and count coins penny, nickel, dime,
quarter, equal,
cents, dollar, equal
value, amount
1.MD
5
I/R/M TC Identify different combinations of
coins with equal values.
2,3,4 Coins, Smartboard
resources, teacher
modeling,
practice,resources at
Illumiinations.NCTM.org,
ohiotreasurechest.org,
Internetforschool.com,
Funbrain.com.
7
Math Curriculum Map
Grade 1
Domain Clusters Key Vocabulary
Co
re S
tan
dard
I/R
/M
OD
E / T
C
Grade Level
Specific Standard
Qu
art
er
Tau
gh
t
Student
Engagement/
Learning Activity /
Special Resource /
Web Link
Geometry Reason with shapes and
their attributes.
closed, open
attribute, sides,
angles
1. G 1 I/R/M ODE Distinguish between defining
attributes (e.g., triangles are closed
and three-sided) versus non-defining
attributes (e.g., color, orientation,
overall size) ; build and draw shapes
to possess defining attributes.
2,3,4 Pattern blocks, Paper
shapes that may be folded,
Geoboards, and bands,
Resources such as
Illumiinations.NCTM.org,
ohiotreasurechest.org,
Internetforschool.com,
Funbrain.com.
Geometry Reason with shapes and
their attributes.
rectangle, square,
trapezoid, triangle,
half circle, quarter
circle, cubes, cones,
cylinders
1. G 2 I/R ODE Compose two-dimensional shapes
(rectangles, squares, trapezoids,
triangles, half-circles, and quarter-
circles) or three-dimensional shapes
(cubes, right rectangular prisms, right
circular cones, and right circular
cylinders) to create a composite
shape, and compose new shapes
from the composite shape.
3,4 Pattern blocks, Paper
shapes that may be folded,
Geoboards and bands,
Teacher modeling,
practice, Resources such
as,
Illumiinations.NCTM.org,
ohiotreasurechest.org,
Internetforschool.com,
Funbrain.com.
Geometry Reason with shapes and
their attributes.
circle, rectangle,
decomposing,
fractional part,
equal, half, fourth,
quarter
1. G 3 I/R ODE Partition circles and rectangles into
two and four equal shares, describe
the shares using the words halves,
fourths, and quarters, and use the
phrases half of, fourth of, and quarter
of. Describe the whole as two of, or
four of the shares. Understand for
these examples that decomposing
into more equal shares creates
smaller shares.
3,4 Pattern blocks, paper
shapes that may be folded,
cut, Geoboards and
bands, Smartboard
resources and websites
such as
http://nlvm.usu.edu/en/nav/
vlibrary.html, ABCya.com,
Illuminations.NCTM.org,
Ohiotreasurechest.org,
Internetforschool
8
Math
Curriculum Map
Grade 2
Domain Clusters Key Vocabulary
Co
re S
tan
dard
I/R
/M
OD
E / T
C
Grade Level
Specific Standard
Qu
art
er
Tau
gh
t
Student
Engagement/
Learning Activity /
Special Resource /
Web Link
Operations
and Algebraic
Thinking
Represent and solve
problems involving addition
and subtraction.
add, subtract,
altogether, in all,
difference, how
many more, more,
less, minus, equal,
addend, sum, join,
related fact, regroup
2.OA1 R/M ODE Use addition and subtraction within
100 to solve one- and two-step word
problems involving situations of
adding to, taking from, putting
together, taking apart, and
comparing, with unknowns in all
positions, e.g., by using drawings and
equations with a symbol for the
unknown number to represent the
problem.
1, 2, 3, 4 Text book word
problems, unifix
cubes, numberlines, i-
pads, smartboard,
math-4-today, minute
math.
Operations and
Algebraic
Thinking
Add and subtract within 20 add, subtract,
altogether, in all,
difference, how
many more, more,
less, minus, addend,
sum, join, equal,
related fact
2.0A2 R/M ODE Fluently add and subtract within 20
using mental strategies.2 By end of
Grade 2, know from memory all sums
of two one-digit numbers.
1, 2, 3, 4 Textbook, unifix
cubes, numberlines,
minute math, math-4-
today, strategy
instruction,
smartboard.
1
Math
Curriculum Map
Grade 2
Domain Clusters Key Vocabulary
Co
re S
tan
dard
I/R
/M
OD
E / T
C
Grade Level
Specific Standard
Qu
art
er
Tau
gh
t
Student
Engagement/
Learning Activity /
Special Resource /
Web Link
Operations and
Algebraic
Thinking
Work with equal groups of
objects to gain foundations
for multiplication.
even, odd 2.OA3 I/R/M ODE Determine whether a group of objects
(up to 20) has an odd or even number
of members, e.g., by pairing objects
or counting them by 2s; write an
equation to express an even number
as a sum of two equal addends.
1, 2, 3, 4 textbook,
manipulatives,
smartboard
Operations and
Algebraic
Thinking
Work with equal groups of
objects to gain foundations
for multiplication.
array, column, row 2.OA4 I/R ODE Use addition to find the total number
of objects arranged in rectangular
arrays with up to 5 rows and up to 5
columns; write an equation to express
the total as a sum of equal addends.
1, 2, 3, 4 Array activities:
manipulatives, graph
paper, smartboard.
Number and
Operations in
Base 10
Understand Place Value ones, tens,
hundreds,
thousands, digit
2.NBT
1
I/R ODE Understand that the three digits of a
three-digit number represent amounts
of hundreds, tens, and ones; e.g.,
706 equals 7 hundreds, 0 tens, and 6
ones. Understand the following as
special cases:
100 can be thought of as a bundle of
ten tens — called a “hundred.”
The numbers 100, 200, 300, 400,
500, 600, 700, 800, 900 refer to one,
two, three, four, five, six, seven, eight,
or nine hundreds (and 0 tens and 0
ones).
1, 2, 3, 4 Smartboard, base
ten blocks.
2
Math
Curriculum Map
Grade 2
Domain Clusters Key Vocabulary
Co
re S
tan
dard
I/R
/M
OD
E / T
C
Grade Level
Specific Standard
Qu
art
er
Tau
gh
t
Student
Engagement/
Learning Activity /
Special Resource /
Web Link
Number and
Operations in
Base 10
Understand Place Value ones, tens,
hundreds,
thousands, digit,
pattern
2.NBT
2
R/M ODE Count within 1000; skip-count by 5s,
10s, and 100s.
1, 2, 3, 4 Smartboard,
textbook, hundreds
chart, patterning
activities.
Number and
Operations in
Base 10
Understand Place Value ones, tens,
hundreds,
thousands, digit
2.NBT
3
I/R/M ODE Read and write numbers to 1000
using base-ten numerals, number
names, and expanded form.
1, 2, 3, 4 Smartboard,
textbook, modeling,
guided practice.
Number and
Operations in
Base 10
Understand Place Value greater than, less
than, equal,
equivalence
2.NBT
4
I/R/M ODE Compare two three-digit numbers
based on meanings of the hundreds,
tens, and ones digits, using >, =, and
< symbols to record the results of
comparisons.
1, 2, 3, 4 Smartboard,
manipulatives, visual
aid ie. Alligator
mouth,pacmann,
arrow pointing to
smaller number.
Number and
Operations in
Base 10
Use place value
understanding and properties
of operations to add and
subtract.
ones, tens,
hundreds,
thousands, digit
2.NBT
5
I/R/M ODE Fluently add and subtract within 100
using strategies based on place
value, properties of operations, and/or
the relationship between addition and
subtraction.
1, 2, 3, 4 Smartboard, base 10
blocks, 100's chart,
addition/subtraction
strategies.
Number and
Operations in
Base 10
Use place value
understanding and properties
of operations to add and
subtract.
ones, tens,
hundreds,
thousands, digit
2.NBT
6
I/R/M ODE Add up to four two-digit numbers
using strategies based on place value
and properties of operations.
1, 2, 3, 4 Practice w/ paper
and pencil, online,
games, study island,
base ten blocks.
3
Math
Curriculum Map
Grade 2
Domain Clusters Key Vocabulary
Co
re S
tan
dard
I/R
/M
OD
E / T
C
Grade Level
Specific Standard
Qu
art
er
Tau
gh
t
Student
Engagement/
Learning Activity /
Special Resource /
Web Link
Number and
Operations in
Base 10
Use place value
understanding and properties
of operations to add and
subtract.
ones, tens,
hundreds,
thousands, digit
2.NBT
7
I/R ODE Add and subtract within 1000, using
concrete models or drawings and
strategies based on place value,
properties of operations, and/or the
relationship between addition and
subtraction; relate the strategy to a
written method. Understand that in
adding or subtracting three-digit
numbers, one adds or subtracts
hundreds and hundreds, tens and
tens, ones and ones; and sometimes
it is necessary to compose or
decompose tens or hundreds.
1, 2, 3, 4 Practice w/ paper
and pencil, online,
games, study island,
base ten blocks.
Number and
Operations in
Base 10
Use place value
understanding and properties
of operations to add and
subtract.
ones, tens,
hundreds,
thousands, digit
2.NBT
8
R/M ODE Mentally add 10 or 100 to a given
number 100–900, and mentally
subtract 10 or 100 from a given
number 100–900.
1, 2, 3, 4 Arrow Math, Block
Math, Fill in the 100
Chart, Online math
games.
Number and
Operations in
Base 10
Use place value
understanding and properties
of operations to add and
subtract.
ones, tens,
hundreds,
thousands, digit
2.NBT
9
I/RM ODE Explain why addition and subtraction
strategies work, using place value
and the properties of operations.
1, 2, 3, 4 Manipulatives.
Number and
Operations in
Base 10
Represent fractions using
words, numerals and physical
models.
halves,thirds,
fourths, sixths,
eighths
2.N BT
9a
I TC Compare and order physical models
of halves, thirds and fourths in
relation to 0 and 1.
2,3 Manipulatives
4
Math
Curriculum Map
Grade 2
Domain Clusters Key Vocabulary
Co
re S
tan
dard
I/R
/M
OD
E / T
C
Grade Level
Specific Standard
Qu
art
er
Tau
gh
t
Student
Engagement/
Learning Activity /
Special Resource /
Web Link
Measurement
& Data
Measure and estimate
lengths in standard units.
Measure, length 2.MD1 R/M ODE Measure the length of an object by
selecting and using appropriate tools
such as rulers, yardsticks, meter
sticks, and measuring tapes.
2, 3, 4 Use rulers,
yardsticks, meter
sticks to measure
classroom objects.
Measurement
& Data
Measure and estimate
lengths in standard units.
liter, cup, pint, quart 2.M
D1a
R TC Measure volume (capacity) using
liters, cups, pints, or quarts
2, 3, 4 Use measuring cups,
liters to measure
volume. Estimate
and compare like
quantities (ie. Quarts
and liters).
Measurement
& Data
Measure and estimate
lengths in standard units.
grams, ounces,
pound
2.M
D1b
R TC Measure weight using grams,
ounces, or pounds.
2, 3, 4 Use scales, balance
beams to weigh
classroom objects.
Measurement
& Data
Measure and estimate
lengths in standard units.
2.MD2 R/M ODE Measure the length of an object twice,
using length units of different lengths
for the two measurements; describe
how the two measurements relate to
the size of the unit chosen.
2, 3, 4 Measure with rulers,
yardsticks, meter
sticks.
Measurement
& Data
Measure and estimate
lengths in standard units.
inches, feet,
centimeter, meter
2.MD3 I/R/M ODE Estimate lengths using units of
inches, feet, centimeters, and meters.
2, 3, 4 Measure with rulers,
yardsticks, meter
sticks. Instruction in
common references.
5
Math
Curriculum Map
Grade 2
Domain Clusters Key Vocabulary
Co
re S
tan
dard
I/R
/M
OD
E / T
C
Grade Level
Specific Standard
Qu
art
er
Tau
gh
t
Student
Engagement/
Learning Activity /
Special Resource /
Web Link
Measurement
& Data
Measure and estimate
lengths in standard units.
standard unit 2.MD4 I/R/M ODE Measure to determine how much
longer one object is than another,
expressing the length difference in
terms of a standard length unit.
2, 3, 4 Measure with rulers,
yardsticks, meter
sticks. Instruction in
common references.
Measurement
& Data
Relate addition and
subtraction to length
equivalent 2.MD5 R/M ODE Use addition and subtraction within
100 to solve word problems involving
lengths that are given in the same
units, e.g., by using drawings (such
as drawings of rulers) and equations
with a symbol for the unknown
number to represent the problem.
2, 3, 4 Smartboard, ODE
website, ORC.
Measurement
& Data
Relate addition and
subtraction to length
2.MD6 R/M ODE Represent whole numbers as lengths
from 0 on a number line diagram with
equally spaced points corresponding
to the numbers 0, 1, 2, ..., and
represent whole-number sums and
differences within 100 on a number
line diagram.
2, 3, 4 Use numberline with
standard
measurement (ruler,
yardstick, etc.)
Measurement
& Data
Work with time and money. analog, digital,
minute, hour
2.MD7 I/R/M ODE Tell and write time from analog and
digital clocks to the nearest five
minutes, using a.m. and p.m.
2, 3, 4 Classroom clock,
Judy Clocks,
smartboard tools,
online math websites.
6
Math
Curriculum Map
Grade 2
Domain Clusters Key Vocabulary
Co
re S
tan
dard
I/R
/M
OD
E / T
C
Grade Level
Specific Standard
Qu
art
er
Tau
gh
t
Student
Engagement/
Learning Activity /
Special Resource /
Web Link
Measurement
& Data
Work with time and money. penney, nickel,
dime, quarter, dollar,
2.MD8 I/R/M ODE Solve word problems involving dollar
bills, quarters, dimes, nickels, and
pennies, using $ and ¢ symbols
appropriately. Example: If you have 2
dimes and 3 pennies, how many
cents do you have?
2, 3, 4 School money, play
money, smartboard
tools, online
websites.
Measurement
& Data
Work with time and money. change 2.MD8
a
I/R TC Count money and make change
using coins and a dollar bill.
2, 3, 4 School money, play
money, smartboard
tools, online
websites, class store.
Measurement
& Data
Represent and interpret data. data, graph, 2.MD9 R/M ODE Generate measurement data by
measuring lengths of several objects
to the nearest whole unit, or by
making repeated measurements of
the same object. Show the
measurements by making a line plot,
where the horizontal scale is marked
off in whole-number units.
2, 3, 4 Graph paper, online
websites.
7
Math
Curriculum Map
Grade 2
Domain Clusters Key Vocabulary
Co
re S
tan
dard
I/R
/M
OD
E / T
C
Grade Level
Specific Standard
Qu
art
er
Tau
gh
t
Student
Engagement/
Learning Activity /
Special Resource /
Web Link
Measurement
& Data
Represent and interpret data. data, graph, 2.MD
10
R/M ODE Draw a picture graph and a bar graph
(with single-unit scale) to represent a
data set with up to four categories.
Solve simple put-together, take-apart,
and compare problems1 using
information presented in a bar graph.
2, 3, 4 Blank graphs, graph
paper.
Geometry Reason with shapes and their
attributes.
angle, side, vertex,
edge, face, plane
shape, solid figure,
cube, rectangular
prism, sphere,
pyramid, cylinder,
cone, flat surface,
2.G1 I/R ODE Recognize and draw shapes having
specified attributes, such as a given
number of angles or a given number
of equal faces. Identify triangles,
quadrilaterals, pentagons, hexagons,
and cubes.
2, 3, 4 Pattern blocks, solid
figures,smartboard
tools, online
websites.
Geometry Reason with shapes and their
attributes.
array, column, row 2.G2 R/M ODE Partition a rectangle into rows and
columns of same-size squares and
count to find the total number of
them.
2, 3, 4 Manipulatives, online
websites.
8
Math
Curriculum Map
Grade 2
Domain Clusters Key Vocabulary
Co
re S
tan
dard
I/R
/M
OD
E / T
C
Grade Level
Specific Standard
Qu
art
er
Tau
gh
t
Student
Engagement/
Learning Activity /
Special Resource /
Web Link
Geometry Reason with shapes and their
attributes.
fraction, equal,
halves, thirds,
fourths, unequal
2.G3 R/M ODE Partition circles and rectangles into
two, three, or four equal shares,
describe the shares using the words
halves, thirds, half of, a third of, etc.,
and describe the whole as two
halves, three thirds, four fourths.
Recognize that equal shares of
identical wholes need not have the
same shape.
2, 3, 4 Manipulatives, online
websites.
9
Math
Curriculum Map
Grade 3
Domain Clusters Key Vocabulary
Co
re S
tan
dard
I/R
/M
OD
E / T
C
Grade Level
Specific Standard
Qu
art
er
Tau
gh
t Student
Engagement/
Learning
Activity / Special
Resource / Web
Link
Operations and
Algebraic Thinking
Represent and solve problems
involving multiplication and
division.
array, product,
factor, dividend,
divisor, quotient
3.OA
1
I/R
/M
ODE Interpret products of whole numbers,
e.g., interpret 5 × 7 as the total
number of objects in 5 groups of 7
objects each
1,2,3,4 Counters,
tiles,cereal,
candies,number
lines, arrays
Operations and
Algebraic Thinking
Represent and solve problems
involving multiplication and
division.
array, product,
factor, dividend,
divisor, quotient
3.OA
2
I/R
/M
ODE Interpret whole-number quotients of
whole numbers, e.g., interpret 56 ÷ 8
as the number of objects in each
share when 56 objects are partitioned
equally into 8 shares, or as a number
of shares when 56 objects are
partitioned into equal shares of 8
objects each.
1,2,3,4 Counters,
tiles,cereal,
candies,number
lines, arrays
Operations and
Algebraic Thinking
Represent and solve problems
involving multiplication and
division.
array, product,
factor, dividend,
divisor, quotient
3.OA
3
I/R ODE Use multiplication and division within
100 to solve word problems in
situations involving equal groups,
arrays, and measurement quantities,
e.g., by using drawings and equations
with a symbol for the unknown
number to represent the problem.
1,2,3,4 Counters,
tiles,cereal,
candies,number
lines, arrays
Operations and
Algebraic Thinking
Represent and solve problems
involving multiplication and
division.
array, product,
factor, dividend,
divisor, quotient
3.OA
4
I/R ODE Determine the unknown whole
number in a multiplication or division
equation relating three whole
numbers.
1,2,3,4 Counters,
tiles,cereal,
candies,number
lines, arrays
Operations and
Algebraic Thinking
Understand properties of
multiplication and the relationship
between multiplication and
division.
associative property,
commutative
property, distributive
property
3.OA
5
I/R
/M
ODE Apply properties of operations as
strategies to multiply and divide.
1,2,3,4 Counters,
tiles,cereal,
candies,number
lines, arrays
1
Math
Curriculum Map
Grade 3
Domain Clusters Key Vocabulary
Co
re S
tan
dard
I/R
/M
OD
E / T
C
Grade Level
Specific Standard
Qu
art
er
Tau
gh
t Student
Engagement/
Learning
Activity / Special
Resource / Web
Link
Operations and
Algebraic Thinking
Understand properties of
multiplication and the relationship
between multiplication and
division.
property 3.OA
6
I/R ODE Understand division as an unknown-
factor problem
1,2,3,4 Counters,
tiles,cereal,
candies,number
lines, arrays
Operations and
Algebraic Thinking
Multiply and divide within 100. rectangular array,
multiply, divide,
product, factor,
dividend, divisor,
quotient
3.OA
7
I/R ODE Fluently multiply and divide within
100, using strategies such as the
relationship between multiplication
and division
1,2,3,4 Unifix cubes, graph
paper, counters
Operations and
Algebraic Thinking
Solve problems involving the four
operations, and identify and
explain patterns in arithmetic.
operation, multiply,
divide, add, subtract,
sum, difference,
assocaitive proprty,
commutative
property, product
3.OA
8
I/R ODE Solve two-step word problems using
the four operations. Represent these
problems using equations with a letter
standing for the unknown quantity.
Assess the reasonableness of
answers using mental computation
and estimation strategies including
rounding.
1,2,3,4 Dice, cards
Operations and
Algebraic Thinking
Solve problems involving the four
operations, and identify and
explain patterns in arithmetic.
addends, products 3.OA
9
I/R
/M
ODE Identify arithmetic patterns (including
patterns in the addition table or
multiplication table), and explain them
using properties of operations.
1,2,3,4 Addition and
multiplication charts
Number and
Operations in Base
Ten
Use place value understanding
and properties of operations to
perform multi-digit arithmetic.
round up, round
down, estimate
3.NB
T1
R/
M
ODE Use place value understanding to
round whole numbers to the nearest
10 or 100.
1,2,3,4 Place value chart,
number line, 100's
chart
Number and
Operations in Base
Ten
Use place value understanding
and properties of operations to
perform multi-digit arithmetic.
alogorithm 3.NB
T2
R/
M
ODE Fluently add and subtract within 1000
using strategies and algorithms
based on place value, properties of
operations, and/or the relationship
between addition and subtraction.
1,2,3,4 Place value chart,
number line, 100's
chart
2
Math
Curriculum Map
Grade 3
Domain Clusters Key Vocabulary
Co
re S
tan
dard
I/R
/M
OD
E / T
C
Grade Level
Specific Standard
Qu
art
er
Tau
gh
t Student
Engagement/
Learning
Activity / Special
Resource / Web
Link
Number and
Operations in Base
Ten
Use place value understanding
and properties of operations to
perform multi-digit arithmetic.
3.NB
T3
I/R
/M
ODE Multiply one-digit whole numbers by
multiples of 10 in the range 10–90
(e.g., 9 × 80, 5 × 60) using strategies
based on place value and properties
of operations.
1,2,3,4 Place value chart,
number line, 100's
chart
Number and
Operations-
Fractions
Develop understanding of
fractions as numbers.
whole number,
mixed number,
numerator,
denominator,
equivalent, greater
than, less than
3.NF
1
I/R
/M
ODE Understand a fraction 1/b as the
quantity formed by 1 part when a
whole is partitioned into b equal parts;
understand a fraction a/b as the
quantity formed by a parts of size 1/b.
3,4 Fraction bars or
strips, geoboards,
venn diagram,grid
paper, models
Number and
Operations-Fractions
Develop understanding of
fractions as numbers.
number line,
numerator,
denominator
3.
NF2
I/R ODE Understand a fraction as a number on
the number line; represent fractions
on a number line diagram.
3,4 Fraction bars or
strips, geoboards,
venn diagram,grid
paper, models
Number and
Operations-Fractions
Develop understanding of
fractions as numbers.
number line 3.2
NF a
I/R ODE a. Represent a fraction 1/b on a
number line diagram by defining the
interval from 0 to 1 as the whole and
partitioning it into b equal parts.
Recognize that each part has size 1/b
and that the endpoint of the part
based at 0 locates the number 1/b on
the number line.
3,4 Fraction bars or
strips, geoboards,
venn diagram,grid
paper, models
Number and
Operations-Fractions
Develop understanding of
fractions as numbers.
number line 3.2
NF b
I/R ODE b. Represent a fraction a/b on a
number line diagram by marking off a
lengths 1/b from 0. Recognize that
the resulting interval has size a/b and
that its endpoint locates the number
a/b on the number line.
3,4 Fraction bars or
strips, geoboards,
venn diagram,grid
paper, models
3
Math
Curriculum Map
Grade 3
Domain Clusters Key Vocabulary
Co
re S
tan
dard
I/R
/M
OD
E / T
C
Grade Level
Specific Standard
Qu
art
er
Tau
gh
t Student
Engagement/
Learning
Activity / Special
Resource / Web
Link
Number and
Operations-Fractions
Develop understanding of
fractions as numbers.
greater than, less
than, equivalent
fractions
3.3
NF
I/R
/M
ODE Explain equivalence of fractions in
special cases, and compare fractions
by reasoning about their size.
3,4 Fraction bars or
strips, geoboards,
venn diagram,grid
paper, models
Number and
Operation-Fractions
Develop understanding of
fractions as numbers.
equivalent fractions 3.3N
F a
I/R ODE a. Understand two fractions as
equivalent (equal) if they are the
same size, or the same point on a
number line.
3,4 Fraction bars or
strips, geoboards,
venn diagram,grid
paper, models
Number and
Operations-Fractions
Develop understanding of
fractions as numbers.
equivalent fractions 3.3
NF b
I/R ODE b. Recognize and generate simple
equivalent fractions, e.g., 1/2 = 2/4,
4/6 = 2/3). Explain why the fractions
are equivalent, e.g., by using a visual
fraction model.
3,4 Fraction bars or
strips, geoboards,
venn diagram,grid
paper, models
Number and
Operations-Fractions
Develop understanding of
fractions as numbers.
equivalent fractions 3.3
NF c
I/R ODE c. Express whole numbers as
fractions, and recognize fractions that
are equivalent to whole
numbers.Examples: Express 3 in the
form 3 = 3/1; recognize that 6/1 = 6;
locate 4/4 and 1 at the same point of
a number line diagram.
3,4 Fraction bars or
strips, geoboards,
venn diagram,grid
paper, models
4
Math
Curriculum Map
Grade 3
Domain Clusters Key Vocabulary
Co
re S
tan
dard
I/R
/M
OD
E / T
C
Grade Level
Specific Standard
Qu
art
er
Tau
gh
t Student
Engagement/
Learning
Activity / Special
Resource / Web
Link
Number and
Operations-Fractions
Develop understanding of
fractions as numbers.
greater than, less
than, equivalent
fractions
3.3
NF d
I/R ODE d. Compare two fractions with the
same numerator or the same
denominator by reasoning about their
size. Recognize that comparisons are
valid only when the two fractions refer
to the same whole. Record the results
of comparisons with the symbols >, =,
or <, and justify the conclusions, e.g.,
by using a visual fraction model.
3,4 Fraction bars or
strips, geoboards,
venn diagram,grid
paper, models
Measurement and
Data
Solve problems involving
measurement and estimation of
intervals of time, liquid volumes,
and masses of objects.
hour hand, minute
hand, elasped time
3.
MD 1
I/R
/M
ODE Tell and write time to the nearest
minute and measure time intervals in
minutes. Solve word problems
involving addition and subtraction of
time intervals in minutes, e.g., by
representing the problem on a
number line diagram.
1,2,3,4 clocks- analog and
digital
Measurement and
Data
Solve problems involving
measurement and estimation of
intervals of time, liquid volumes,
and masses of objects.
mass, volume 3.
MD 2
I/R ODE Measure and estimate liquid volumes
and masses of objects using
standard units of grams (g),
kilograms (kg), and liters (l). Add,
subtract, multiply, or divide to solve
one-step word problems involving
masses or volumes that are given in
the same units, e.g., by using
drawings (such as a beaker with a
measurement scale) to represent the
problem.
3,4 beakers, graduated
cylinders, measuring
cups, balnce scales,
weights (g or kg),
objects to weigh
5
Math
Curriculum Map
Grade 3
Domain Clusters Key Vocabulary
Co
re S
tan
dard
I/R
/M
OD
E / T
C
Grade Level
Specific Standard
Qu
art
er
Tau
gh
t Student
Engagement/
Learning
Activity / Special
Resource / Web
Link
Measurement and
Data
Represent and interpret data. pictograph, bar
graph, line plot
graph, symbol
3.3
MD 3
I/R
/M
ODE Draw a scaled picture graph and a
scaled bar graph to represent a data
set with several categories. Solve one-
and two-step “how many more” and
“how many less” problems using
information presented in scaled bar
graphs.
2 bar graphs, counters,
Measurement and
Data
Represent and interpret data. measure, length,
inch
3.4
MD 4
I/R
/M
ODE Generate measurement data by
measuring lengths using rulers
marked with halves and fourths of an
inch. Show the data by making a line
plot, where the horizontal scale is
marked off in appropriate
units—whole numbers, halves, or
quarters
3,4 rulers
Measurement and
Data
Geometric measurement:
understand concepts of area and
relate area to multiplication and to
addition.
area 3.5
MD a
I/R
/M
ODE Recognize area as an attribute of
plane figures and understand
concepts of area measurement.
a. A square with side length 1 unit,
called “a unit square,” is said to have
“one square unit” of area, and can be
used to measure area.
b. A plane figure which can be
covered without gaps or overlaps by n
unit squares is said to have an area
of n square units
3,4 tiles, Cheeze-its
Measurement and
Data
Geometric measurement:
understand concepts of area and
relate area to multiplication and to
addition.
area 3.6
MD
I/R
/M
ODE Measure areas by counting unit
squares (square cm, square m,
square in, square ft, and improvised
units).
3,4 tiles, Cheeze-its
6
Math
Curriculum Map
Grade 3
Domain Clusters Key Vocabulary
Co
re S
tan
dard
I/R
/M
OD
E / T
C
Grade Level
Specific Standard
Qu
art
er
Tau
gh
t Student
Engagement/
Learning
Activity / Special
Resource / Web
Link
Measurement and
Data
Geometric measurement:
understand concepts of area and
relate area to multiplication and to
addition.
perimeter, area 3.7 I/R
/M
ODE Relate area to the operations of
multiplication and addition.
3,4
Measurement and
Data
Geometric measurement:
understand concepts of area and
relate area to multiplication and to
addition.
area 3.7 a I/R
/M
ODE a. Find the area of a rectangle with
whole-number side lengths by tiling it,
and show that the area is the same
as would be found by multiplying the
side lengths.
3,4 tiles
Measurement and
Data
Geometric measurement:
understand concepts of area and
relate area to multiplication and to
addition.
perimeter 3.7 b I/R
/M
ODE b. Multiply side lengths to find areas
of rectangles with whole number side
lengths in the context of solving real
world and mathematical problems,
and represent whole-number
products as rectangular areas in
mathematical reasoning.
3,4 tiles
Measurement and
Data
Geometric measurement:
understand concepts of area and
relate area to multiplication and to
addition.
area 3.7
MD c
I/R ODE c. Use tiling to show in a concrete
case that the area of a rectangle with
whole-number side lengths a and b +
c is the sum of a × b and a × c. Use
area models to represent the
distributive property in mathematical
reasoning.
3,4 tiles
Measurement and
Data
Geometric measurement:
understand concepts of area and
relate area to multiplication and to
addition.
area 3.7
MD d
I/R ODE d. Recognize area as additive. Find
areas of rectilinear figures by
decomposing them into non-
overlapping rectangles and adding
the areas of the non-overlapping
parts, applying this technique to solve
real world problems.
3,4
7
Math
Curriculum Map
Grade 3
Domain Clusters Key Vocabulary
Co
re S
tan
dard
I/R
/M
OD
E / T
C
Grade Level
Specific Standard
Qu
art
er
Tau
gh
t Student
Engagement/
Learning
Activity / Special
Resource / Web
Link
Measurement and
Data
Geometric measurement:
recognize perimeter as an
attribute of plane figures and
distinguish between linear and
area measures.
perimeter, area 3.8
MD
I/R ODE Solve real world and mathematical
problems involving perimeters of
polygons, including finding the
perimeter given the side lengths,
finding an unknown side length, and
exhibiting rectangles with the same
perimeter and different areas or with
the same area and different
perimeters.
3,4 tiles, 1 inch/cm grid
paper, string,
geoboards, rubber
bands
Measurement and
Data
Counting back change to $10.00 penny, nickel,
quarter, dime, bills
3.9
MD
I/R TC Ability to count back change using
coins and bills the simplest way.
Money (bills and
coins)
Geometry Reason with shapes and their
attributes
two dimensional,
attributes, rhombus,
rectangle,
quadrilateral
3. G
1
I/R
/M
ODE Understand that shapes in different
categories (e.g., rhombuses,
rectangles, and others) may share
attributes (e.g., having four sides),
and that the shared attributes can
define a larger category (e.g.,
quadrilaterals). Recognize
rhombuses, rectangles, and squares
as examples of quadrilaterals, and
draw examples of quadrilaterals that
do not belong to any of these
subcategories
3,4 attribute blocks
Geometry Reason with shapes and their
attributes
equal parts 3.G 2 I/R
/M
ODE Partition shapes into parts with equal
areas. Express the area of each part
as a unit fraction of the whole.
3,4 Fraction bars,
Fraction circles
8
Math
Curriculum Map
Grade 4
Domain ClustersKey
Vocabulary
Co
re S
tan
dard
I/R
/M
OD
E / T
C
Grade Level
Specific Standard
Qu
art
er
Tau
gh
t Student
Engagement/
Learning
Activity / Special
Resource / Web
Link
Operations and
Algebraic Thinking
Use the four operations
with whole numbers to
solve problems.
multiplication
equation, number
sentence, array,
product, factors,
Commutative
Property, Zero
Property, Identity
Property,
operations,
inverse operation,
fact family, mental
computation
4.OA.1 R/M ODE Interpret a multiplication equation
as a comparison, e.g., interpret 35
= 5 × 7 as a statement that 35 is 5
times as many as 7 and 7 times as
many as 5. Represent verbal
statements of multiplicative
comparisons as multiplication
equations.
1,2,3,4 grid paper, place
value blocks, coloring
tools, counters, index
cards, technology
Operations and
Algebraic Thinking
Use the four operations
with whole numbers to
solve problems.
equations,
symbol,
multiplication,
division, product,
factors, partial
product,
quotients,
dividend, divisor
4.AO.2 I/R ODE Multiply or divide to solve word
problems involving multiplicative
comparison, e.g., by using drawings
and equations with a symbol for the
unknown number to represent the
problem, distinguishing
multiplicative comparison from
additive comparison.
1,2,3,4 grid paper, coloring
tools, counters,
technology
1
Math
Curriculum Map
Grade 4
Domain ClustersKey
Vocabulary
Co
re S
tan
dard
I/R
/M
OD
E / T
C
Grade Level
Specific Standard
Qu
art
er
Tau
gh
t Student
Engagement/
Learning
Activity / Special
Resource / Web
Link
Operations and
Algebraic Thinking
Use the four operations
with whole numbers to
solve problems.
multistep,
remainders,
operations,
reasonableness,
estimate
4.AO.3 I/R ODE Solve multistep word problems
posed with whole numbers and
having whole-number answers
using the four operations, including
problems in which remainders must
be interpreted. Represent these
problems using equations with a
letter standing for the unknown
quantity. Assess the
reasonableness of answers using
mental computation and estimation
strategies including rounding.
1,2,3,4 grid paper, coloring
tools, counters,
technology
Operations and
Algebraic Thinking
Gain familiarity with
factors and multiples.
factors, multiples,
prime, composite,
range, Distributive
Property
4.AO.4 I/R ODE Find all factor pairs for a whole
number in the range 1-100.
Recognize that a whole number is a
multiple of each of its factors.
Determine whether a given whole
number is the range 1-100 is a
multiple of a given one-digit
number. Determine whether a given
whole number in the range 1-100 is
prime or composite.
1,2,3,4 grid paper, coloring
tools, counters, index
cards, technology
2
Math
Curriculum Map
Grade 4
Domain ClustersKey
Vocabulary
Co
re S
tan
dard
I/R
/M
OD
E / T
C
Grade Level
Specific Standard
Qu
art
er
Tau
gh
t Student
Engagement/
Learning
Activity / Special
Resource / Web
Link
Operations and
Algebraic Thinking
Generate and analyze
patterns.
pattern, shape
pattern, number
pattern, multiple,
sequence,
repeating rule
4.AO.5 I/R ODE Generate a number or shape
pattern that follows a given rule.
Identify apparent features of the
pattern that were not explicit in the
rule itself.
For example, given the rule “Add 3”
and the starting number 1, generate
terms in the resulting sequence and
observe that the terms appear to
alternate between odd and even
numbers. Explain informally why the
numbers will continue to alternate in
this way.
1,2,3,4 hundred chart,
pattern blocks,
tangram pieces, two-
color counters, grid
paper, cubes,
technology
Number and
operations in base
ten
Generalize place value
understanding for multi-
digit whole numbers.
place value,
mental multiplying
and dividing by
10's, multi-digit
number
4.NBT.
1
I/R ODE Recognize that in a multi-digit whole
number, a digit in one place
represents ten times what it
represents in the place to its right.
For example, recognize that 700 ÷
70 = 10 by applying concepts of
place value and division.
1,2,3,4 place value chart,
place value blocks,
index card, coloring
tools, two-color
counters, technology
Number and
operations in base
ten
Generalize place value
understanding for multi-
digit whole numbers.
place value, base
ten, expanded
form, standard
form, word form,
greater than, less
than, equal to,
compare, order,
symbols
4.NBT.
2
I/R/M ODE
TC
Read and write multi-digit whole
numbers using base-ten numerals,
number names, and expanded
form. Compare two multi-digit
numbers based on meanings of the
digits in each place, using >, =, and
< symbols to record the results of
comparisons.
1,2,3,4 place value chart,
place value blocks,
technology
3
Math
Curriculum Map
Grade 4
Domain ClustersKey
Vocabulary
Co
re S
tan
dard
I/R
/M
OD
E / T
C
Grade Level
Specific Standard
Qu
art
er
Tau
gh
t Student
Engagement/
Learning
Activity / Special
Resource / Web
Link
Number and
operations in base
ten
Generalize place value
understanding for multi-
digit whole numbers.
place value,
rounding,
breaking apart
4.NBT.
3
R/M ODE Use place value understanding to
round multi-digit whole numbers to
any place.
1,2,3,4 number lines, place
value chart, place
value blocks, coloring
tools, technology
Number and
operations in base
ten
Use place value
understanding and
properties of operations
to perform multi-digit
arithmetic.
addend, sum,
difference, digit,
numeral,
regrouping,
inverse operation,
addition,
subtraction
4.NBT.
4
R/M ODE Fluently add and subtract multi-digit
whole numbers using the standard
algorithm.
1,2,3,4 place value chart,
place value blocks,
technology
Number and
operations in base
ten
Use place value
understanding and
properties of operations to
perform multi-digit
arithmetic.
Distributive,
Associative,
Commutative,
Identity Properties
of multiplication,
array, regrouping,
partial products,
compensation,
equation,
compatible
numbers,
calculation,
illustrate
4.NBT.
5
I/R ODE Multiply a whole number of up to
four digits by a one-digit whole
number, and multiply two two-digit
numbers, using strategies based on
place value and the properties of
operations. Illustrate and explain the
calculation by using equations,
rectangular arrays, and/or area
models.
1,2,3,4 grid paper, block
value blocks, coloring
tools, number lines,
calculators,
technology
4
Math
Curriculum Map
Grade 4
Domain ClustersKey
Vocabulary
Co
re S
tan
dard
I/R
/M
OD
E / T
C
Grade Level
Specific Standard
Qu
art
er
Tau
gh
t Student
Engagement/
Learning
Activity / Special
Resource / Web
Link
Number and
operations in base
ten
Use place value
understanding and
properties of operations to
perform multi-digit
arithmetic.
divide, quotient,
dividend, divisor,
remainder,
models, arrays,
equations, inverse
operation,
repeated
subtraction, area
models, arrays
4.NBT.
6
I/R ODE Find whole-number quotients and
remainders with up to four-digit
dividends and one-digit divisors,
using strategies based on place
value, the properties of operations,
and/or the relationship between
multiplication and division. Illustrate
and explain the calculation by using
equations, rectangular arrays,
and/or area models.
1,2,3,4 calculators, coloring
tools, two-color
counters, place value
blocks, grid paper,
technology
Number and
Operations –
Fractions
Extend understanding of
fraction equivalence and
ordering.
fraction,
equivalent
fractions,
numerator,
denominator,
models
4.NF.1 I/R ODE Explain why a fraction a/b is
equivalent to a fraction (n × a)/(n ×
b) by using visual fraction models,
with attention to how the number
and size of the parts differ even
though the two fractions themselves
are the same size. Use this
principle to recognize and generate
equivalent fractions.
1,2,3,4 fraction strips,
number lines, strips
of paper, masking
tape, technology
5
Math
Curriculum Map
Grade 4
Domain ClustersKey
Vocabulary
Co
re S
tan
dard
I/R
/M
OD
E / T
C
Grade Level
Specific Standard
Qu
art
er
Tau
gh
t Student
Engagement/
Learning
Activity / Special
Resource / Web
Link
Number and
Operations –
Fractions
Extend understanding of
fraction equivalence and
ordering.
fraction,
equivalent
fractions,
numerator,
denominator,
benchmark
fractions, fraction
models, compare,
common
denominator
4.NF.2 I/R ODE Compare two fractions with different
numerators and different
denominators, e.g., by creating
common denominators or
numerators, or by comparing to a
benchmark fraction such as 1/2.
Recognize that comparisons are
valid only when the two fractions
refer to the same whole. Record the
results of comparisons with symbols
>, =, or <, and justify the
conclusions, e.g., by using a visual
fraction model.
1,2,3,4 fraction strips,
number lines, strips
of paper, masking
tape, technology
6
Math
Curriculum Map
Grade 4
Domain ClustersKey
Vocabulary
Co
re S
tan
dard
I/R
/M
OD
E / T
C
Grade Level
Specific Standard
Qu
art
er
Tau
gh
t Student
Engagement/
Learning
Activity / Special
Resource / Web
Link
Number and
Operations –
Fractions
Build fractions from unit
fractions by applying and
extending previous
understandings of
operations on whole
numbers.
fraction,
numerator,
denominator,
improper fraction,
mixed number,
simplify, reduce,
decompose
4.NF.3 I/R ODE Understand a fraction a/b with a > 1
as a sum of fractions 1/b.
a. Understand addition and
subtraction of fractions as joining
and separating parts referring to the
same whole.
b. Decompose a fraction into a sum
of fractions with the same
denominator in more than one way,
recording each decomposition by
an equation. Justify
decompositions, e.g., by using a
visual fraction model.
Examples: 3/8 = 1/8 + 1/8 + 1/8 ;
3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8
= 8/8 + 8/8 + 1/8.
c. Add and subtract mixed numbers
with like denominators, e.g., by
replacing each mixed number with
an equivalent fraction, and/or by
using properties of operations and
the relationship between addition
and subtraction.
d. Solve word problems involving
addition and subtraction of fractions
referring to the same whole and
having like denominators, e.g., by
using visual fraction models and
equations to represent the problem.
1,2,3,4 fraction strips or
circles, number lines,
strips of paper,
masking tape,
coloring tools,
scissors, grid paper,
technology
7
Math
Curriculum Map
Grade 4
Domain ClustersKey
Vocabulary
Co
re S
tan
dard
I/R
/M
OD
E / T
C
Grade Level
Specific Standard
Qu
art
er
Tau
gh
t Student
Engagement/
Learning
Activity / Special
Resource / Web
Link
Number and
Operations –
Fractions
Build fractions from unit
fractions by applying and
extending previous
understandings of
operations on whole
numbers.
fraction, whole
number, unit
fraction,
numerator,
denominator,
models,
equations
4.NF.4 I/R ODE Apply and extend previous
understandings of multiplication to
multiply a fraction by a whole
number.
a. Understand a fraction a/b as a
multiple of 1/b.
For example, use a visual fraction
model to represent 5/4 as the
product 5 × (1/4), recording the
conclusion by the equation 5/4 = 5 ×
(1/4).
b. Understand a multiple of a/b as a
multiple of 1/b, and use this
understanding to multiply a fraction
by a whole number.
For example, use a visual fraction
model to express 3 × (2/5) as 6 ×
(1/5), recognizing this product as
6/5. (In general, n × (a/b) = (n ×
a)/b.)
c. Solve word problems involving
multiplication of a fraction by a
whole number, e.g., by using visual
fraction models and equations to
represent the problem.
For example, if each person at a
party will eat 3/8 of a pound of roast
beef, and there will be 5 people at
the party, how many pounds of
roast beef will be needed? Between
what two whole numbers does your
answer lie?
1,2,3,4 paper strips,
scissors, fraction
strips, technology
8
Math
Curriculum Map
Grade 4
Domain ClustersKey
Vocabulary
Co
re S
tan
dard
I/R
/M
OD
E / T
C
Grade Level
Specific Standard
Qu
art
er
Tau
gh
t Student
Engagement/
Learning
Activity / Special
Resource / Web
Link
Number and
Operations –
Fractions
Understand decimal
notation for fractions,
and compare decimal
fractions.
fraction,
numerator,
denominator,
equivalent
fraction, express
4.NF.5 I/R ODE Express a fraction with denominator
10 as an equivalent fraction with
denominator 100, and use this
technique to add two fractions with
respective denominators 10 and
100.
For example, express 3/10 as
30/100, and add 3/10 + 4/100 =
34/100.
1,2,3,4 decimals models,
number lines, grid
paper, coloring tools,
decimal place value
chart, technology
Number and
Operations –
Fractions
Understand decimal
notation for fractions, and
compare decimal fractions.
decimal, decimal
point, decimal
notation, fraction,
tenths,
hundredths,
convert
4.NF.6 I/R ODE Use decimal notation for fractions
with denominators 10 or 100.
For example, rewrite 0.62 as
62/100; describe a length as 0.62
meters; locate 0.62 on a number
line diagram.
1,2,3,4 rulers, number line
diagrams, decimal
place value chart,
technology
Number and
Operations –
Fractions
Understand decimal
notation for fractions, and
compare decimal fractions.
tenths,
hundredths,
decimal point
4.NF.7 I/R ODE Compare two decimals to
hundredths by reasoning about their
size. Recognize that comparisons
are valid only when the two
decimals refer to the same whole.
Record the results of comparisons
with the symbols >, =, or <, and
justify the conclusions, e.g., by
using a visual model.
1,2,3,4 base 10 blocks,
number line, grid
paper
9
Math
Curriculum Map
Grade 4
Domain ClustersKey
Vocabulary
Co
re S
tan
dard
I/R
/M
OD
E / T
C
Grade Level
Specific Standard
Qu
art
er
Tau
gh
t Student
Engagement/
Learning
Activity / Special
Resource / Web
Link
Measurement and
Data
Solve problems involving
measurement and
conversion of
measurement from a
larger unit to a smaller
unit.
length, inch (in),
foot (ft.), yard
(yd.), mile (mi),
millimeter (mm),
centimeter
(cm),decimeter
(dm), meter (m),
kilometer (km),
capacity,
gallon(gal) , quart
(qt), pint (pt.), cup
(c), tablespoon
Tbsp.), liter (l),
milliliter (ml),
weight, ton (T),
pound (lb.), ounce
(oz.), mass, gram
(g), milligram
(mg), time, hour
(hr.), minute
(min), seconds
(sec), conversion,
measurement
system,
equivalent,
elapsed time,
scale, equivalent
measurement,
money, quantity
4.MD.
1
I/R ODE Know relative sizes of
measurement units within one
system of units including km, m,
cm; kg, g; lb., oz.; l, ml; hr., min,
sec. Within a single system of
measurement, express
measurements in a larger unit in
terms of a smaller unit. Record
measurement equivalents in a two
column table.
For example, know that 1 ft. is 12
times as long as 1 in. Express the
length of a 4 ft. snake as 48 in.
Generate a conversion table for feet
and inches listing the number pairs
(1, 12), (2, 24), (3, 36), ...
1,2,3,4 ruler, yardstick,
meter stick, masking
tape, containers
(gallon, quart, pint,
cup, tablespoon), liter
bottle, eyedropper,
funnel, scale,
weights, clock face,
place value blocks,
technology
10
Math
Curriculum Map
Grade 4
Domain ClustersKey
Vocabulary
Co
re S
tan
dard
I/R
/M
OD
E / T
C
Grade Level
Specific Standard
Qu
art
er
Tau
gh
t Student
Engagement/
Learning
Activity / Special
Resource / Web
Link
Measurement and
Data
Solve problems involving
measurement and
conversion of
measurement from a larger
unit to a smaller unit.
distance, length,
time intervals
(elapsed), liquid
volume, mass,
money, fractions,
decimals,
4.MD.
2
I/R ODE Use the four operations to solve
word problems involving distances,
intervals of time, liquid volumes,
masses of objects, and money,
including problems involving simple
fractions or decimals, and problems
that require expressing
measurements given in a larger unit
in terms of a smaller unit.
Represent measurement quantities
using diagrams such as number
line diagrams that feature a
measurement scale.
1,2,3,4 grid paper, bills and
coins, ruler,
yardstick, meter
stick, masking tape,
containers (gallon,
quart, pint, cup,
tablespoon), liter
bottle, eyedropper,
funnel, scale,
weights, clock face,
place value blocks,
technology
Measurement and
Data
Solve problems involving
measurement and
conversion of
measurement from a larger
unit to a smaller unit.
perimeter, area,
formulas,
rectangles,
length, width,
squared, tiles
4.MD.
3
I/R ODE Apply the area and perimeter
formulas for rectangles in real world
and mathematical problems.
1,2,3,4 grid paper, coloring
tools, cut out shapes,
technology
Measurement and
Data
Represent and interpret
data
line plot, data set
fractions, range
4.MD.
4
I/R ODE Make a line plot to display a data
set of measurements in fractions of
a unit (1/2, 1/4, 1/8). Solve
problems involving addition and
subtraction of fractions by using
information presented in line plots.
For example, from a line plot find
and interpret the difference in length
between the longest and shortest
specimens in an insect collection.
1,2,3,4 graph paper,
technology
11
Math
Curriculum Map
Grade 4
Domain ClustersKey
Vocabulary
Co
re S
tan
dard
I/R
/M
OD
E / T
C
Grade Level
Specific Standard
Qu
art
er
Tau
gh
t Student
Engagement/
Learning
Activity / Special
Resource / Web
Link
Measurement and
Data
Geometric measurement:
understand concepts of
angle and measure
angles.
degree, angle,
endpoint, vertex,
angle
measurement,
circle, circular arc
4.MD.
5
I/R ODE Recognize angles as geometric
shapes that are formed wherever
two rays share a common endpoint,
and understand concepts of angle
measurement:
a. An angle is measured with
reference to a circle with its center
at the common endpoint of the rays,
by considering the fraction of the
circular arc between the points
where the two rays intersect the
circle. An angle that turns through
1/360 of a circle is called a “one-
degree angle,” and can be used to
measure angles.
b. An angle that turns through n one-
degree angles is said to have an
angle measure of n degrees.
1,2,3,4 clock face, pattern
blocks, technology
Measurement and
Data
Geometric measurement:
understand concepts of
angle and measure angles.
protractor,
degree, angle,
4.MD.
6
I/R ODE Measure angles in whole-number
degrees using a protractor. Sketch
angles of specified measure.
1,2,3,4 protractor, ruler
12
Math
Curriculum Map
Grade 4
Domain ClustersKey
Vocabulary
Co
re S
tan
dard
I/R
/M
OD
E / T
C
Grade Level
Specific Standard
Qu
art
er
Tau
gh
t Student
Engagement/
Learning
Activity / Special
Resource / Web
Link
Measurement and
Data
Geometric measurement:
understand concepts of
angle and measure angles.
angle, additive,
decompose, non-
overlapping parts,
sum, diagram,
symbol, equation,
angle
measurement
4.MD.
7
I/R ODE Recognize angle measure as
additive. When an angle is
decomposed into non-overlapping
parts, the angle measure of the
whole is the sum of the angle
measures of the parts. Solve
addition and subtraction problems
to find unknown angles on a
diagram in real world and
mathematical problems, e.g., by
using an equation with a symbol for
the unknown angle measure.
1,2,3,4 coloring tools,
protractor,
technology
Geometry Draw and identify lines
and angles, and classify
shapes by properties of
their lines and angles.
point, plane, line,
line segment, ray,
angle, vertex,
endpoint,
perpendicular
lines, parallel
lines, intersecting
lines, right angle,
acute angle,
obtuse angle,
straight angle, two-
dimensional
figure
4.G.1 I/R/M ODE Draw points, lines, line segments,
rays, angles (right, acute, obtuse),
and perpendicular and parallel lines.
Identify these in two-dimensional
figures.
1,2,3,4 grid paper, coloring
tools, straws,
Playdoh, dot paper,
technology
13
Math
Curriculum Map
Grade 4
Domain ClustersKey
Vocabulary
Co
re S
tan
dard
I/R
/M
OD
E / T
C
Grade Level
Specific Standard
Qu
art
er
Tau
gh
t Student
Engagement/
Learning
Activity / Special
Resource / Web
Link
Geometry Draw and identify lines and
angles, and classify shapes
by properties of their lines
and angles.
classify, category,
sort, two-
dimensional
figure, parallel
lines,
perpendicular
lines, angle,
triangle, right
triangle, acute
angle, obtuse
angle, equilateral
triangle, isosceles
triangle, scalene
triangle, polygon,
regular, irregular,
quadrilateral,
pentagon,
hexagon,
octagon,
parallelogram,
rectangle, square,
rhombus,
trapezoid,
geometric shapes
4.G.2 I/R ODE Classify two-dimensional figures
based on the presence or absence
of parallel or perpendicular lines, or
the presence or absence of angles
of a specified size. Recognize right
triangles as a category, and identify
right triangles.
1,2,3,4 geoboards, graph
paper, cut out
shapes, spaghetti,
Playdoh, straws,
pattern blocks, ruler,
protractor,
technology
14
Math
Curriculum Map
Grade 4
Domain ClustersKey
Vocabulary
Co
re S
tan
dard
I/R
/M
OD
E / T
C
Grade Level
Specific Standard
Qu
art
er
Tau
gh
t Student
Engagement/
Learning
Activity / Special
Resource / Web
Link
Geometry Draw and identify lines and
angles, and classify shapes
by properties of their lines
and angles.
line symmetry,
two-dimensional
figure, matching
parts, fold
4.G.3 I/R/M ODE Recognize a line of symmetry for a
two-dimensional figure as a line
across the figure such that the
figure can be folded along the line
into matching parts. Identify line-
symmetric figures and draw lines of
symmetry.
1,2,3,4 cut out shapes,
technology
15
Math
Curriculum Map
Grade 5
Domain Cluster Key Vocabulary
Co
re S
tan
dard
I/R
/M
OD
E / T
C
Grade Level
Specific Standard
Qu
art
er
Tau
gh
t
Student Engagement/
Learning Activity /
Special Resource / Web
Link
Operations &
Algebraic
Thinking
Write and interpret
numerical
expressions.
order of operations,
numerical
expressions,
equations, evaluate
5.OA.
1
I, R ODE Use parentheses, brackets, or braces in
numerical expressions, and evaluate
expressions with these symbols.
1, 2, 3, 4 modeling, student practice,
technology
Operations &
Algebraic Thinking
Write and interpret
numerical
expressions.
variable, algebraic
expressions
5.OA.
2
R ODE Write simple expressions that record
calculations with numbers, and interpret
numerical expressions without
evaluating them. For example, express
the calculation “add 8 and 7, then
multiply by 2” as 2 × (8 + 7). Recognize
that 3 × (18932 + 921) is three times as
large as 18932 + 921, without having to
calculate the indicated sum or product.
1, 2, 3, 4 modeling, student practice,
technology
Operations &
Algebraic Thinking
Analyze patterns
and relationships.
corresponding,
sequence, term,
coordinate plane,
ordered pairs, origin,
x-axis, y-axis
5.OA.
3
I, R ODE Generate two numerical patterns using
two given rules. Identify apparent
relationships between corresponding
terms. Form ordered pairs consisting of
corresponding terms from the two
patterns, and graph the ordered pairs on
a coordinate plane. For example, given
the rule “Add 3” and the starting number
0, and given the rule “Add 6” and the
starting number 0, generate terms in the
resulting sequences, and observe that
the terms in one sequence are twice the
corresponding terms in the other
sequence. Explain informally why this is
so.
1, 2, 3, 4 modeling, student practice,
technology, grid paper, rulers
1
Math
Curriculum Map
Grade 5
Domain Cluster Key Vocabulary
Co
re S
tan
dard
I/R
/M
OD
E / T
C
Grade Level
Specific Standard
Qu
art
er
Tau
gh
t
Student Engagement/
Learning Activity /
Special Resource / Web
Link
Number &
Operations in
Base Ten
Understand the
place value system.
digits, value, standard
form, expanded form,
word form
5.NB
T.1
R, M ODE Recognize that in a multi-digit number, a
digit in one place represents 10 times as
much as it represents in the place to its
right and 1/10 of what it represents in the
place to its left.
1, 2, 3, 4 modeling, student practice,
technology, grid paper, place
value chart
Number &
Operations in Base
Ten
Understand the place
value system.
factors, product,
multiple, exponential
notation, exponent,
base, standard form,
expanded form,
squared, cubed,
power
5.NB
T.2
I, R ODE Explain patterns in the number of zeros
of the product when multiplying a
number by powers of 10, and explain
patterns in the placement of the decimal
point when a decimal is multiplied or
divided by a power of 10. Use whole-
number exponents to denote powers of
10.
1, 2, 3, 4 modeling, student practice,
technology, number cards or
tiles, calculators
Number &
Operations in Base
Ten
Understand the place
value system.
decimals, tenths,
hundredths,
thousandths
5.NB
T.3
I, R ODE Read, write, and compare decimals to
thousandths.
1, 2, 3, 4 modeling, student practice,
technology, grid paper, place
value chart
Number &
Operations in Base
Ten
Understand the place
value system.
equivalent decimals 5.NB
T.3.a
I, R ODE Read and write decimals to thousandths
using base-ten numerals, number
names, and expanded form, e.g.,
347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 ×
(1/10) + 9 × (1/100) + 2 × (1/1000).
1, 2, 3, 4 modeling, student practice,
technology
Number &
Operations in Base
Ten
Understand the place
value system.
greater than, less
than
5.NB
T.3.b
I, R ODE Compare two decimals to thousandths
based on meanings of the digits in each
place, using >, =, and < symbols to
record the results of comparisons.
1, 2, 3, 4 modeling, student practice,
technology, grid paper
2
Math
Curriculum Map
Grade 5
Domain Cluster Key Vocabulary
Co
re S
tan
dard
I/R
/M
OD
E / T
C
Grade Level
Specific Standard
Qu
art
er
Tau
gh
t
Student Engagement/
Learning Activity /
Special Resource / Web
Link
Number &
Operations in Base
Ten
Understand the place
value system
rounding 5.NB
T.4
I, R ODE Use place value understanding to round
decimals to any place.
1, 2, 3, 4 modeling, student practice,
technology, number line,
rounding rap
Number &
Operations in Base
Ten
Perform operations
with multi-digit whole
numbers and with
decimals to
hundredths.
underestimate,
overestimate,
distributive property,
partial products
5.NB
T.5
I, R ODE Fluently multiply multi-digit whole
numbers using the standard algorithm.
1, 2, 3, 4 modeling, student practice,
technology, grid paper,
whiteboards
Number &
Operations in Base
Ten
Perform operations
with multi-digit whole
numbers and with
decimals to
hundredths.
commutative property
of multiplication,
associative property
of multiplication,
identity property of
multiplication, zero
property of
multiplication,
dividend, divisor,
quotient
5.NB
T.6
R ODE Find whole-number quotients of whole
numbers with up to four-digit dividends
and two-digit divisors, using strategies
based on place value, the properties of
operations, and/or the relationship
between multiplication and division.
Illustrate and explain the calculation by
using equations, rectangular arrays,
and/or area models.
1, 2, 3, 4 modeling, student practice,
technology, grid paper, arrays,
whiteboards, division acrostic
Number &
Operations in Base
Ten
Perform operations
with multi-digit whole
numbers and with
decimals to
hundredths.
commutative
property, associative
property, compatible
numbers,
compensation
5.NB
T.7
I, R ODE Add, subtract, multiply, and divide
decimals to hundredths, using concrete
models or drawings and strategies
based on place value, properties of
operations, and/or the relationship
between addition and subtraction; relate
the strategy to a written method and
explain the reasoning used.
1, 2, 3, 4 modeling, student practice,
technology, base-ten blocks
3
Math
Curriculum Map
Grade 5
Domain Cluster Key Vocabulary
Co
re S
tan
dard
I/R
/M
OD
E / T
C
Grade Level
Specific Standard
Qu
art
er
Tau
gh
t
Student Engagement/
Learning Activity /
Special Resource / Web
Link
Number &
Operations -
Fractions
Use equivalent
fractions as a
strategy to add and
subtract fractions.
equivalent fractions,
simplest form,
common multiple,
least common
multiple (LCM),
common
denominator, least
common
denominator (LCD),
proper fraction,
improper fraction,
mixed number
5.NF.
1
R ODE Add and subtract fractions with unlike
denominators (including mixed
numbers) by replacing given fractions
with equivalent fractions in such a way
as to produce an equivalent sum or
difference of fractions with like
denominators. For example, 2/3 + 5/4 =
8/12 + 15/12 = 23/12. (In general, a/b +
c/d = (ad + bc)/bd.)
1, 2, 3, 4 modeling, student practice,
technology, fraction strips,
fraction circles
Number &
Operations -
Fractions
Use equivalent
fractions as a strategy
to add and subtract
fractions.
benchmark fraction 5.NF.
2
R ODE Solve word problems involving addition
and subtraction of fractions referring to
the same whole, including cases of
unlike denominators, e.g., by using
visual fraction models or equations to
represent the problem. Use benchmark
fractions and number sense of fractions
to estimate mentally and assess the
reasonableness of answers. For
example, recognize an incorrect result
2/5 + 1/2 = 3/7, by observing that 3/7 <
1/2.
1, 2, 3, 4 modeling, student practice,
technology, fraction strips,
fraction circles, measuring
cups
4
Math
Curriculum Map
Grade 5
Domain Cluster Key Vocabulary
Co
re S
tan
dard
I/R
/M
OD
E / T
C
Grade Level
Specific Standard
Qu
art
er
Tau
gh
t
Student Engagement/
Learning Activity /
Special Resource / Web
Link
Number &
Operations -
Fractions
Apply and extend
previous
understandings of
multiplication and
division to multiply
and divide fractions.
numerator,
denominator,
improper fraction,
mixed number
5.NF.
3
I, R ODE Interpret a fraction as division of the
numerator by the denominator (a/b = a ÷
b). Solve word problems involving
division of whole numbers leading to
answers in the form of fractions or mixed
numbers, e.g., by using visual fraction
models or equations to represent the
problem. For example, interpret 3/4 as
the result of dividing 3 by 4, noting that
3/4 multiplied by 4 equals 3, and that
when 3 wholes are shared equally
among 4 people each person has a
share of size 3/4. If 9 people want to
share a 50-pound sack of rice equally
by weight, how many pounds of rice
should each person get? Between what
two whole numbers does your answer
lie?
1, 2, 3, 4 modeling, student practice,
technology, fraction strips,
fraction circles
Number &
Operations -
Fractions
Apply and extend
previous
understandings of
multiplication and
division to multiply
and divide fractions.
numerator,
denominator,
improper fraction,
mixed number
5.NF.
4
I, R ODE Apply and extend previous
understandings of multiplication to
multiply a fraction or whole number by a
fraction.
1, 2, 3, 4 modeling, student practice,
technology, fraction strips,
fraction circles
5
Math
Curriculum Map
Grade 5
Domain Cluster Key Vocabulary
Co
re S
tan
dard
I/R
/M
OD
E / T
C
Grade Level
Specific Standard
Qu
art
er
Tau
gh
t
Student Engagement/
Learning Activity /
Special Resource / Web
Link
Number &
Operations -
Fractions
Apply and extend
previous
understandings of
multiplication and
division to multiply
and divide fractions.
equation, product,
quotient, order of
operations
5.NF.
4.a
I, R ODE Interpret the product (a/b) × q as a parts
of a partition of q into b equal parts;
equivalently, as the result of a sequence
of operations a × q ÷ b. For example,
use a visual fraction model to show (2/3)
× 4 = 8/3, and create a story context for
this equation. Do the same with (2/3) ×
(4/5) = 8/15. (In general, (a/b) × (c/d) =
ac/bd.)
1, 2, 3, 4 modeling, student practice,
technology, fraction strips,
fraction circles
Number &
Operations -
Fractions
Apply and extend
previous
understandings of
multiplication and
division to multiply
and divide fractions.
area, square units 5.NF.
4.b
I, R ODE Find the area of a rectangle with
fractional side lengths by tiling it with unit
squares of the appropriate unit fraction
side lengths, and show that the area is
the same as would be found by
multiplying the side lengths. Multiply
fractional side lengths to find areas of
rectangles, and represent fraction
products as rectangular areas.
1, 2, 3, 4 modeling, student practice,
technology, color tiles, grid
paper
Number &
Operations -
Fractions
Apply and extend
previous
understandings of
multiplication and
division to multiply
and divide fractions.
resizing, scaling, 5.NF.
5
R ODE Interpret multiplication as scaling
(resizing), by:
1, 2, 3, 4 modeling, student practice,
technology
Number &
Operations -
Fractions
Apply and extend
previous
understandings of
multiplication and
division to multiply
and divide fractions.
factors, product 5.NF.
5.a
R ODE Comparing the size of a product to the
size of one factor on the basis of the
size of the other factor, without
performing the indicated multiplication.
1, 2, 3, 4 modeling, student practice,
technology
6
Math
Curriculum Map
Grade 5
Domain Cluster Key Vocabulary
Co
re S
tan
dard
I/R
/M
OD
E / T
C
Grade Level
Specific Standard
Qu
art
er
Tau
gh
t
Student Engagement/
Learning Activity /
Special Resource / Web
Link
Number &
Operations -
Fractions
Apply and extend
previous
understandings of
multiplication and
division to multiply
and divide fractions.
resizing, scaling,
equivalent fractions
5.NF.
5.b
R ODE Explaining why multiplying a given
number by a fraction greater than 1
results in a product greater than the
given number (recognizing multiplication
by whole numbers greater than 1 as a
familiar case); explaining why multiplying
a given number by a fraction less than 1
results in a product smaller than the
given number; and relating the principle
of fraction equivalence a/b = (n × a)/(n ×
b) to the effect of multiplying a/b by 1.
1, 2, 3, 4 modeling, student practice,
technology
Number &
Operations -
Fractions
Apply and extend
previous
understandings of
multiplication and
division to multiply
and divide fractions.
equations, improper
fractions, mixed
numbers
5.NF.
6
R ODE Solve real world problems involving
multiplication of fractions and mixed
numbers, e.g., by using visual fraction
models or equations to represent the
problem.
1, 2, 3, 4 modeling, student practice,
technology, fraction strips,
fraction circles
Number &
Operations -
Fractions
Apply and extend
previous
understandings of
multiplication and
division to multiply
and divide fractions.
fraction, numerator,
denominator,
reciprocal
5.NF.
7
I, R ODE Apply and extend previous
understandings of division to divide unit
fractions by whole numbers and whole
numbers by unit fractions. (Students
able to multiply fractions in general can
develop strategies to divide fractions in
general, by reasoning about the
relationship between multiplication and
division. But division of a fraction by a
fraction is not a requirement at this
grade.)
1, 2, 3, 4 modeling, student practice,
technology
7
Math
Curriculum Map
Grade 5
Domain Cluster Key Vocabulary
Co
re S
tan
dard
I/R
/M
OD
E / T
C
Grade Level
Specific Standard
Qu
art
er
Tau
gh
t
Student Engagement/
Learning Activity /
Special Resource / Web
Link
Number &
Operations -
Fractions
Apply and extend
previous
understandings of
multiplication and
division to multiply
and divide fractions.
fraction, numerator,
denominator,
reciprocal
5.NF.
7.a
I, R ODE Interpret division of a unit fraction by a
non-zero whole number, and compute
such quotients. For example, create a
story context for (1/3) ÷ 4, and use a
visual fraction model to show the
quotient. Use the relationship between
multiplication and division to explain that
(1/3) ÷ 4 = 1/12 because (1/12) × 4 =
1/3.
1, 2, 3, 4 modeling, student practice,
technology, fractions strips,
fraction circles
Number &
Operations -
Fractions
Apply and extend
previous
understandings of
multiplication and
division to multiply
and divide fractions.
fraction, numerator,
denominator,
reciprocal
5.NF.
7.b
I, R ODE Interpret division of a whole number by a
unit fraction, and compute such
quotients. For example, create a story
context for 4 ÷ (1/5), and use a visual
fraction model to show the quotient. Use
the relationship between multiplication
and division to explain that 4 ÷ (1/5) =
20 because 20 × (1/5) = 4.
1, 2, 3, 4 modeling, student practice,
technology, fraction strips,
fraction circles
Number &
Operations -
Fractions
Apply and extend
previous
understandings of
multiplication and
division to multiply
and divide fractions.
fraction, numerator,
denominator,
reciprocal
5.NF.
7c.
I, R ODE Solve real world problems involving
division of unit fractions by non-zero
whole numbers and division of whole
numbers by unit fractions, e.g., by using
visual fraction models and equations to
represent the problem. For example,
how much chocolate will each person
get if 3 people share 1/2 lb of chocolate
equally? How many 1/3-cup servings
are in 2 cups of raisins?
1, 2, 3, 4 modeling, student practice,
technology, fraction strips,
fraction circles
8
Math
Curriculum Map
Grade 5
Domain Cluster Key Vocabulary
Co
re S
tan
dard
I/R
/M
OD
E / T
C
Grade Level
Specific Standard
Qu
art
er
Tau
gh
t
Student Engagement/
Learning Activity /
Special Resource / Web
Link
Measurement &
Data
Convert like
measurement units
within a given
measurement
system.
metric, customary,
meters, liters, grams,
kilo-, centi-, milli-
5.MD.
1
R ODE Convert among different-sized standard
measurement units within a given
measurement system (e.g., convert 5
cm to 0.05 m), and use these
conversions in solving multi-step, real
world problems.
1, 2, 3, 4 modeling, student practice,
technology, metric acrostic,
rulers, meter sticks, measuring
cups, empty containers (pint,
quart, liter, etc.)
Measurement &
Data
Represent and
interpret data.
line plot, outlier,
survey, data, sample,
frequency table
5.MD.
2
R ODE Make a line plot to display a data set of
measurements in fractions of a unit (1/2,
1/4, 1/8). Use operations on fractions for
this grade to solve problems involving
information presented in line plots. For
example, given different measurements
of liquid in identical beakers, find the
amount of liquid each beaker would
contain if the total amount in all the
beakers were redistributed equally.
1, 2, 3, 4 modeling, student practice,
technology, rulers
Measurement &
Data
Geometric
measurement:
understand
concepts of volume
and relate volume to
multiplication and
to addition.
volume, three-
dimensional shape,
cube, face, edge,
vertex, vertices,
prism, cylinder, cone,
pyramid
5.MD.
3
I, R ODE Recognize volume as an attribute of
solid figures and understand concepts of
volume measurement.
1, 2, 3, 4 modeling, student practice,
technology, solids
Measurement &
Data
Geometric
measurement:
understand concepts
of volume and relate
volume to
multiplication and to
addition.
volume, cubic unit 5.MD.
3.a
I, R ODE A cube with side length 1 unit, called a
“unit cube,” is said to have “one cubic
unit” of volume, and can be used to
measure volume.
1, 2, 3, 4 modeling, student practice,
technology, centimeter cubes
9
Math
Curriculum Map
Grade 5
Domain Cluster Key Vocabulary
Co
re S
tan
dard
I/R
/M
OD
E / T
C
Grade Level
Specific Standard
Qu
art
er
Tau
gh
t
Student Engagement/
Learning Activity /
Special Resource / Web
Link
Measurement &
Data
Geometric
measurement:
understand concepts
of volume and relate
volume to
multiplication and to
addition.
volume, cubic unit 5.MD.
3.b
I, R ODE A solid figure which can be packed
without gaps or overlaps using n unit
cubes is said to have a volume of n
cubic units.
1, 2, 3, 4 modeling, student practice,
technology, centimeter cubes,
small cardboard boxex
Measurement &
Data
Geometric
measurement:
understand concepts
of volume and relate
volume to
multiplication and to
addition.
volume, cubic unit 5.MD.
4
I, R ODE Measure volumes by counting unit
cubes, using cubic cm, cubic in, cubic ft,
and improvised units.
1, 2, 3, 4 modeling, student practice,
technology, centimeter cubes,
rulers, meter sticks
Measurement &
Data
Geometric
measurement:
understand concepts
of volume and relate
volume to
multiplication and to
addition.
volume, cubic unit 5.MD.
5
I, R ODE Relate volume to the operations of
multiplication and addition and solve real
world and mathematical problems
involving volume.
1, 2, 3, 4 modeling, student practice,
technology
Measurement &
Data
Geometric
measurement:
understand concepts
of volume and relate
volume to
multiplication and to
addition.
volume, cubic unit 5.MD.
5.a
I, R ODE Find the volume of a right rectangular
prism with whole-number side lengths by
packing it with unit cubes, and show that
the volume is the same as would be
found by multiplying the edge lengths,
equivalently by multiplying the height by
the area of the base. Represent
threefold whole-number products as
volumes, e.g., to represent the
associative property of multiplication.
1, 2, 3, 4 modeling, student practice,
technology, centimeter cubes,
small cardboard boxes
10
Math
Curriculum Map
Grade 5
Domain Cluster Key Vocabulary
Co
re S
tan
dard
I/R
/M
OD
E / T
C
Grade Level
Specific Standard
Qu
art
er
Tau
gh
t
Student Engagement/
Learning Activity /
Special Resource / Web
Link
Measurement &
Data
Geometric
measurement:
understand concepts
of volume and relate
volume to
multiplication and to
addition.
volume, cubic unit,
rectangular prism
5.MD.
5.b
I, R ODE Apply the formulas V = l × w × h and V =
b × h for rectangular prisms to find
volumes of right rectangular prisms with
whole-number edge lengths in the
context of solving real world and
mathematical problems.
1, 2, 3, 4 modeling, student practice,
technology
Measurement &
Data
Geometric
measurement:
understand concepts
of volume and relate
volume to
multiplication and to
addition.
volume, cubic unit,
rectangular prism
5.MD.
5.c
I, R ODE Recognize volume as additive. Find
volumes of solid figures composed of
two non-overlapping right rectangular
prisms by adding the volumes of the non-
overlapping parts, applying this
technique to solve real world problems.
1, 2, 3, 4 modeling, student practice,
technology,
11
Math
Curriculum Map
Grade 5
Domain Cluster Key Vocabulary
Co
re S
tan
dard
I/R
/M
OD
E / T
C
Grade Level
Specific Standard
Qu
art
er
Tau
gh
t
Student Engagement/
Learning Activity /
Special Resource / Web
Link
Geometry Graph points on the
coordinate plane to
solve real-world and
mathematical
problems.
coordinate grid, x-
axis, y-axis, origin,
ordered pair, x-
coordinate, y-
coordinate
5.G.1 I, R ODE Use a pair of perpendicular number
lines, called axes, to define a coordinate
system, with the intersection of the lines
(the origin) arranged to coincide with the
0 on each line and a given point in the
plane located by using an ordered pair of
numbers, called its coordinates.
Understand that the first number
indicates how far to travel from the origin
in the direction of one axis, and the
second number indicates how far to
travel in the direction of the second axis,
with the convention that the names of
the two axes and the coordinates
correspond (e.g., x -axis and x -
coordinate, y -axis and y -coordinate).
1, 2, 3, 4 modeling, student practice,
technology, grid paper, rulers,
Geometry Graph points on the
coordinate plane to
solve real-world and
mathematical
problems.
coordinate grid, x-
axis, y-axis, origin,
ordered pair, x-
coordinate, y-
coordinate, quadrant
I
5.G.2 I, R ODE Represent real world and mathematical
problems by graphing points in the first
quadrant of the coordinate plane, and
interpret coordinate values of points in
the context of the situation.
1, 2, 3, 4 modeling, student practice,
technology, grid paper
12
Math
Curriculum Map
Grade 5
Domain Cluster Key Vocabulary
Co
re S
tan
dard
I/R
/M
OD
E / T
C
Grade Level
Specific Standard
Qu
art
er
Tau
gh
t
Student Engagement/
Learning Activity /
Special Resource / Web
Link
Geometry Classify two-
dimensional figures
into categories
based on their
properties.
polygon, regular
polygon, triangle,
quadrilateral,
pentagon, hexagon,
octagon, equilateral
triange, isosceles
triangle, scalene
triangle, right triangle,
acute triangle, obtuse
triangle,
parallelogram,
trapezoid, rectangle,
rhombus, square,
generalization
5.G.3 R, M ODE Understand that attributes belonging to a
category of two-dimensional figures also
belong to all subcategories of that
category. For example, all rectangles
have four right angles and squares are
rectangles, so all squares have four
right angles.
1, 2, 3, 4 modeling, student practice,
technology, quadrilateral
flowchart, pattern blocks, The
Greedy Triangle by Marilyn
Burns
Geometry Classify two-
dimensional figures
into categories based
on their properties.
congruent, parallel
sides, right angles
5.G.4 R, M ODE Classify two-dimensional figures in a
hierarchy based on properties.
1, 2, 3, 4 modeling, student practice,
technology, pattern blocks,
geoboards
13
Math
Curriculum Map
Grade 6
Domain Cluster Key Vocabulary
Co
re S
tan
dard
I/R
/M
OD
E / T
C
Grade Level
Specific Standard
Qu
art
er
Tau
gh
t Student
Engagement/
Learning
Activity / Special
Resource / Web
Link
Ratio &
Proportions
Understand ratio concepts
and use ratio reasoning to
solve problems.
ratio, unit rate,
proportion,
equivalent ratios
6.RP.1 I ODE Understand the concept of a ratio
and use ratio language to describe
a ratio relationship between two
quantities. For example, “The ratio
of wings to beaks in the bird house
at the zoo was 2:1, because for
1,2,3,4 Interactive smart
board activities with
whole group
instruction
Ratio &
Proportions
Understand ratio concepts
and use ratio reasoning to
solve problems.
ratio, unit rate,
proportion,
equivalent ratios
6.RP.2 I ODEUnderstand the concept of a unit
rate a/b associated with a ratio a:b
with b ≠ 0, and use rate language in
the context of a ratio relationship.
For example, “This recipe has a
ratio of 3 cups of flour to 4 cups of
sugar, so there is 3/4 cup of flour
for each cup of sugar.” “We paid
$75 for 15 hamburgers, which is a
rate of $5 per hamburger.”1
1,2,3,4 Use real world
example to
demonstrate
relationship
Ratio &
Proportions
Understand ratio concepts and
use ratio reasoning to solve
problems.
ratio, unit rate,
proportion,
equivalent ratios,
6.RP.3 I ODE Use ratio and rate reasoning to solve
real-world and mathematical
problems, e.g., by reasoning about
tables of equivalent ratios, tape
diagrams, double number line
diagrams, or equations.
1,2,3,4 Use real world
example to
demonstrate
relationship using
tables, number lines,
diagrams
1
Math
Curriculum Map
Grade 6
Domain Cluster Key Vocabulary
Co
re S
tan
dard
I/R
/M
OD
E / T
C
Grade Level
Specific Standard
Qu
art
er
Tau
gh
t Student
Engagement/
Learning
Activity / Special
Resource / Web
Link
Number
system
Apply and extend previous
understandings of
multiplication and division
to divide fractions by
fractions.
Factors, Prime
Factorization,
Estimation, Greatest
Common Factor,
Least Common
Multiple ,Quotient,
Divident
6.NS.1. R ODEInterpret and compute quotients
of fractions, and solve word
problems involving division of
fractions by fractions, e.g., by
using visual fraction models and
equations to represent the
problem. For example, create a
story context for (2/3) ÷ (3/4) and
use a visual fraction model to
show the quotient; use the
relationship between
multiplication and division to
explain that (2/3) ÷ (3/4) = 8/9
because 3/4 of 8/9 is 2/3. (In
general, (a/b) ÷ (c/d) = ad/bc.)
How much chocolate will each
person get if 3 people share 1/2 lb
of chocolate equally? How many
3/4-cup servings are in 2/3 of a
cup of yogurt? How wide is a
rectangular strip of land with
length 3/4 mi and area 1/2 square
mi? Compute fluently with multi-
digit numbers and find common
factors and multiples.
1,2,3,4 Interactive smart
board activities with
whole group
instruction
2
Math
Curriculum Map
Grade 6
Domain Cluster Key Vocabulary
Co
re S
tan
dard
I/R
/M
OD
E / T
C
Grade Level
Specific Standard
Qu
art
er
Tau
gh
t Student
Engagement/
Learning
Activity / Special
Resource / Web
Link
Number
system
Compute fluently with multi-
digit numbers and find
common factors and multiples
Factors, Prime
Factorization,
Estimation, Greatest
Common Factor,
Least Common
Multiple ,Quotient,
Divident
6.NS.2 I ODE
Fluently divide multi-digit numbers
using the standard algorithm
1,2,3,4 Interactive smart board
activities with whole
group instruction
Number
systemApply and extend previous
understandings of
multiplication and division to
divide fractions by fractions.
Factors, Prime
Factorization,
Estimation, Greatest
Common Factor,
Least Common
Multiple ,Quotient,
Divident
6.NS.3. R ODE
TC
Fluently add, subtract, multiply, and
divide multi-digit decimals using the
standard algorithm for each operation
1,2,3,4 multiplication charts
& Calculators
Number
system
Apply and extend previous
understandings of
multiplication and division to
divide fractions by fractions.
Factors, Prime
Factorization,
Estimation, Greatest
Common Factor,
Least Common
Multiple ,Quotient,
Divident
6.NS.4. R ODE
Find the greatest common factor
of two whole numbers less than
or equal to 100 and the least
common multiple of two whole
numbers less than or equal to 12.
Use the distributive property to
express a sum of two whole
numbers 1–100 with a common
factor as a multiple of a sum of
two whole numbers with no
common factor. For example,
express 36 + 8 as 4 (9 + 2).
Apply and extend previous
understandings of numbers to the
system of rational numbers.
1,2,3,4 multiplication charts
& Calculators
3
Math
Curriculum Map
Grade 6
Domain Cluster Key Vocabulary
Co
re S
tan
dard
I/R
/M
OD
E / T
C
Grade Level
Specific Standard
Qu
art
er
Tau
gh
t Student
Engagement/
Learning
Activity / Special
Resource / Web
Link
Number
system
Apply and extend previous
understandings of numbers
to the system of rational
numbers.
Positive & Negative
integers,
6.NS.5. R ODEUnderstand that positive and
negative numbers are used
together to describe quantities
having opposite directions or values
(e.g., temperature above/below
zero, elevation above/below sea
level, credits/debits,
positive/negative electric charge);
use positive and negative numbers
to represent quantities in real-world
contexts, explaining the meaning of
0 in each situation.
1,2,3,4 Number lines using
positive and negative
integers, counters,
thermometer
Number
systemApply and extend previous
understandings of numbers
to the system of rational
numbers.
Positive & Negative
integers, origin,
quadrants
6.NS.6. R ODE Understand a rational number as a
point on the number line. Extend
number line diagrams and coordinate
axes familiar from previous grades to
represent points on the line and in the
plane with negative number
coordinates
1,2,3,4
Number
system
Apply and extend previous
understandings of numbers to
the system of rational numbers
Positive & Negative
integers, origin,
quadrants
6.NS.6. a R ODE Recognize opposite signs of numbers
as indicating locations on opposite
sides of 0 on the number line;
recognize that the opposite of the
opposite of a number is the number
itself, e.g., –(–3) = 3, and that 0 is its
own opposite
1,2,3,4 Number lines using
positive and negative
integers, counters,
thermometer
4
Math
Curriculum Map
Grade 6
Domain Cluster Key Vocabulary
Co
re S
tan
dard
I/R
/M
OD
E / T
C
Grade Level
Specific Standard
Qu
art
er
Tau
gh
t Student
Engagement/
Learning
Activity / Special
Resource / Web
Link
Number
system
Apply and extend previous
understandings of numbers to
the system of rational numbers
Positive & Negative
integers, origin,
quadrants
6.NS.6. b R ODE
Understand signs of numbers in
ordered pairs as indicating locations
in quadrants of the coordinate plane;
recognize that when two ordered
pairs differ only by signs, the
locations of the points are related by
reflections across one or both axes
1,2,3,4 Interactive smart board
activities with whole
group instruction, graph
paper
Number
system
Apply and extend previous
understandings of numbers to
the system of rational numbers
Positive & Negative
integers, origin,
quadrants
6.NS.6. c R ODE Find and position integers and other
rational numbers on a horizontal or
vertical number line diagram; find and
position pairs of integers and other
rational numbers on a coordinate
plane
1,2,3,4 Use real world example
to demonstrate
relationship using
tables, number lines,
diagrams
Number
systemApply and extend previous
understandings of numbers to
the system of rational numbers
Positive & Negative
integers, origin,
quadrants
6.NS.7 R ODE
Understand ordering and absolute
value of rational numbers.
1,2,3,4 Small group flash cards
and have students put
in order without talking
each has a number
card
Number
system
Apply and extend previous
understandings of numbers to
the system of rational numbers
Positive & Negative
integers, origin,
quadrants
6.NS.7 a R ODE Interpret statements of inequality as
statements about the relative
position of two numbers on a
number line diagram. For example,
interpret –3 > –7 as a statement
that –3 is located to the right of –7
on a number line oriented from left
to right.
1,2,3,4 Smart board activity
with number line
5
Math
Curriculum Map
Grade 6
Domain Cluster Key Vocabulary
Co
re S
tan
dard
I/R
/M
OD
E / T
C
Grade Level
Specific Standard
Qu
art
er
Tau
gh
t Student
Engagement/
Learning
Activity / Special
Resource / Web
Link
Number
system
Apply and extend previous
understandings of numbers to
the system of rational numbers
Positive & Negative
integers, origin,
quadrants
6.NS.7 b I ODE Write, interpret, and explain
statements of order for rational
numbers in real-world contexts. For
example, write –3 co. > –7 co. to
express the fact that –3 co. is warmer
than –7 co.
1,2,3,4 Small group to
collaborate on writing
and statements using
real-world examples
Number
system
Apply and extend previous
understandings of numbers to
the system of rational numbers
Positive & Negative
integers, origin,
quadrants, absolute
value
6.NS.7 c R ODE
Understand the absolute value of a
rational number as its distance from 0
on the number line; interpret absolute
value as magnitude for a positive or
negative quantity in a real-world
situation. For example, for an
account balance of –30 dollars, write
1,2,3,4 Tutorial video using
real world situations
Number
system
Apply and extend previous
understandings of numbers to
the system of rational numbers
Positive & Negative
integers, origin,
quadrants
6.NS.7 d R Distinguish comparisons of absolute
value from statements about order.
For example, recognize that an
account balance less than –30
dollars represents a debt greater
than 30 dollars
1,2,3,4 Interactive smart board
activities with whole
group instruction
Number
system
Apply and extend previous
understandings of numbers to
the system of rational numbers
Positive & Negative
integers, origin,
quadrants, absolute
value
6.NS.8. R ODESolve real-world and
mathematical problems by
graphing points in all four
quadrants of the coordinate plane.
Include use of coordinates and
absolute value to find distances
between points with the same first
coordinate or the same second
coordinate.
1,2,3,4 Interactive smart board
activities with whole
group instruction
Expressions
& Equations
Apply and extend previous
understandings of arithmetic to
algebraic expressions
Algebra, evaluate,
exponents, variable
6.EE.1. R ODE Write and evaluate numerical
expressions involving whole-
number exponents.
1,2,3,4 Smart board activities
6
Math
Curriculum Map
Grade 6
Domain Cluster Key Vocabulary
Co
re S
tan
dard
I/R
/M
OD
E / T
C
Grade Level
Specific Standard
Qu
art
er
Tau
gh
t Student
Engagement/
Learning
Activity / Special
Resource / Web
Link
Expressions &
Equations
Apply and extend previous
understandings of arithmetic to
algebraic expressions
Algebra, coefficient,
evaluate, exponents,
quotient, variable
6.EE.2. R ODE Write, read, and evaluate expressions
in which letters stand for numbers.
1,2,3,4 Smart board activities
Expressions &
Equations
Apply and extend previous
understandings of arithmetic to
algebraic expressions
Algebra, coefficient,
evaluate, exponents,
quotient, variable
6.EE.2. a R ODE Write expressions that record
operations with numbers and with
letters standing for numbers. For
example, express the calculation
“Subtract y from 5” as 5 – y.
1,2,3,4 smart board
activities, copies,
calculators
Expressions &
Equations
Apply and extend previous
understandings of arithmetic to
algebraic expressions
Algebra, coefficient,
evaluate, exponents,
quotient, variable
6.EE.2. b R ODE Identify parts of an expression using
Algebra Creating Equations Create equations that describe
numbers or relationship
equation, inequalitiy,
variable, coefficient,
constant
A-
CED.1
R ODE Create equations and inequalities in one
variable and use them to solve problems.
Include equations
arising from linear and quadratic
functions, and simple rational and
exponential functions.
1
Algebra Creating Equations Create equations that describe
numbers or relationship
equation, inequalitiy,
variable, coefficient,
constant
A-
CED.2
R ODE Create equations in two or more variables
to represent relationships between
quantities; graph
equations on coordinate axes with labels
and scales
1,3
Algebra Creating Equations Create equations that describe
numbers or relationship
equation, inequalitiy,
variable, coefficient,
constant
A-
CED.3
R ODE Represent constraints by equations or
inequalities, and by systems of equations
and/or inequalities,
and interpret solutions as viable or non-
viable in a modeling context.
1,3
Algebra Creating Equations Create equations that describe
numbers or relationship
equation, formula,
variable, coefficient,
constant
A-
CED.4
R ODE Rearrange formulas to highlight a quantity
of interest, using the same reasoning as in
solving
equations.
2
Algebra Reasoning with Equations and
Inequalities
Understand solving equations as a
process of reasoning and explain the
reasoning.
Rational equations,
radical equations,
variable
A-
REI.2
R ODE Solve simple rational and radical
equations in one variable, and give
examples showing how
extraneous solutions may arise.
2
Algebra Reasoning with Equations and
Inequalities
Solve equations and inequalities in
one variable
linear equation, linear
inequality, variable,
coefficient
A-
REI.3
a
R ODE Solve linear equations and inequalities in
one variable, including equations with
coefficients represented by letters
1
7
Honors Pre-Calculus
Curriculum Map
Strand Domain Cluster Key Vocabulary
Co
re S
tan
dard
I/R
/M
OD
E /
TC
Grade Level
Specific Standard
Qu
art
er
Tau
gh
t
Algebra Reasoning with Equations and
Inequalities
Solve equations and inequalities in
one variable
quadratic equation A-
REI.3
b
R ODE Solve quadratic equations in one
variable. (a) Use the method of
completing the square to transform any
quadratic equation in x into an equation of
the form (x – p)^2 = q that has the same
solutions. Derive the quadratic formula
from this form.
2
Algebra Reasoning with Equations and
Inequalities
Solve equations and inequalities in
one variable
quadratic equation A-
REI.4
R ODE Solve quadratic equations in one
variable.
(b) Solve quadratic equations by
inspection (e.g., for x^2 = 49), taking
square roots, completing the square, the
quadratic formula and factoring, as
appropriate to the initial form of the
equation. Recognize when the quadratic
formula gives complex solutions and write
them in a ± bi for real numbers a and b.
2
Algebra Reasoning with Equations and
Inequalities
Solve systems of equations system, variable A-
REI.5
R ODE Prove that a system of two equations in
two variables, replacing one equation by
the sum of that equation and a multiple of
the other produces a system with the
same solutions.
3
Algebra Reasoning with Equations and
Inequalities
Solve systems of equations system, variable A-
REI.6
R ODE Solve systems of linear equations exactly
and approximately (e.g., with graphs),
focusing on pairs of linear equations in
two variables.
1,3
Algebra Reasoning with Equations and
Inequalities
Solve systems of equations system, quadratic
equation
A-
REI.7
I ODE Solve a simple system consisting of a
linear equation and a quadratic equation
in two variables algebraically and
graphically. For example, find the points of
intersection between the line y = –3x and
the circle x2 + y2 = 3
3
8
Honors Pre-Calculus
Curriculum Map
Strand Domain Cluster Key Vocabulary
Co
re S
tan
dard
I/R
/M
OD
E /
TC
Grade Level
Specific Standard
Qu
art
er
Tau
gh
t
Algebra Reasoning with Equations and
Inequalities
Solve systems of equations system, matrix, linear
equation
A-
REI.8
R ODE (+) Represent a system of linear equations as
a single matrix equation in a vector
variable
3
Algebra Reasoning with Equations and
Inequalities
Solve systems of equations inverse of a matrix,
system, linear equation
A-
REI.9
R ODE (+) Find the inverse of a matrix if it exists and
use it to solve systems of linear equations
(using technology for matrices of
dimension 3x3 or greater)
3
Algebra Reasoning with Equations and
Inequalities
Represent and solve equations and
inequalities graphically
graph, set of all
solutions, coordinate
plane
A-
REI.1
0
R ODE Understand that the graph of an equation
in two variables is the set of all its
solutions plotted in the coordinate plane,
often forming a curve (which could be a
line).
1
Algebra Reasoning with Equations and
Inequalities
Represent and solve equations and
inequalities graphically
x-coordinate, y-
coordinate, function
A-
REI.1
1
R ODE Explain why the x-coordinates of the
points where the graphs of the equations y
= f(x) and y = g(x) intersect are the
solutions of the equation f(x) = g(x); find
the solutions approximately, e.g., using
technology to graph the functions, make
tables of values, or find successive
approximations. Include cases where f(x)
and/or g(x) are linear, polynomial, rational,
absolute value, exponential, and
logarithmic functions.
1
Algebra Reasoning with Equations and
Inequalities
Represent and solve equations and
inequalities graphically
graph, linear inequality,
boundary, system
A-
REI.1
2
R ODE Graph the solutions to a linear inequality
in two variables as a half-plane (excluding
the boundary in the case of a strict
inequality), and graph the solution set to a
system of linear inequalities in two
variables as the intersection of the
corresponding half-planes.
3
9
Honors Pre-Calculus
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Strand Domain Cluster Key Vocabulary
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TC
Grade Level
Specific Standard
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Functions Interpreting Functions Understand the concept of a function
and use function notation
domain, range, set,
function
F-IF.1 R ODE Understand that a function from one set
(called the domain) to another set (called
the range) assigns to each element of the
domain exactly one element of the range.
If f is a function and x is an element of its
domain, the f(x) denotes the output of f
corresponding to the input x. The graph of
f is the graph of the equation y = f(x).
1
Functions Interpreting Functions Understand the concept of a function
and use function notation
function, domain, input F-IF.2 R ODE Use function notation, evaluate functions
for inputs in their domains, and interpret
statements that use function notation in
terms of a context.
1
Functions Interpreting Functions Interpret functions that arise in
applications in terms of the context
intercepts; intervals
where the function is
increasing, decreasing,
positive, or negative;
relative maximums and
minimums;
symmetries; end
behavior; and
periodicity.
F-IF.4 R ODE For a function that models a relationship
between two quantities, interpret key
features of graphs and tables in terms of
the quantities, and sketch graphs showing
key features given a verbal description of
the relationship.
2
Functions Interpreting Functions Interpret functions that arise in
applications in terms of the context
domain, quantiative F-IF.5 R ODE Relate the domain of a function to its
graph and, where applicable, to the
quantitative relationship it describes.
1
Functions Interpreting Functions Interpret functions that arise in
applications in terms of the context
rate of change F-IF.6 I ODE Calculate and interpret the average rate of
change of a function (presented
symbolically or as a table) over a specified
interval. Estimate the rate of change from
a graph.
1
10
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Strand Domain Cluster Key Vocabulary
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Grade Level
Specific Standard
Qu
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Functions Interpreting Functions Analyze functions using different
representations
linear, quadratic,
intercepts, maxima,
minima
F-
IF.7a
R ODE Graph functions expressed
symbolically and show key features of
the graph, by hand in simple cases and
using technology for more complicated
cases. (a) Graph linear and quadratic
functions and show intercepts, maxima,
and minima
2
Functions Interpreting Functions Analyze functions using different
representations
roots, piecewise, step-
function, absolute
value
F-
IF.7b
R ODE Graph functions expressed
symbolically and show key features of
the graph, by hand in simple cases and
using technology for more complicated
cases. b. Graph square root, cube root,
and piecewise-defined functions, including
step functions and absolute value
functions
2
Functions Interpreting Functions Analyze functions using different
representations
polynomial, zeros,
factorizations
F-
IF.7c
R ODE Graph functions expressed
symbolically and show key features of
the graph, by hand in simple cases and
using technology for more complicated
cases. (c) Graph polynomial functions,
identifying zeros when suitable
factorizations are available, and showing
end behavior
2
Functions Interpreting Functions Analyze functions using different
representations
rational, zeros,
asymptotes
F-
IF.7d
R ODE (+) Graph functions expressed
symbolically and show key features of
the graph, by hand in simple cases and
using technology for more complicated
cases. (d) Graph rational functions,
identifying zeros and asymptotes when
suitable factorizations are available, and
showing end behavior.
2
11
Honors Pre-Calculus
Curriculum Map
Strand Domain Cluster Key Vocabulary
Co
re S
tan
dard
I/R
/M
OD
E /
TC
Grade Level
Specific Standard
Qu
art
er
Tau
gh
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Functions Interpreting Functions Analyze functions using different
representations
logarithmic,
exponential, intercepts,
end behavior, period,
midline, amplitutde
F-
IF.7e
R ODE Graph functions expressed
symbolically and show key features of
the graph, by hand in simple cases and
using technology for more complicated
cases. (e) Graph exponential and
logarithmic functions, showing intercepts
and end behavior, and trigonometric
functions, showing period, midline, and
amplitude.
1,2
Functions Building Functions Build a function that models a
relationship between two quantities
function F-
BF.1
R ODE Write a function that describes a
relationship between two quantities. (a)
Determine an explicit expression, a
recursive process, or steps for calculation
from a context. (b) Combine standard
function types using arithmetic operations
2
Functions Building Functions Build a function that models a
relationship between two quantities
arithmetic and
geometric sequence
F-
BF.2
R ODE Write arithmetic and geometric sequences
both recursively and with an explicit
formula; use them to model situations,
and translate between the two forms.
4
Functions Building Functions Building new functions from existing
functions
inverse function F-
BF.4a
R ODE Find inverse functions.
(a) Solve an equation of the form f(x) = c
for a simple function f that has an inverse
and write an expression for the inverse.
1
Functions Building Functions Building new functions from existing
functions
inverse, exponents,
logarithms
F-
BF.5
R ODE (+) Understand the inverse relationship
between exponents and logarithms and
use this relationship to solve problems
involving logarithms and exponents
2
12
Honors Pre-Calculus
Curriculum Map
Strand Domain Cluster Key Vocabulary
Co
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tan
dard
I/R
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TC
Grade Level
Specific Standard
Qu
art
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Tau
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Functions Linear and Exponential Models Construct and compare linear and
exponential modesl and solve
problems
linear functions,
intervals, exponential
functions
F-
LE.1a
R ODE Distinguish between situations that
can be modeled with linear functions
and with exponential functions.
a. Prove that linear functions grow by
equal differences over equal intervals,
and that exponential functions grow by
equal factors over equal intervals.
2
Functions Linear and Exponential Models Construct and compare linear and
exponential modesl and solve
problems
rate F-
LE.1b
R ODE Distinguish between situations that
can be modeled with linear functions
and with exponential functions.
b. Recognize situations in which one
quantity changes at a constant rate per
unit interval relative to another.
2
Functions Linear and Exponential Models Construct and compare linear and
exponential modesl and solve
problems
growth, decay, rate F-
LE.1c
R ODE Distinguish between situations that
can be modeled with linear functions
and with exponential functions.
c. Recognize situations in which a quantity
grows or decays by a constant percent
rate per unit interval relative to another.
2
Functions Linear and Exponential Models Construct and compare linear and
exponential modesl and solve
problems
linear and exponential
functions, arithemetic
and geometric
sequence, input, output
F-
LE.2
R ODE Construct linear and exponential
functions, including arithmetic and
geometric sequences, given a graph, a
description of a relationship, or two input-
output pairs (include reading these from a
table.)
2,4
13
Honors Pre-Calculus
Curriculum Map
Strand Domain Cluster Key Vocabulary
Co
re S
tan
dard
I/R
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OD
E /
TC
Grade Level
Specific Standard
Qu
art
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Tau
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Functions Linear and Exponential Models Construct and compare linear and
exponential modesl and solve
problems
linearlly, quadratically,
polynomial
F-
LE.3
R ODE Observe using graphs and tables that a
quantity increasing exponentially
eventually exceeds a quantity increasing
linearly, quadratically, or (more generally)
as a polynomial function.
2
Functions Linear and Exponential Models Construct and compare linear and
exponential modesl and solve
problems
logarithm F-
LE.4
R ODE For exponential models, express as a
logarithm the solution to abct = d where a,
c, and d are numbers and the base b is 2,
10, or e; evaluate the logarithm using
technology.
2
Functions Linear and Exponential Models Interpret expresiions for functions in
terms of the situation they model
parameters F-
LE.5
R ODE Interpert the parameters in a linear or
exponetial function in terms of a context
2
Functions Trigonometric Functions Extend the domain of trigonometrtic
functions using the unit circle
radian, arc length F-
TF.1
I ODE Understand radian measure of an angle
as the length of the arc on the unit circle
subtended by the angle.
1
Functions Trigonometric Functions Extend the domain of trigonometrtic
functions using the unit circle
unit circle, trigoometric
functions, traversed
F-
TF.2
I ODE Explain how the unit circle in the
coordinate plane enables the extension of
trigonometric functions to all real
numbers, interpreted as radian measures
of angles traversed counterclockwise
around the unit circle.
1
Functions Trigonometric Functions Extend the domain of trigonometrtic
functions using the unit circle
special right triangles,
trionometric functions
F-
TF.3
I ODE (+) Use special triangles to determine
geometrically the values of sine, cosine,
tangent for π/3, π/4 and π/6, and use the
unit circle to express the values of sine,
cosines, and tangent for x, π + x, and 2π
– x in terms of their values for x, where x
is any real number.
1
14
Honors Pre-Calculus
Curriculum Map
Strand Domain Cluster Key Vocabulary
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re S
tan
dard
I/R
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TC
Grade Level
Specific Standard
Qu
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Functions Trigonometric Functions Extend the domain of trigonometrtic
functions using the unit circle
unit circle, odd and
even symmetry
F-
TF.4
I ODE (+) Use the unit circle to explain symmetry
(odd and even) and periodicity of
trigonometric functions.
1
Functions Trigonometric Functions Model periodic phenomena with
trigonometric functions
trigonmetric functions F-
TF.5
I ODE Choose trigonometric functions to model
periodic phenomena with specified
amplitude, frequency, and midline.
1
Functions Trigonometric Functions Model periodic phenomena with
trigonometric functions
trigonmetric functions,
domain
F-
TF.6
I ODE (+) Understand that restricting a trigonometric
function to a domain on which it is always
increasing or always decreasing allows its
inverse to be constructed.
1
Functions Trigonometric Functions Model periodic phenomena with
trigonometric functions
inverse functions,
trigonometric functions
F-
TF.7
I ODE (+) Use inverse functions to solve
trigonometric equations that arise in
modeling contexts; evaluate the solutions
using technology, and interpret them in
terms of the context
1
Functions Trigonometric Functions Prove and apply trigonometric
identities
Pythagorean Theorem F-
TF.8
I ODE Prove the Pythagorean identity sin2(θ) +
cos2(θ) = 1 and use it to find sin(θ),
cos(θ), or tan(θ) given sin(θ), cos(θ), or
tan(θ) and the quadrant of the angle.
1
Functions Trigonometric Functions Prove and apply trigonometric
identities
trigonometric identities F-
TF.9
I ODE (+) Prove the addition and subtraction
formulas for sine, cosine, and tangent and
use them to solve problems.
1
15
Honors Pre-Calculus
Curriculum Map
Strand Domain Cluster Key Vocabulary
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re S
tan
dard
I/R
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TC
Grade Level
Specific Standard
Qu
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Geometry Similarity, Right Triangles, and
Trigonometry
Understand similarity in terms of
similarity transformations
Pythagorean Theorem G-
SRT 4
R ODE Prove theorems about triangles.
Theorems include: a line parallel to one
side of a triangle divides the other two
proportionally, and conversely; the
Pythagorean Theorem proved using
triangle similarity.
1,2
Geometry Similarity, Right Triangles, and
Trigonometry
Understand similarity in terms of
similarity transformations
congruence G-
SRT 5
R,
M
ODE Use congruence and similarity criteria for
triangles to solve problems and to prove
relationships in geometric figures.
1,2
Geometry Similarity, Right Triangles, and
Trigonometry
Define trigonometric ratios and solve
problems invovling right angles
right triangles, acute
angles
G-
SRT 6
R,
M
ODE Understand that by similarity, side ratios in
right triangles are properties of the angles
in the triangle, leading to definitions of
trigonometric ratios for acute angles.
1,2
Geometry Similarity, Right Triangles, and
Trigonometry
Define trigonometric ratios and solve
problems invovling right angles
sine and cosine G-
SRT 7
R,
M
ODE Explain and use the relationship between
the sine and cosine of complementary
angles
1,2
Geometry Similarity, Right Triangles, and
Trigonometry
Define trigonometric ratios and solve
problems invovling right angles
Pythagorean Theorem G-
SRT 8
R,
M
ODE Use trigonometric ratios and the
Pythagorean Theorem to solve right
triangles in applied problems
1,2
Geometry Similarity, Right Triangles, and
Trigonometry
Apply trigonometry to general
triangles
area of a triangle G-
SRT 9
I ODE (+) Derive the formula A = 1/2 ab sin(C) for
the area of a triangle by drawing an
auxiliary line from a vertex perpendicular
to the opposite side.
1,2
Geometry Similarity, Right Triangles, and
Trigonometry
Apply trigonometry to general
triangles
law of sines, law of
cosines
G-
SRT
10
I ODE (+) Prove the Laws of Sines and Cosines and
use them to solve problems.
1,2
16
Honors Pre-Calculus
Curriculum Map
Strand Domain Cluster Key Vocabulary
Co
re S
tan
dard
I/R
/M
OD
E /
TC
Grade Level
Specific Standard
Qu
art
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Tau
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Geometry Similarity, Right Triangles, and
Trigonometry
Apply trigonometry to general
triangles
law of sines, law of
cosines
G-
SRT
11
I ODE (+) Understand and apply the Law of Sines
and the Law of Cosines to find unknown
measurements in right and non-right
triangles (e.g., surveying problems,
resultant forces).
1,2
Geometry Circles Find arc lengths and areas of sectors
of circles
arc length, area of
sector
G-C 5 R ODE Derive using similarity the fact that the
length of the arc intercepted by an angle
is proportional to the radius, and define
the radian measure of the angle as the
constant of proportionality; derive the
formula for the area of a sector.
1,2
Geometry Expressing Geometric Properties with
Equations
Translate between the geometric
description and the equation for a
conic section
circle, radius,
Pythagorean Theorem
G-
GPE 1
R ODE Derive the equation of a circle of given
center and radius using the Pythagorean
Theorem; complete the square to find the
center and radius of a circle given by an
equation.
3,4
Geometry Expressing Geometric Properties with
Equations
Translate between the geometric
description and the equation for a
conic section
circle, radius,
Pythagorean Theorem
G-
GPE 2
I,R ODE Derive the equation of a parabola given a
focus and directrix
4
Geometry Expressing Geometric Properties with
Equations
Translate between the geometric
description and the equation for a
conic section
circle, radius,
Pythagorean Theorem
G-
GPE 3
I ODE (+) Derive the equations of ellipses and
hyperbolas given the foci, using the fact
that the sum or difference of distances
from the foci is constant.
4
Statistics Interpreting Categorical and
Quantiative Data
Interpret Linear Models slope, intercepts S-ID.7 M ODE Interpret the slope (rate of change) and
the intercept (constant term) of a linear
model in the context of the data.
3
17
Honors Pre-Calculus
Curriculum Map
Strand Domain Cluster Key Vocabulary
Co
re S
tan
dard
I/R
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OD
E /
TC
Grade Level
Specific Standard
Qu
art
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Statistics Interpreting Categorical and
Quantiative Data
Interpret Linear Models scatter plot, linear fit S-ID.8 M ODE Compute (using technology) and interpret
the correlation coefficient of a linear fit.
3
Statistics Interpreting Categorical and
Quantiative Data
Interpret Linear Models correlation, causation S-ID.9 R ODE Distinguish between correlation and
causation.
1,2,3,4
18
AP Calculus
Curriculum Map
Strand Domain Cluster Key Vocabulary
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TC
Grade Level
Specific Standard
Qu
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Number and Quantity Quantities Reason quantitatively and use units to
solve problems
units, scale, origing N-Q 1 R ODE Use units as a way to understand
problems and to guide the solution of
multi-step problems; choose and interpret
units consistently in formulas; choose and
interpret the scale and the origin in graphs
and data display
1,2,3,4
Number and Quantity Vector and Matrix Quantities Represent and model with vector
quantities
velocity, quantities N-VM
3
I ODE Solve problems involving velocity and
other quantities that can be represented
by vectors
1,2,3,4
Algebra Creating Equations Create equations that describe
numbers or relationship
equations, variables,
axes, quantities
A-
CED 2
R ODE Create equations in two or more variables
to represent relationships between
quantities; graph equations on coordinate
axes with labels and scale
1,2,3,4
Functions Interpreting Functions Interpret functions that arise in
applications in terms of the context
domain, quantiative F-IF.5 R ODE Relate the domain of a function to its
graph and, where applicable, to the
quantitative relationship it describes.
1,2,3,4
Functions Interpreting Functions Analyze functions using different
representations
roots, piecewise, step-
function, absolute
value
F-
IF.7b
M ODE Graph functions expressed
symbolically and show key features of
the graph, by hand in simple cases and
using technology for more complicated
cases. b. Graph square root, cube root,
and piecewise-defined functions, including
step functions and absolute value
functions
4
1
AP Calculus
Curriculum Map
Strand Domain Cluster Key Vocabulary
Co
re S
tan
dard
I/R
/M
OD
E /
TC
Grade Level
Specific Standard
Qu
art
er
Tau
gh
t
Functions Interpreting Functions Analyze functions using different
representations
polynomial, zeros,
factorizations
F-
IF.7c
M ODE Graph functions expressed
symbolically and show key features of
the graph, by hand in simple cases and
using technology for more complicated
cases. (c) Graph polynomial functions,
identifying zeros when suitable
factorizations are available, and showing
end behavior
3
Functions Interpreting Functions Analyze functions using different
representations
rational, zeros,
asymptotes
F-
IF.7d
M ODE (+) Graph functions expressed
symbolically and show key features of
the graph, by hand in simple cases and
using technology for more complicated
cases. (d) Graph rational functions,
identifying zeros and asymptotes when
suitable factorizations are available, and
showing end behavior.
3
Functions Interpreting Functions Analyze functions using different
representations
logarithmic,
exponential, intercepts,
end behavior, period,
midline, amplitutde
F-
IF.7e
M ODE Graph functions expressed
symbolically and show key features of
the graph, by hand in simple cases and
using technology for more complicated
cases. (e) Graph exponential and
logarithmic functions, showing intercepts
and end behavior, and trigonometric
functions, showing period, midline, and
amplitude.
1,2,3,4
Functions Interpreting Functions Analyze functions using different
representations
functions, equivalent F-IF 8 R ODE Write a function defined by an expression
in different but equivalent forms to reveal
and explain different properties of the
function
1,2,3,4
2
AP Calculus
Curriculum Map
Strand Domain Cluster Key Vocabulary
Co
re S
tan
dard
I/R
/M
OD
E /
TC
Grade Level
Specific Standard
Qu
art
er
Tau
gh
t
Functions Interpreting Functions Analyze functions using different
representations
functions, equivalent F-IF.9 M ODE Compre properties of two functions each
represented in a different way
(algebraically, graphincally, numberically
in tables, or by vertbal description)
1,2,3,4
Functions Linear and Exponential Models Construct and compare linear and
exponential modesl and solve
problems
linearlly, quadratically,
polynomial
F-
LE.3
M ODE Observe using graphs and tables that a
quantity increasing exponentially
eventually exceeds a quantity increasing
linearly, quadratically, or (more generally)
as a polynomial function.
1,2
Geometry Expressing Geometric Properties with
Equations
Using Coordinates to prove simple
geometric theorems algebraically
parallel and
perpendicular lines
G-
GPE 5
R ODE Prove the slope criteria for parallel and
perpendicular lines and use them to solve
geometric problems (e.g., find the
equation of a line parallel or perpendicular
to a given line that passes through a given
point).
1,2,3,4
Geometry Geometric Measurement and
Dimension
Explain volume formulas and use
them to solve problems
cylinder, pyramids,
cones, spheres
G-
GMD
3
R,
M
ODE Use volume formulas for cylinders,
pyramids, cones, and spheres to solve
problems
1,2
Geometry Geometric Measurement and
Dimension
Explain volume formulas and use
them to solve problems
cross sections G-
GMD
4
M ODE Identify the shapes of two-dimensional
cross-sections of three-dimensional
objects, and identify three-dimensional
objects generated by rotations of two-
dimensional objects.
3,4
*Additionally: AP Calculus will follow all standards set forth by the College Board for Calculus A/B. See AP Calculus Curriculum Word Document.
3
AP® Calculus AB - THS Page 1
AP®
Calculus AB Tippecanoe High School
Course Overview AP calculus AB is primarily concerned with developing understanding of the concepts of calculus and providing experience with methods and applications. The course has a multirepresentational approach that includes four types of expression: graphical, numerical, analytical, and verbal. Students are encouraged to use all representations with fluency between the four types. Importance is placed on verbal explanations since that reflects a true understanding of concepts. Students are required to use widely-accepted mathematical vocabulary and notation in their explanations. Conceptual themes, rather than memorization of formulas, are emphasized throughout the course. The course is approached as a coherent body of knowledge unified by the overlapping themes of limits, derivatives, and definite and indefinite integrals. Common themes reappear throughout the year. Modeling and application are also emphasized. Technology, specifically a graphing calculator, is used regularly and appropriately, but does not take precedence over intuitive understanding of concepts. AP Calculus AB is taught as a college-level course. Students should be attempting to earn college credit or advanced placement in calculus through the AP exam, a college placement exam, or any other method employed by the college.
Goals Upon completion of this course, students should be able to:
Work with functions represented in a variety of ways: graphically, numerically, analytically, and verbally. They should understand the connections among these types of representations.
Understand the meaning of the derivative in terms of a rate of change and local linear approximation. They should be able to use derivatives to solve a variety of problems.
Understand the meaning of the definite integral both as a limit of Riemann sums and as the net accumulation of change. They should be able to use integrals to solve a variety of problems.
Understand the relationship between the derivative and the definite integral as expressed in both parts of the Fundamental Theorem of Calculus.
Communicate mathematics and explain solutions to problems both verbally and in written sentences.
Model a written description of a physical situation with a function, a differential equation, or an integral.
AP® Calculus AB - THS Page 2
Use technology to help solve problems, experiment, interpret results, and support conclusions.
Determine the reasonableness of solutions, including sign, size, relative accuracy, and units of measurement.
Develop an appreciation of calculus as a coherent body of knowledge and as a great human accomplishment.
Materials Textbook (provided): A Single Variable Calculus Early Transcendental textbook will be provided. Calculator (required; as needed, a limited number of calculators will be available for students for short-term or long-term loan): Texas Instruments graphing calculator (TI-83+ or higher)
AP® Calculus AB - THS Page 3
AP®
Calculus AB Course Outline Topics labeled as “optional” may or may not be covered.
Functions and Models
The following topics are pre-requisites for incoming students. The schedule does not allow time for these topics to be taught in this course.
Topic Description
1. Four Ways to Represent a Function - Verbal, numeric, graphic, and symbolic representation of functions discussed - Domain and range of a function - Calculator approximations of values and functions - Piecewise functions - Using calculus to predict and to explain local and global behavior of a function
2. Mathematical Models: A Catalog of Essential Functions
- The modeling process: developing, analyzing, and interpreting a mathematical model - Classes of functions: linear, quadratic, rational, algebraic, trigonometric, exponential, and transcendental - Characteristics of each class of function
3. New Functions from Old Functions - Transformations on functions - The arithmetic of functions - Composing functions
4. Graphing Calculators - Finding roots with graphing calculators - Using graphing calculators to describe the behavior of functions - Appropriate viewing windows - Misleading or wrong answers given by graphing calculators
5. Exponential Functions - Algebraic and geometric properties of exponential functions - Translation and reflection of exponential functions - Exponential functions as models of growth and decay
6. Inverse Functions and Logarithms - Verbal, numeric, graphic, and algebraic representations of inverse functions - Algebraic and geometric properties of logarithmic functions
- The property of (-1(x)) = x
AP® Calculus AB - THS Page 4
Limits and Derivatives 4 weeks
Topic Description
1. The Tangent and Velocity Problems -Average vs instantaneous velocity described numerically, graphically, and in physical terms -The tangent line as the limit of secant lines -Using the graphing calculator to zoom in on a smooth function to show local linearity -Approximating the slope of the tangent line with slopes of secant lines
2. The Limit of a Function -An intuitive understanding of the limiting process -Estimating limits from graphs or tables of data -The advantages and disadvantages of geometrically or numerically computing a limit with a graphing calculator -Optional: the delta-epsilon definition of limit
3. Calculating Limits Using the Limit Laws -Calculating limits using algebraic methods -Examples where limits do not exist
4. Continuity -An intuitive understanding of continuity -Continuity defined in terms of limits -Intermediate Value Theorem -Examples of discontinuity: removable, jump, infinite, oscillating
5. Limits Involving Infinity -Understanding asymptotes in terms of graphical behavior -Describing asymptotic behavior in terms of limits involving infinity -Comparing relative magnitudes of functions and their rates of change (relative growth of polynomials, exponential functions, and logarithmic functions)
6. Tangents, Velocities, and Other Rates of Change
-Tangent line to a curve at a point -Instantaneous rate of change as the limit of average rate of change -Approximate rates of change from graphs and tables of values
7. Derivatives -The derivative represented geometrically, numerically, and algebraically -The derivative interpreted as an instantaneous rate of change
AP® Calculus AB - THS Page 5
-Derivative defined as the limit of the difference quotient -Equations involving derivatives: verbal descriptions are translated into equations involving derivatives, and vice versa
8. The Derivative as a Function -Relationship between differentiability and continuity -Slope of a curve at a point -The concept of a differentiable function, treated graphically, algebraically, and verbally,
including obtaining ’ by first considering the derivative at x, and then treating x as a variable
-Sketching the derivative of from the graph
of
9. What Does ’ Say About ? -Corresponding characteristics of the graphs of
and ’ -Relationship between increasing and
decreasing behavior of and the sign of ’ -Corresponding characteristics of the graphs of
, ’, and ’’
-Relationship between the concavity of and
the sign of ’’ -Instantaneous rate of change as the limit of average rate of change
Differentiation Rules 5 weeks
Topic Description
1. Derivatives of Polynomials -Power Rule for positive integer powers of x -Sum and Difference Rule
2. The Product and Quotient Rules -Product Rule -Quotient Rule
3. Rates of Change in the Natural and Social Sciences
-Interpretation of the derivative as a rate of change in varied applied contexts, including velocity, speed, and acceleration -Equations involving derivatives: verbal descriptions are translated into equations involving derivatives, and vice versa
4. Derivatives of Trigonometric Functions -Derivatives of trigonometric functions
5. The Chain Rule -Chain rule
6. Implicit Differentiation -Implicit functions and implicit curves
AP® Calculus AB - THS Page 6
-Implicit differentiation -Implicit differentiation to find the derivative of an inverse function -Derivatives of inverse trigonometric functions
7. Derivatives of Exponential and Logarithmic Functions
-The definition of e
-Derivatives of exponential and logarithmic functions -Logarithmic differentiation
8. Linear Approximations and Differentials
-Tangent line to a curve and local linear approximation
Optional: Taylor Polynomials -Taylor and Maclaurin polynomials
Applications of Differentiation 4 weeks
Topic Description
1. Related Rates -Modeling rates of change with related rate problems -Solution strategy for related rate problems
2. Maximum and Minimum Values of a Function
-Extreme Value Theorem: the graphical interpretation -Fermat’s Theorem -Critical values -Finding extreme values of a function on open and closed intervals
3. Derivatives and the Shapes of Curves -Corresponding characteristics of the graphs of
and ’ -Relationship between increasing and
decreasing behavior of and the sign of ’ -Mean Value Theorem and its geometric consequences -Corresponding characteristics of the graphs of
, ’, and ’’
-Relationship between the concavity of and
the sign of ’’ -Points of inflection -Analysis of curves, including the notions of monotonicity and concavity
4. Optimization Problems -Optimization, both absolute and relative extrema -Solution strategy for optimization problems -Checking results graphically with a graphing calculator
AP® Calculus AB - THS Page 7
5. Applications to Business and Economics
-Concepts from economics: marginals, demand function, revenue function, average cost -The marginal as a derivative
6. Antiderivatives -Antiderivatives from derivatives of basic functions -Slope or direction fields -Initial value and boundary value problems -Position, velocity, and acceleration
Integrals 5 weeks
Topic Description
1. Areas and Distances -The area problem: the difficulty in finding area under a curve -Computation of Riemann sums using left, right, and midpoint evaluation points -Riemann sums used to model physical, social, and economic situations
2. The Definite Integral -Computation of Riemann sums using left, right, and midpoint evaluation points -The definite integral as a limit of Riemann sums over subintervals -The definite integral as the net results of accumulation of a rate of change -Basic properties of definite integrals -Use of Riemann sums to approximate definite integrals of functions represented algebraically, geometrically, and numerically -The geometric and comparison properties of definite integrals developed as statements about area
3. Evaluating Definite Integrals -The definite integral of the rate of change of a quantity over an interval interpreted as the net change of the quantity over the interval -Using the definite integral of a rate of change to give accumulated change: area of a region, distance traveled by a particle on a line -Antiderivatives of basic functions -The definite integral as the difference of the values of the antiderivative of the integrand at the limits of integration
4. The Fundamental Theorem of Calculus -The definite integral of the rate of change of
AP® Calculus AB - THS Page 8
a quantity over an interval interpreted as the net change of the quantity over the interval -Use of the Fundamental Theorem to evaluate definite integrals -Use of the Fundamental Theorem to represent a particular antiderivative, and the analytical and graphical analysis of functions so defined -Indefinite integrals
5. The Substitution Rule -Substitution Rule interpreted in terms of the Chain Rule -Antiderivatives by substitution of variables -Using substitution to evaluate definite integrals
6. (optional) Integration by Parts -Integration by Parts interpreted in terms of the Product Rule -Choosing u and dv
7. Approximate Integration -Riemann sums using left, right, and midpoint evaluation points revisited -Trapezoidal Rule -Optional: Simpson’s Rule
Applications of Integration 3 weeks
Topic Description
1. More About Areas -Finding the area between curves with definite integrals -When it is advantageous to integrate with respect to y instead of with respect to x
2. Volumes -Finding the volume of a solid with known cross-sections -Finding the volume of a solid of revolution using washers
3. Average Value of a Function -Finding the average value of a function -Geometric interpretation of the Mean Value Theorem for Integrals
4. Applications to Physics and Engineering -Work -Hydrostatic pressure -Centers of mass
5. Applications to Economics and Biology -Blood flow -Cardiac output -Consumer surplus
Optional Topic: Probability -Probability density functions
AP® Calculus AB - THS Page 9
-Algebraic and geometric definitions of a mean -The normal distribution
Differential Equations 4 weeks
Topic Description
1. Modeling with Differential Equations -Differential equations: verbal descriptions are translated into equations involving derivatives, and vice versa -General and particular solutions to differential equations -Initial value and boundary value problems
2. Slope fields -Interpreting slope or direction fields -Autonomous differential equations -Qualitative analysis of differential equations
3. Separable Equations -Solving separable differential equations and using them in modeling
4. Exponential Growth and Decay -The equation y’ = ky and exponential growth
5. The Logistic Equation -Logistic vs. unconstrained exponential growth -Interpreting the slope field of the logistic equation -The analytic solution of the logistic equation
Post-AP Exam 3 weeks (additional optional topics)
Topic Description
1. Partial Fractions -Using the method of partial fractions to evaluate integrals
2. Trigonometric Substitution -Using trigonometric substitution to evaluate integrals
3. Integrands with Powers of Sine and Cosine
-Integration of powers of the sine and cosine functions
4. Derivatives Project -Roller coaster development using continuity and differentiation for “smoothness”
5. Integration Project -Integrating acceleration curves from crash testing to develop appropriate velocity functions – focus on approximation techniques of integration (Riemann sums)
This schedule leaves a few weeks for flexibility if more time is required for students to better understand particular topics. It also allows time for cumulative review and to administer practice AP exams
AP Statistics
Curriculum Map
Strand Domain Cluster Key Vocabulary
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Grade Level
Specific Standard
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Algebra Seeing the structure of expressions Write expressions in equivalent forms
to solve problems
geometric series A-
SSE 4
M ODE Derive the formula for the sum of a finite
geometric series (when the common ratio
is not 1), and use the formula to solve
problems
1,2,3,4
Statistics and
Probability
Interpreting Categorical and
Quantitative Data
Summarize, represent, and interpret
data on a single count or
measurement variable
dot plots, histograms,
box plots
S-ID 1 M ODE Represent data with plots on the real
number line (dot plots, histograms, and
box plots).
1,2,3,4
Statistics and
Probability
Interpreting Categorical and
Quantitative Data
Summarize, represent, and interpret
data on a single count or
measurement variable
mean, median,
interquartile range,
standard deviation
S-ID 2 M ODE Use statistics appropriate to the shape of
the data distribution to compare center
(median, mean) and spread (interquartile
range, standard deviation) of two or more
different data sets.
1,2,3,4
Statistics and
Probability
Interpreting Categorical and
Quantitative Data
Summarize, represent, and interpret
data on a single count or
measurement variable
outliers S-ID 3 M ODE Interpret differences in shape, center, and
spread in the context of the data sets,
accounting for possible effects of extreme
data points (outliers).
1,2,3,4
Statistics and
Probability
Interpreting Categorical and
Quantitative Data
Summarize, represent, and interpret
data on a single count or
measurement variable
population percentages S-ID 4 I ODE Use the mean and standard deviation of a
data set to fit it to a normal distribution
and to estimate population percentages.
Recognize that there are data sets for
which such a procedure is not
appropriate. Use calculators,
spreadsheets, and tables to estimate
areas under the normal curve.
1,2,3,4
1
AP Statistics
Curriculum Map
Strand Domain Cluster Key Vocabulary
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Grade Level
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Statistics and
Probability
Interpreting Categorical and
Quantitative Data
Summarize, represent, and interpret
data on two categorical and
quantitative variables
frequency tables S-ID 5 I ODE Summarize categorical data for two
categories in two-way frequency tables.
Interpret relative frequencies in the
context of the data (including joint,
marginal, and conditional relative
frequencies). Recognize possible
associations and trends in the data.
1,2,3,4
Statistics and
Probability
Interpreting Categorical and
Quantitative Data
Summarize, represent, and interpret
data on two categorical and
quantitative variables
scatter plot S-ID
6a
R ODE Represent data on two quantitative
variables on a scatter plot, and
describe how the variables are related.
a. Fit a function to the data; use functions
fitted to data to solve problems in the
context of the data. Use given functions or
choose a function suggested by the
context. Emphasize linear, quadratic, and
exponential models.
1,2,3,4
Statistics and
Probability
Interpreting Categorical and
Quantitative Data
Summarize, represent, and interpret
data on two categorical and
quantitative variables
scatter plot S-ID
6b
I ODE Represent data on two quantitative
variables on a scatter plot, and
describe how the variables are related.
b. Informally assess the fit of a function by
plotting and analyzing residuals.
1,2,3,4
2
AP Statistics
Curriculum Map
Strand Domain Cluster Key Vocabulary
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/M
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Grade Level
Specific Standard
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Statistics and
Probability
Interpreting Categorical and
Quantitative Data
Summarize, represent, and interpret
data on two categorical and
quantitative variables
scatter plot S-ID
6c
M ODE Represent data on two quantitative
variables on a scatter plot, and
describe how the variables are related.
c. Fit a linear function for a scatter plot
that suggests a linear association.
1,2,3,4
Statistics and
Probability
Interpreting Categorical and
Quantitative Data
Interpret Linear Models slope, intercept S-ID 7 M ODE Interpret the slope (rate of change) and
the intercept (constant term) of a linear
model in the context of the data.
1,2,3,4
Statistics and
Probability
Interpreting Categorical and
Quantitative Data
Interpret Linear Models correclation coefficient S-ID 8 M ODE Compute (using technology) and interpret
the correlation coefficient of a linear fit.
1,2,3,4
Statistics and
Probability
Interpreting Categorical and
Quantitative Data
Interpret Linear Models correlation and
causation
S-ID 9 I ODE Distinguish between correlation and
causation.
1,2,3,4
Statistics and
Probability
Making Inferences and Justifying
Conclusions
Understand and evaluate random
processes underlying statistical
experiments
population parameters,
random sample
S-IC 1 I ODE Understand statistics as a process for
making inferences about population
parameters based on a random sample
from that population.
1,2,3,4
Statistics and
Probability
Making Inferences and Justifying
Conclusions
Understand and evaluate random
processes underlying statistical
experiments
simulation S-IC 2 R ODE Decide if a specified model is consistent
with results from a given data-generating
process, e.g., using simulation. For
example, a model says a spinning coin
falls heads up with probability 0.5. Would
a result of 5 tails in a row cause you to
question the model?
1,2,3,4
3
AP Statistics
Curriculum Map
Strand Domain Cluster Key Vocabulary
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Grade Level
Specific Standard
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Statistics and
Probability
Making Inferences and Justifying
Conclusions
Make inferences and justify
conclusions from sample surveys,
experiments, and observational
studies
sample survey,
experiments,
observational studies,
randomization
S-IC 3 I ODE Recognize the purposes of and
differences among sample surveys,
experiments, and observational studies;
explain how randomization relates to
each.
1,2,3,4
Statistics and
Probability
Making Inferences and Justifying
Conclusions
Make inferences and justify
conclusions from sample surveys,
experiments, and observational
studies
survey, mean,
proportion, margin of
error
S-IC 4 I ODE Use data from a sample survey to
estimate a population mean or proportion;
develop a margin of error through the use
of simulation models for random
sampling.
1,2,3,4
Statistics and
Probability
Making Inferences and Justifying
Conclusions
Make inferences and justify
conclusions from sample surveys,
experiments, and observational
studies
parameters S-IC 5 I ODE Use data from a randomized experiment
to compare two treatments; use
simulations to decide if differences
between parameters are significant.
1,2,3,4
Statistics and
Probability
Making Inferences and Justifying
Conclusions
Make inferences and justify
conclusions from sample surveys,
experiments, and observational
studies
data S-IC 6 I ODE Evaluate reports based on data. 1,2,3,4
Statistics and
Probability
Conditional Probability and the Rules
of Probability
Understand independence and
conditional probabilty and use them to
interpret data
subsets, sample
space, outcome, union,
intersection,
complements
S-CP
1
I ODE Describe events as subsets of a sample
space (the set of outcomes) using
characteristics (or categories) of the
outcomes, or as unions, intersections, or
complements of other events (“or,” “and,”
“not”).
1,2,3,4
Statistics and
Probability
Conditional Probability and the Rules
of Probability
Understand independence and
conditional probabilty and use them to
interpret data
independent S-CP
2
I ODE Understand that two events A and B are
independent if the probability of A and B
occurring together is the product of their
probabilities, and use this characterization
to determine if they are independent
1,2,3,4
4
AP Statistics
Curriculum Map
Strand Domain Cluster Key Vocabulary
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Grade Level
Specific Standard
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Statistics and
Probability
Conditional Probability and the Rules
of Probability
Understand independence and
conditional probabilty and use them to
interpret data
conditional probability S-CP
3
R ODE Understand the conditional probability of A
given B as P(A and B)/P(B), and interpret
independence of A and B as saying that
the conditional probability of A given B is
the same as the probability of A, and the
conditional probability of B given A is the
same as the probability of B.
1,2,3,4
Statistics and
Probability
Conditional Probability and the Rules
of Probability
Understand independence and
conditional probabilty and use them to
interpret data
frequency tables,
conditional probability
S-CP
4
I ODE Construct and interpret two-way
frequency tables of data when two
categories are associated with each
object being classified. Use the two-way
table as a sample space to decide if
events are independent and to
approximate conditional probabilities.
1,2,3,4
Statistics and
Probability
Conditional Probability and the Rules
of Probability
Understand independence and
conditional probabilty and use them to
interpret data
conditional probability,
independence
S-CP
5
I ODE Recognize and explain the concepts of
conditional probability and independence
in everyday language and everyday
situations.
1,2,3,4
Statistics and
Probability
Conditional Probability and the Rules
of Probability
Use the rules of probability to
compute probabilities of compound
events in a uniform probability model
conditional probability,
outcomes
S-CP
6
I ODE Find the conditional probability of A given
B as the fraction of B’s outcomes that also
belong to A, and interpret the answer in
terms of the model.
1,2,3,4
Statistics and
Probability
Conditional Probability and the Rules
of Probability
Use the rules of probability to
compute probabilities of compound
events in a uniform probability model
addition rule S-CP
7
I ODE Apply the Addition Rule, P(A or B) = P(A)
+ P(B) – P(A and B), and interpret the
answer in terms of the model.
1,2,3,4
5
AP Statistics
Curriculum Map
Strand Domain Cluster Key Vocabulary
Co
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I/R
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TC
Grade Level
Specific Standard
Qu
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Statistics and
Probability
Conditional Probability and the Rules
of Probability
Use the rules of probability to
compute probabilities of compound
events in a uniform probability model
multiplication rule S-CP
8
I ODE (+) Apply the general Multiplication Rule in a
uniform probability model, P(A and B) =
P(A)P(B|A) = P(B)P(A|B), and interpret the
answer in terms of the model.
1,2,3,4
Statistics and
Probability
Conditional Probability and the Rules
of Probability
Use the rules of probability to
compute probabilities of compound
events in a uniform probability model
permutations and
combinations
S-CP
9
R ODE (+) Use permutations and combinations to
compute probabilities of compound events
and solve problems.
1,2,3,4
Statistics and
Probability
Using Probability to Make Decisions Calculate expected values and use
them to solve problems
random variable, data
distributions
S-MD
1
I ODE (+) Define a random variable for a quantity of
interest by assigning a numerical value to
each event in a sample space; graph the
corresponding probability distribution
using the same graphical displays as for
data distributions.
1,2,3,4
Statistics and
Probability
Using Probability to Make Decisions Calculate expected values and use
them to solve problems
expected value S-MD
2
I ODE (+) Calculate the expected value of a random
variable; interpret it as the mean of the
probability distribution.
1,2,3,4
Statistics and
Probability
Using Probability to Make Decisions Calculate expected values and use
them to solve problems
probability distribution S-MD
3
I ODE (+) Develop a probability distribution for a
random variable defined for a sample
space in which theoretical probabilities
can be calculated; find the expected value
1,2,3,4
Statistics and
Probability
Using Probability to Make Decisions Calculate expected values and use
them to solve problems
probability distribution S-MD
4
I ODE (+) Develop a probability distribution for a
random variable defined for a sample
space in which probabilities are assigned
empirically; find the expected value.
1,2,3,4
6
AP Statistics
Curriculum Map
Strand Domain Cluster Key Vocabulary
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Grade Level
Specific Standard
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Statistics and
Probability
Using Probability to Make Decisions Use probability to evaluate outcomes
of decisions
payoff values,
expected values
S-MD
5a
I ODE (+) Weigh the possible outcomes of a
decision by assigning probabilities to
payoff values and finding expected
values.
a. Find the expected payoff for a game of
chance. For example, find the expected
winnings from a state lottery ticket or a
game at a fast-food restaurant.
1,2,3,4
Statistics and
Probability
Using Probability to Make Decisions Use probability to evaluate outcomes
of decisions
payoff values,
expected values
S-MD
5b
I ODE (+) Weigh the possible outcomes of a
decision by assigning probabilities to
payoff values and finding expected
values.
b. Evaluate and compare strategies on the
basis of expected values. For example,
compare a high-deductible versus a low-
deductible automobile insurance policy
using various, but reasonable, chances of
having a minor or a major accident.
1,2,3,4
Statistics and
Probability
Using Probability to Make Decisions Use probability to evaluate outcomes
of decisions
decisions S-MD
6
R ODE (+) Use probabilities to make fair decisions
(e.g., drawing by lots, using a random
number generator).
1,2,3,4
Statistics and
Probability
Using Probability to Make Decisions Use probability to evaluate outcomes
of decisions
probability concepts S-MD
7
I ODE (+) Analyze decisions and strategies using
probability concepts (e.g., product testing,
medical testing, pulling a hockey goalie at
the end of a game).
1,2,3,4
AP Statistics will also follow all standards set by College Board. See AP Statistics word document.
7
AP STATISTICS SYLLABUS
PRIMARY TEXTBOOK
Weiss, Neil A. Introductory Statistics. 7th
edition. New York: Pearson
Education, Inc., 2005.
OTHER SOURCES
Sternstein, Martin. How To Prepare For The AP Statistics Advanced Placement
Examination. 2nd
edition. New York: Barron’s Educational Series, Inc., 2000.
Mulekar, Madhuri S. Cracking The AP Statistics Exam. New York: Princeton Review
Publishing, L.L.C., 2004.
Discovery Channel Schools. Understanding Probability and Odds. 27-min. Bethesda,
Maryland: Discovery Communications, Inc. Videocassette 2001.
COURSE DESIGN
This fast-paced Statistics AP course is not dominated by lecture but rather by student
exploration and classroom discussion. Students are able to work in groups to complete
any multitude of tasks. Facilitating discussion and learning as it pertains to statistical
analysis is the main goal of the course. Making connections from the initial design to the
proper analysis and to the conclusion is vital. There is an emphasis on communicating,
orally and written, complete responses throughout the statistical process.
The teaching materials for the course come from textbooks, newspapers, journal writings,
videos, the internet, and some lectures. Each student is provided a formula card and set
of tables that will be needed for the entire year long course. These tables and formulas
are allowed on all activities assigned. Further each student is required to have a TI-83+
calculator to help complete assignments. Minitab is on the seven computers in the
classroom. These computers along with the media center computers, allow the students
to see the benefit in technology within the statistical field. Quick results help them avoid
many tedious calculations as they learn to interpret output from this technology of the TI-
83+, Minitab, and excel. Student assignments vary from reading text, journal responses,
statistical articles, quizzes, tests, various activities, two major projects, and general
homework.
COURSE OUTLINE
The topics are introduced by chapter from primary textbook. Activities are listed below
the topics for a given chapter. Each chapter concludes with a test and a quiz
approximately midway through the material of the chapter. These 16 chapters are
followed by approximately 2 weeks of all AP practice in class. Previously released
extended response questions from prior years are provided from AP site and multiple
choice is practiced from other sources listed above (Sternstein and Mulekar). We
practice the scoring rubric process and strategy on multiple choice. The two projects take
place during the 4th
quarter, the first being while we are preparing directly for the AP
exam and the second after the exam until the end of the year. Project description can be
found at end of course outline. Each chapter below estimates the number of days to
complete including evaluation. Further it shows what major items from the AP Topic
Outline are covered in that particular chapter. Incorporation of TI-83+ (dominant
technology used in class) is indicated, but not limited to, next to topics within course
outline by (TI).
CHAPTER 1
NATURE OF STATISTICS (8 days)
TOPICS
AP STATISTICS COURSE TOPIC
OUTLINE
- differentiating between descriptive and
inferential statistics
- acquiring information various ways;
census, sampling, or experimentation
- representative samples
- simple and systematic random sampling
- cluster sampling
- stratified sampling with proportional
allocation
- observational study
- designed experiment
- principles of experimental design
- completely randomized design and
randomized block design
Activity: Summarize and present briefly
over 3 provided articles
Activity: Designing surveys; each student
presents 1 good and 1 bad survey; class is
then evaluated on identifying each
- IIA overview of methods of data
collection #’s 1, 2, 3, 4
- IIB planning and conducting surveys
#’s 1, 2, 3, 4
- IIC planning and conducting
experiments #’s 1, 2, 3, 4, 5
- IID generalization and types of
conclusions to draw from data
collection
CHAPTER 2
ORGANIZING DATA (8 days)
TOPICS AP STATISTICS COURSE TOPIC
OUTLINE
- differentiating among qualitative and
quantitative variables/data
- differentiating between continuous and
discrete variables/data
- organizing data by single values and
grouped data tables
- organizing with histograms, dotplots, pie
charts, bar graphs, and stem and leaf plots
(TI)
- classification of distribution shapes
- symmetry
- skewness
- misleading graphs
Activity: Find and summarize article with
statistics (graphs) that are misleading
- IA constructing & interpreting
graphical displays of univariate data
#’s 1, 2, 4
- IE exploring categorical data #’s 1, 4
CHAPTER 3
DESCRIPTIVE MEASURES (7 days)
TOPICS AP STATISTICS COURSE TOPIC
OUTLINE
- selecting the most appropriate measure of
central tendency
- measures of variation; sample standard
deviation, sample variance, and range
(TI)
- intro to Empirical Rule and Chebychev’s
Rule
- boxplots and intro into percentiles
- determining possible outliers using
interquartile range
- parameters vs. statistics
- standardizing the data; z-scores (TI)
Activity: Construct a box plot and
analyze for the 40 wealthiest people in
the world
- IB summarizing distributions of
univariate data #’s 1, 2, 3, 4
CHAPTER 4
PROBABILITY, RANDOM VARIABLES,
AND SAMPLING DISTRIBUTIONS (12 days)
TOPICS AP STATISTICS COURSE TOPIC
OUTLINE
- definition of probability
- frequentist interpretation of probability
- sample space and events along with Venn
diagrams
- mutually excusive events
- general addition and complementation
rule
- contingency tables and conditional
probability
- independent and dependent events
- multiplication rule
- differentiate between independent and
mutually exclusive events
- Bayes’s Rule with exhaustive events
- basic counting rule and tree diagrams
- combination and permutation (TI)
Activity: Probability of winning various
lotteries across the US; where is your
best chance?
Activity: Video on probability and odds
- IE exploring categorical data #’s 2, 3
- IIIA probability #’s 1, 3
CHAPTER 5
DISCRETE RANDOM VARIABLES (7 days)
TOPICS AP STATISTICS COURSE TOPIC
OUTLINE
- discrete random variables
- sum of the probabilities of discrete
random variable
- interpreting probability distributions
- mean (expected value) and standard
deviation of a discrete random variable
- Bernoulli Trials
- binomial distribution (TI)
- mean and standard deviation of a
binomial distribution
- geometric and hypergeometric
distributions
- Poisson distribution (TI)
- mean and standard deviation of a Poisson
- IIIA probability #’s 2, 4, 6
random variable
Activity: Simulation of rolling dice and
constructing various distribution graphs
(TI)
Activity: Finding expected values of
various casino games
CHAPTER 6
NORMAL DISTRIBUTION (8 days)
TOPICS AP STATISTICS COURSE TOPIC
OUTLINE
- normal distribution vs. approximately
normal distributions
- standard normal curve and area tables
- finding percentiles
- using a normal probability plot to assess
normality (TI)
- intro to finding binomial probability by
using normal curve and a correction for
continuity
Activity: Are the color of Skittles
normally distributed?
- IIIC the normal distribution #’s 1, 2, 3
CHAPTER 7
SAMPLING DISTRIBUTION OF THE SAMPLE MEAN (6 days)
TOPICS AP STATISTICS COURSE TOPIC
OUTLINE
- sampling error
- sampling distribution of the sample mean
- relationship between sampling error and
sample size
- mean of all samples of a given sample
size equals the population mean
- standard deviation of the variable sample
mean
- sampling distribution of a sample mean
for a normally distributed variable
- central limit theorem
Activity: Simulation with GRE scores;
what does all samples of a particular size
equal? (TI)
- IIID sampling distributions #’s 2, 3
CHAPTER 8
CONFIDENCE INTERVALS FOR ONE POPULATION MEAN (6 days)
TOPICS AP STATISTICS COURSE TOPIC
OUTLINE
- using sample mean to estimate parameter,
population mean
- confidence intervals and levels
- deciding when to use one-sample z-
interval procedure
- relationship between confidence level,
interval length, and precision
- margin of error
- determining a sample size based upon
given confidence level and max error
allowed
- t-distributions and t-curves
- applying t-distributions; one sample t-
interval procedure
Activity: What does it mean to be 90%,
95%, and 99% confident?
- IIID sampling distributions # 7
- IVA estimation with point estimators
and confidence intervals #’s 1, 2, 3, 4,
and 6
CHAPTER 9
HYPOTHESIS TESTS FOR ONE POPULATION (11days)
TOPICS AP STATISTICS COURSE TOPIC
OUTLINE
- intro to hypothesis testing (TI)
- types of error associated with hypothesis
testing
- using critical values
- finding probability of type I error
- finding probability of type II error
(provide assumed true mean)
- power of a hypothesis test
- determine the relationship between
hypothesis test and confidence intervals
- relationship between sample size and
power
- using p-values (TI)
- compare parametric methods to non-
parametric methods
- intro to first non-parametric method;
Wilcoxon Signed-Rank Test
* Activity: Response to article “Freshman
15” and possible hypothesis test to use
- IVB test of significance # 1
CHAPTER 10
INFERENCES FOR TWO POPULATION MEANS (9 days)
TOPICS AP STATISTICS COURSE TOPIC
OUTLINE
- sampling distribution of the difference
between sample means of independent
samples
- pooled t-test and t-interval (TI)
- nonpooled t-test and nonpooled t-interval
(TI)
- non-parametric method; Mann Whitney
Test
- making inferences for two populations
given paired samples
- paired t-test and paired t-interval (TI)
- non-parametric method; Paired Wilcoxon
Signed-Rank Test
- IVA estimation with point estimators
and confidence intervals # 7
- IVB tests of significance # 5
CHAPTER 11
INFERENCES FOR POPULATION STANDARD DEVIATIONS (4 days)
TOPICS AP STATISTICS COURSE TOPIC
OUTLINE
- chi-square distributions
- hypothesis test for a population standard
deviations (TI)
- chi-square test and chi-square interval
(TI)
- f-distributions
- hypothesis test for two population
standard deviations
- f-test and f-interval
- IIID sampling distributions # 8
CHAPTER 12
INFERENCES FOR POPULATION PROPORTIONS (5 days)
TOPICS AP STATISTICS COURSE TOPIC
OUTLINE
- confidence intervals for one population
proportion (TI)
- one sample z test and z interval for
population proportion (TI)
- finding sample size given constraints of
confidence level and max error
- hypothesis test for one and two
population proportions
- IIID sampling distributions # 1
- IVA estimation with point estimators
and confidence intervals #’s 4, 5
- IVB tests of significance #’s 2, 3
CHAPTER 13
CHI-SQUARE PROCEDURES (6 days)
TOPICS AP STATISTICS COURSE TOPIC
OUTLINE
- chi-square goodness-of-fit-test
- chi-square independence test for
univariate and bivariate data (two way
tables) (TI)
- using chi-square to check for association
between two variables
Activity: Colors of M & M’s
- IID generalization of results and
viable conclusions from data
collection
- IVB tests of significance # 6
CHAPTER 14
DESCRIPTIVE METHODS IN REGRESSION AND CORRELATION (8 days)
TOPICS AP STATISTICS COURSE TOPIC
OUTLINE
- regression equation produced from
scatter plot (TI)
- predictor variable and response variable
- extrapolation
- coefficient of determination
- regression identity
- linear correlation coefficient
- interpreting r and r-squared
Activity: Predicting ACT scores from
SAT scores
- ID exploring bivariate data #’s 1, 2, 3,
4
CHAPTER 15
INFERENTIAL METHODS IN REGRESSION AND CORRELATION (7 days)
TOPICS AP STATISTICS COURSE TOPIC
OUTLINE
- estimating regression parameters
- analysis of residuals
- regression hypothesis t-test to check
usefulness of regression equation to make
predictions
- correlation test for normality
- IVA estimation with point estimators
and confidence intervals # 8
- IVB tests of significance # 7
CHAPTER 16
ANALYSIS OF VARIANCE (8 days)
TOPICS AP STATISTICS COURSE TOPIC
OUTLINE
- analysis of variance using ANOVA
- multiple comparison method using Tukey
- non-parametric method of Kruskal-Wallis
- extra material; not applicable to AP
exam
The following is the project description/outline provided to students for both major
projects. The first project comes during the review time for the AP exam. The second
project follows after the AP exam is taken in the first week in May.
STATISTICS PROJECT
Project (125 points)
Due:
Topic: Student may pick any topic of interest for project
The project will include the following:
1. Oral Report: approximately 7-10 minutes in length describing the important
aspects of the study (25 pts)
*must have visual representation of information within study
*must involve the class
*hit all key ideas from report, Meat and Potatoes, talk statistics (vocab)
*question at hand, objective of study
*how was data collected and analyzed
*conclusion
*possible bias involved
*how could study be improved
2. Written Report: Typed with no minimum length (20 pts/section)
a. List of Data Collection
b. Description of the method of analysis with assumptions
c. Relevant graphs and/or statistics
d. Statement of conclusions
e. Reasons why the results might not be correct, along with a description of
ways in which the study could be improved, given sufficient time and
money. Incorporate research from the internet dealing with your study
that supports or does not support your data.
*Written Report must have all the information.
*Oral Report – visual representation must be seen by all
*You can collect your own data through experiments or observational studies. It is
absolutely essential to analyze the method used to collect the data, because data
carelessly collected may become completely useless. Look carefully for bias in the way
data are collected. Many procedures are based upon one working with a simple random
sample, meaning every possible sample of the same size has the same chance of being
selected. If a sample is self-selected (voluntary response), it is worthless for making
inferences about a population.
*Consider each of the following if it applies:
Center: mean and median
Variation: range and standard deviation
Distribution: a graph showing the distribution of the data
Outliers: explain if applicable
Time: is the population stable or is changing over time
*Inferences: Estimating Parameters and Hypothesis Testing. Be sure to use your
textbook when deciding which procedure to use when analyzing the data.