Page 1
Curriculum Pacing Guide
6th grade
2011 - 2012
First Nine Weeks at a Glance:
• SOL 6.15 Measures of central
tendency
• SOL 6.14 Graphing data and
data analysis
• SOL 6.17 Geometric and
arithmetic sequences
• SOL 6.19 Properties of real
numbers
• SOL 6.16 Probability
Second Nine Weeks at a Glance:
• SOL 6.18 Linear equations
• SOL 6.20 Graphing inequalities
• SOL 6.11 Coordinate Planes
• SOL 6.10c Area and Perimeter
• SOL 6.10 d Volume and Surface
area
• SOL 6.10 a, b Circumference and
area of circle
Third Nine Weeks at a Glance:
• SOL 6.9 Customary and Metric
measurement systems
• SOL 6.2 Fractions, decimals,
percents
• SOL 6.1 Ratios
• SOL 6.4 Number sense: Fractions
• SOL 6.6 Problem solving
Fractions
• SOL 6.7 Problem solving
decimals
• SOL 6.3 Integers
• SOL 6.5 Positive exponents and
perfect squares (*Scientific
notation)
Fourth Nine Weeks at a Glance:
• SOL 6.8 Order of operations
• SOL 6.12 Congruence and
similarities
• SOL 6.13 Properties of
Quadrilaterals
Time Strand, Big Idea, & Student Objectives
Essential Knowledge, Skills, Processes
Instructional Strategies and Model Lessons Assessment Items
Quarter
1
Week 1
Pretesting of Grade 6 SOLs, Fact Drills, Basic computation skills Instructional Strategies:
• Teach students to add, subtract, multiply, and divide whole numbers
• Drill students on addition, subtraction, multiplication, and division facts
(Continue throughout the year to give children several chances to
master facts).
Resources:
Glencoe Course 1: Prerequisite skills
Virginia SOL Mathematics Coach Grade 6 Pretest
Virginia SOL Mathematics Coach Grade 6
Pretest, Pretest of Math Facts
Quarter
1 Week
2
Probability and Statistics
SOL 6.15
The student will
a) describe mean as balance point; and
b) decide which measure of center is appropriate for a given
purpose.
Essential Understandings
• What does the phrase “measure of center” mean?
This is a collective term for the 3 types of averages for a set of data – mean,
Instructional Strategies:
• Review of division (concept and method) will be helpful prior to teaching
mean.
• Have students keep track of their grades on tests, quizzes, and
homework. Have them find the mean, median, mode, and range of the
data. Have the students look for trends in their grades.
• Pass around a bucket of color cubes and have each student pick one.
Students, who have a particular color cube, are asked to link their cubes
together. In order for the students to count the number o cubes, of each
color, place the columns of cubes on a desk. Next, the students organize
Open response:
Explain how to find the median of a set
of
data that has an even number of data in
the set. List six numbers such that the
mean is 14, the median is 14, the modes
are 12 and 14, and the range is 5.
Describe a real-life situation in which the
mean is lower than the median.
Writing prompts:
Explain how to find the median of a set
of
Page 2
Curriculum Pacing Guide
6th grade
2011 - 2012 median, and mode.
• What is meant by mean as balance point? Mean can be defined as the
point on a number line where the data distribution is balanced. This
means that the sum of the distances from the mean of all the points above
the mean is equal to the sum of the distances of all the data points below
the mean. This is the concept of mean as the balance point.
• Understand that measures of central tendency are types of averages for a
set of data.
• Understand that mean, median, and mode are measures of central
tendency that are useful for describing data in different situations.
• Understand that the range indicates how data is spread out or dispersed.
• Understand and appropriately use measures of central tendency for a data
set.
Essential Knowledge and Skills
• Find the mean for a set of data.
• Describe the three measures of center and a situation in which each
would best represent a set of data.
• Identify and draw a number line that demonstrates the concept of mean
as balance point for a set of data.
• Solve problems by finding the mean of a set of no more than 20 numbers.
• Solve problems by finding the median of a set of data of no more than 20
numbers when the numbers are arranged from least to greatest, including
data sets that have one middle number and data sets that have two
middle numbers.
• Solve problems by finding the mode of a set of data of no more than 20
numbers.
• Identify the mode in a set of data, given that there may be one, more than
one, or no mode.
• Examine the range to understand spread or dispersion of the data.
• Solve problems by finding the range of a set of data of no more than 20
numbers.
the data in a table and determine the mean, median, mode, and range
of the data.
• Have students use real-life data from various sources and then
determine the mean, median, mode, and range of the data.
• Students collect the scores for their favorite team or player in ten games
and find the average score, mode, and the median.
Model Lessons:
Enhanced Scope and Sequence, Grade 6
“Balancing Act,”
Resources:
Course 1: 2-6, 2-7
Glencoe Teacher ‘s Resource Kit
Understanding Math
Virginia SOL Mathematics Coach Grade 6
data that has an even number of data in
the set.
Explain how you can use a stem-and-leaf
plot to determine the median of a set of
data.
SOL-like Multiple Choice:
VDOE Released SOL items (6.15)
Pretests, Posttest, Formative
assessments, Bellwork, Classwork, and
Homework
Page 3
Curriculum Pacing Guide
6th grade
2011 - 2012
Teacher Notes
• Measures of center are types of averages for a data set. They represent
numbers that describe a data set. Mean, median, and mode are measures
of center that are useful for describing the average for different situations.
– Mean works well for sets of data with no very high or low numbers.
– Median is a good choice when data sets have a couple of values
much higher or lower than most of the others.
– Mode is a good descriptor to use when the set of data has some
identical values or when data are not conducive to computation
of other measures of central tendency, as when working with
data in a yes or no survey.
• The mean is the numerical average of the data set and is found by adding
the numbers in the data set together and dividing the sum by the number
of data pieces in the set.
• In grade 5 mathematics, mean is defined as fair- share.
• Mean can be defined as the point on a number line where the data
distribution is balanced. This means that the sum of the distances from
the mean of all the points above the mean is equal to the sum of the
distances of all the data points below the mean. This is the concept of
mean as the balance point.
• Defining mean as balance point is a prerequisite for understanding
standard deviation.
• The range is the difference between the greatest and least values in a set
of data and shows the spread in a set of data.
Quarter
1
Week 3
& 4
Probability and Statistics
SOL 6.14
The student, given a problem situation, will
a) construct circle graphs;
b) draw conclusions and make predictions, using circle
graphs; and
c) compare and contrast graphs that present information
from the same data set.
Essential Understandings
• What types of data are best presented in a circle graph? Circle graphs are
best used for data showing a relationship of the parts to the whole.
Instructional Strategies:
• Review of division (concept and method) will be helpful prior to teaching
mean.
• Have students keep track of their grades on tests, quizzes, and
homework. Have them find the mean, median, mode, and range of the
data. Have the students look for trends in their grades.
• Pass around a bucket of color cubes and have each student pick one.
Students, who have a particular color cube, are asked to link their cubes
together. In order for the students to count the number o cubes, of each
color, place the columns of cubes on a desk. Next, the students organize
the data in a table and determine the mean, median, mode, and range
of the data.
Open response:
Explain how to find the median of a set
of data that has an even number of data
in the set. List six numbers such that the
mean is 14, the median is 14, the modes
are 12 and 14, and the range is 5.
Describe a real-life situation in which the
mean is lower than the median.
Writing prompts:
Explain how to find the median of a set
of
data that has an even number of data in
the set. Explain how you can use a stem-
Page 4
Curriculum Pacing Guide
6th grade
2011 - 2012
• Understand that data can be displayed in a variety of graphical
representations.
• Select and use appropriate statistical methods to analyze data.
• Understand that different types of representations can tell different things
about the same data.
• Understand that graphs tell a story.
Essential Knowledge and Skills
• Collect, organize and display data in circle graphs by depicting information
as fractional.
• Draw conclusions and make predictions about data presented in a circle
graph.
• Compare and contrast data presented in a circle graph with the same data
represented in other graphical forms.
• Collect data sets of no more than 20 items by using tally sheets, surveys,
observations, questionnaires, interviews, and polls.
• Organize data by using lists, charts, tables, frequency distributions, and
line plots.
• Organize and display data in bar and line graphs, displaying the
information as clearly as possible by using increments of whole numbers,
fractions, and decimals rounded to the nearest tenth.
• Decide which type of graph is appropriate for a given situation.
• Bar graphs are used to display categorical (discrete) data.
• Line graphs are used to display continuous data.
• Circle graphs are used to show a relationship of the parts to a whole.
• Interpret data from line, bar, and circle graphs and from stem-and-leaf
and box and-whisker plots.
• Collect, analyze, display, and interpret a data set of no more than 20
items, using stem-and-leaf plots where the stem is listed in ascending
order and the leaves are in ascending order with or without commas
between leaves.
• Have students use real-life data from various sources and then
determine the mean, median, mode, and range of the data.
• Students collect the scores for their favorite team or player in ten games
and find the average score, mode, and the median.
Model Lessons:
Enhanced Scope and Sequence, Grade 6
“May I Have Fries with That?”
Enhanced Scope and Sequence, Grade 5
“It’s In the Bag” SOL 5.14
“Enough Room?” SOL 5.6
Resources:
Course 1:2-1, 2-2, 2-3, 2-5, 2-6, 2-7, 2-7b, 2-7
Glencoe Teacher ‘s Resource Kit
Understanding Math
Virginia SOL Mathematics Coach Grade 6
and-leaf plot to determine the median of
a set of data.
SOL-like Multiple Choice:
VDOE Released SOL items (6.14)
Pretests, Posttest, Formative
assessments, Bellwork, Classwork, and
Homework
Page 5
Curriculum Pacing Guide
6th grade
2011 - 2012
• Organize, analyze, display, and interpret data sets of no more than 20
numbers in box-and-whisker plots, identifying the lower extreme
(minimum), lower quartile, median, upper quartile, and upper extreme
(maximum). Use the critical points in a box-and-whisker plot to determine
the range and the interquartile range (IQR).
• Determine patterns and relationships within data sets (e.g., trends).
• Add charts, graphs, and tables into a project from another file on the
computer, from the internet, or from a software gallery.
• Format and insert a table with data into a document.
• Utilize short cut keys to manipulate and format data.
• Evaluate data and draw conclusions from tables and graphs.
• Manipulate an existing spreadsheet template to add content
• Identify cells, row, and columns by their alpha/numeric label.
• Convert data in a spreadsheet into various graphs.
• Export graphs, charts, and data to other applications to present
information about a concept or skill.
• Analyze collected information in a spreadsheet to draw conclusions.
Teacher Notes
• To collect data for any problem situation, an experiment can be designed,
a survey can be conducted, or other data-gathering strategies can be used.
The data can be organized, displayed, analyzed, and interpreted to answer
the problem.
• Different types of graphs are used to display different types of data.
– Bar graphs use categorical (discrete) data (e.g., months or eye color).
– Line graphs use continuous data (e.g., temperature and time).
– Circle graphs show a relationship of the parts to a whole.
• All graphs include a title, and data categories should have labels.
• A scale should be chosen that is appropriate for the data.
• A key is essential to explain how to read the graph.
Page 6
Curriculum Pacing Guide
6th grade
2011 - 2012
• A title is essential to explain what the graph represents.
• Data are analyzed by describing the various features and elements of a
graph.
Quarter
1
Week 5
Patterns, Functions, and Algebra
SOL 6.17
The student will identify and extend geometric and arithmetic sequences.
Essential Understandings
• What is the difference between arithmetic and a geometric sequence?
While both are numerical patterns, arithmetic sequences are additive and
geometric sequences are multiplicative.
• Understand that mathematical patterns can be represented in various
forms, geometrically or numerically.
• Understand that patterns regularly occur in everyday life.
• Understand that patterns can be recognized, extended, or generalized.
• Understand that numerical patterns may involve adding or multiplying by
the same number.
• Understand that geometric patterns may involve shape, size, angles,
transformations of shapes, and growth.
• Understand that patterns in mathematics are often represented by using a
rule that relates elements in one set to elements in another set.
Essential knowledge and Skills
• Investigate and apply strategies to recognize and describe the change
between terms in arithmetic patterns.
• Investigate and apply strategies to recognize and describe geometric
patterns.
• Describe verbally and in writing the relationships between consecutive
terms in an arithmetic or geometric sequence.
• Extend and apply arithmetic and geometric sequences to similar
Instructional Strategies:
• Given a list of numbers or a table of values, have the students determine
the nth value(s). Have them find the rule that applies to the particular
list or table. Explain and develop strategies to solve problems involving
numerical patterns, then create an algebraic equation. Given a series of
blocks, have the students create the next 5 figures. Have the students
explain orally and in writing how the pattern works.
• Have students write number sequences for other students to complete,
by finding and continuing a pattern. Ask the problem solvers to state the
rule used.
• Have students work in pairs to create a pattern using centimeter grid
paper. Have them challenge their classmates to find the next 2 figures in
the pattern.
• Suggested manipulatives include pattern blocks, grid paper, and quilting
patterns.
Model Lessons:
Enhanced Scope and Sequence, Grade 6
“Growing Patterns and Sequences”
ARI Curriculum Companion
“ Patterns, Functions, and Algebra”, p. 33-37
Resources:
Course 1: 7-6a, 7-6
Course 2: 1-7, 1-7b, 3-6a
NCTM Illuminations 6-8
“Chairs”, “Limits”
MathScience Innovation Center
“Playing with Patterns”
http://www.mathinscience.info/public/playing_with_patterns/PlayingWithPatt
erns.htm
Open response:
Consider the following sequence: 1, 4, 7,
10, 13… Is 100 a member of this
sequence? Explain your reasoning. If you
saved $2.00 on January 1, $4.00 on
February 1, $6.00 on March 1, and $8.00
on April 1 and so on, how much money
would you save in one year?
Explain how you would find the missing
terms in the following geometric
sequence:
_, _, 3, _, _, 1/9
Writing prompts:
Create a pattern in which the fifth
picture in the series would be the picture
shown below. Describe your pattern.
Groups of campers were going to an
island. On the first day, 10 went over and
2 came back. On the second day, 12
went over and 3 came back. If this
pattern continues, how many would be
on the island at the end of a week? Draw
a table. Write a minimum of 3 sentences
to explain the pattern and how you
found out the number of campers on the
island at the end of the week.
SOL-like Multiple Choice:
VDOE Released SOL items (6.17)
Pretests, Posttest, Formative
assessments, Bellwork, Classwork, and
Homework
Page 7
Curriculum Pacing Guide
6th grade
2011 - 2012 situations.
• Extend arithmetic and geometric sequences in a table by using a given rule
or mathematical relationship.
• Compare and contrast arithmetic and geometric sequences.
• Identify the common difference for a given arithmetic sequence.
• Identify the common ratio for a given geometric sequence.
• Analyze numeric and geometric sequences to discover a variety of
patterns.
• Create numerical and geometric patterns by using a given rule or
mathematical relationship.
• Describe numerical and geometric patterns, including triangular numbers.
Teacher Notes:
• Integrate patterns in the curriculum throughout the entire year.
• Numerical patterns may include linear and exponential growth, perfect
squares, triangular and other polygonal numbers, or Fibonacci numbers.
• Arithmetic and geometric sequences are types of numerical patterns.
• In the numerical pattern of an arithmetic sequence, students must
determine the difference, called the common difference, between each
succeeding number in order to determine what is added to each previous
number to obtain the next number. Sample numerical patterns are 6, 9,
12, 15, 18… and 5, 7, 9, 11, 13…
• In geometric number patterns, student must determine what each
number is multiplied by to obtain the next number in the geometric
sequence. This multiplier is called the common ratio. Sample geometric
number patterns include 2, 4, 8, 16, 32… 1, 5, 25, 125, 625… and 80, 20, 5,
1.25…
• Strategies to recognize and describe the differences between terms in
numerical patterns include, but are not limited to, examining the change
between consecutive terms, and finding common factors. An example is
the pattern 1, 2, 4, 7, 11, 16…
Glencoe Teacher’s Resource Kit
Understanding Math
Virginia SOL Mathematics Coach Grade 6
Page 8
Curriculum Pacing Guide
6th grade
2011 - 2012 Quarter
1 Week
6
Patterns, Functions, and Algebra
SOL 6.19
The student will investigate and recognize
a) the identity properties for addition and multiplication;
b) the multiplicative property of zero; and
c) the inverse property for multiplication.
Esssential Understandings
• How are the identity properties for multiplication and addition the same?
Different? For each operation the identity elements are numbers that
combine with other numbers without changing the value of the other
numbers. The additive identity is zero (0). The multiplicative identity is one
(1).
• What is the result of multiplying any real number by zero? The product is
always zero.
• Do all real numbers have a multiplicative inverse? No. Zero has no
multiplicative inverse because there is no real number that can be
multiplied by zero resulting in a product of one.
Essential Knowledge and Skills
• Identify a real number equation that represents each property of
operations with real numbers, when given several real number equations.
• Test the validity of properties by using examples of the properties of
operations on real numbers.
• Identify the property of operations with real numbers that is illustrated by
a real number equation.
• NOTE: The commutative, associative and distributive properties are taught
in previous grades.
Teacher Notes
• Identity elements are numbers that combine with other numbers without
changing the other numbers. The additive identity is zero (0). The
multiplicative identity is one (1). There are no identity elements for
subtraction and division.
Instructional Strategies
• Model 2 x 4 = 4 x 2 by showing 2 groups of 4 and 4 groups of 2 both
equal to 8.
• Use index cards and markers to create flash cards for properties.
Students will illustrate the property on one side and the property name
on the other side.
• Students can match cards naming properties to examples of each
property.
• Use Venn Diagrams to compare and contrast Identity property of
addition and multiplication
• Use Inverse properties when solving one step equations.
Model Lessons:
Enhanced Scope and Sequence, Grade 6
“Pick and Choose”
ARI Curriculum Companion
“Modeling Properties”, p. 9 – 26
Resources:
Course 1: 9-1
Course 2: 1-6, 3-4, 3-6, 6-5
Glencoe Teacher ‘s Resource Kit
Understanding Math
Virginia SOL Mathematics Coach Grade 6
Open Response:
Explain how properties are used when
solving equations like
x + 5 = 12.
Provide students with information for
one side of a statement and ask students
to apply a particular property and
demonstrate the result.
(i.e. “(2 + 3) + 7 =” use the associative
property of addition to write an
equivalent statement.)
Writing prompts:
You have to buy 3 video games and the
prices are $37, $42, and $23. Explain
how these numbers can be added
mentally and what property you would
use and why.
SOL-like Multiple Choice:
VDOE Released SOL items (6.1)
Pretests, Posttest, Formative
assessments, Bellwork, Classwork, and
Homework
Page 9
Curriculum Pacing Guide
6th grade
2011 - 2012
• The additive identity property states that the sum of any real number and
zero is equal to the given real number (e.g., 5 + 0 = 5).
• The multiplicative identity property states that the product of any real
number and one is equal to the given real number (e.g., 8 · 1 = 8).
• Inverses are numbers that combine with other numbers and result in
identity elements.
• The multiplicative inverse property states that the product of a number
and its multiplicative inverse (or reciprocal) always equals one (e.g., 4 · 1
4 =
1).
• Zero has no multiplicative inverse.
• The multiplicative property of zero states that the product of any real
number and zero is zero.
• Division by zero is not a possible arithmetic operation. Division by zero is
undefined.
Quarter
1
Week 7
& 8
Probability and Statistics
SOL 6.16
The student will
a) compare and contrast dependent and independent
events; and
b) determine probabilities for dependent and independent
events.
Essential Understandings
• How can you determine if a situation involves dependent or independent
events? Events are independent when the outcome of one has no effect
on the outcome of the other. Events are dependent when the outcome of
one event is influenced by the outcome of the other.
• Understand how to use and interpret information given a sample space.
• Understand that a probability can be expressed as a ratio, decimal, or
percent.
• What is the Fundamental (Basic) Counting Principle? The Fundamental
(Basic) Counting Principle is a computational procedure used to determine
the number of possible outcomes of several events.
Instructional Strategies:
• Students work in pairs with two number cubes. Each pair brainstorm to
list all the possible outcomes of rolling two number cubes. When the
pair of students have completed their list they will get the teacher to
check it. Afterwards, the students will give, in ratio form:
- favorable number of outcomes/total number of outcomes
- P(two 3’s)
- P(same number on both cubes)
- P(one or two 6’s)
- P(the sum of numbers showing 7)
• Use real-life examples involving coins, dice, clothing, and food.
• Students study the chances of winning in the Virginia Lottery Pick 3 and
Pick 4 daily events using the Basic
• Counting Principle. Compare the chances of winning with the size of the
prize.
SOL-like Multiple Choice:
VDOE Released SOL items (6.16)
Pretests, Posttest, Formative
assessments, Bellwork, Classwork, and
Homework
Page 10
Curriculum Pacing Guide
6th grade
2011 - 2012
• What is the role of the Fundamental (Basic) Counting Principle in
determining the probability of compound events? The Fundamental
(Basic) Counting Principle is used to determine the number of outcomes of
several events. It is the product of the number of outcomes for each event
that can be chosen individually.
• What is the difference between the theoretical and experimental
probability of an event? Theoretical probability of an event is the expected
probability and can be found with a formula. The experimental probability
of an event is determined by carrying out a simulation or an experiment.
In experimental probability, as the number of trials increases,
Essential Knowledge and Skills
• Determine whether two events are dependent or independent.
• Compare and contrast dependent and independent events.
• Determine the probability of two dependent events.
• Plan and carry out experiments that use concrete materials to find a
sample space.
• Determine the number of possible arrangements for selected experiments
and represent the sample space for no more than three types of objects as
a list, chart, picture, and tree diagram.
• Compute the number of possible arrangements of no more than three
types of objects by using the Fundamental (Basic) Counting Principle.
• Given a sample space, determine the probability of a simple event.
Represent the probability as a ratio, fraction, decimal, or percent where
the fraction’s denominator does not exceed 20, decimals are rounded to
tenths, and percent is rounded to 1/10 of a percent.
• Determine the theoretical probability of an event.
• Determine the experimental probability of an event.
• Describe changes in the experimental probability as the number of trials
increases.
• Investigate and describe the difference between the probability of an
event found through experiment or simulation versus the theoretical
probability of that same event.
Model Lessons:
Enhanced Scope and Sequence, Grade 6
“It Could Happen”
Enhanced Scope and Sequence, Grade 7
“What are the Chances?” SOL 7.9
ARI Curriculum Companion
“ Probability”, p. 8-14, 25-32
Resources:
Course 1: 11-1, 11-1b, 11-2, 11-5
Course 2: 9-1, 9-2, 9-3, 9-6, 9-6b, 9-7
Understanding Math Software
Glencoe Teacher ‘s Resource Kit
Virginia SOL Mathematics Coach Grade 6
Page 11
Curriculum Pacing Guide
6th grade
2011 - 2012
• Compute the number of possible outcomes by using the Fundamental
(Basic) Counting Principle.
Teacher Notes
• The probability of an event occurring is equal to the ratio of desired
outcomes to the total number of possible outcomes (sample space).
• The probability of an event occurring can be represented as a ratio or the
equivalent fraction, decimal, or percent.
• The probability of an event occurring is a ratio between 0 and 1.
• A probability of 0 means the event will never occur.
• A probability of 1 means the event will always occur.
• A simple event is one event (e.g., pulling one sock out of a drawer and
examining the probability of getting one color).
• Events are independent when the outcome of one has no effect on the
outcome of the other. For example, rolling a number cube and flipping a
coin are independent events.
• The probability of two independent events is found by using the following
formula: ( ) ( ) ( )P Aand B P A P B= ⋅
Ex: When rolling two number cubes simultaneously, what is the
probability of rolling a 3 on one
cube and a 4 on the other?
1 1 1(3 4) (3) (4)
6 6 36P and P P= ⋅ = ⋅ =
• Events are dependent when the outcome of one event is influenced by the
outcome of the other. For example, when drawing two marbles from a
bag, not replacing the first after it is drawn affects the outcome of the
second draw.
• The probability of two dependent events is found by using the following
formula:
( ) ( ) ( )P Aand B P A P B after A= ⋅
Page 12
Curriculum Pacing Guide
6th grade
2011 - 2012
Ex: You have a bag holding a blue ball, a red ball, and a yellow ball.
What is the probability of
picking a blue ball out of the bag on the first pick and then without
replacing the blue ball in the
bag, picking a red ball on the second pick?
1 1 1(blue red) (blue) (red blue)
3 2 6P and P P after= ⋅ = ⋅ =
• A sample space is the set of all possible outcomes of an experiment.
• A sample space can be organized by using a list, chart, picture, or tree
diagram.
• The sample space for tossing two coins is (H,H), (H,T), (T,H), and (T,T).
• The probability of an event occurring is equal to the ratio of desired
outcomes to the total number of possible outcomes (sample space).
• The probability of an event occurring can be represented as a ratio or the
equivalent fraction, decimal, or percent.
• The probability of an event occurring is a ratio between 0 and 1.
– A probability of 0 means the event will never occur.
– A probability of 1 means the event will always occur.
• A simple event is one event (e.g., pulling one sock out of a drawer and
examining the probability of getting one color).
Quarter
1
Week 9
Review for Benchmarks Use old release test items from past years revised to higher level of thinking
Use Virginia SOL Coach
Benchmark 1 Assessment
(Oct. 29 – Nov. 5)
Quarter
2
Week 1
Patterns, Functions, and Algebra
SOL 6.18
The student will solve one-step linear equations in one variable involving
whole number coefficients and positive rational solutions.
Essential Understandings
Instructional Strategies:
• Stress vocabulary and use continuously throughout the course.
• Use only whole numbers in your expressions and equations.
• Have students complete an equation magic square. Once they have
solved the equation in each square correctly, their sum across, down and
Open response:
Give students balance-scale pictures and
have them record the steps taken along
with the resulting equations.
Writing prompts:
Have students write a description how
Page 13
Curriculum Pacing Guide
6th grade
2011 - 2012
• When solving an equation, why is it necessary to perform the same
operation on both sides of an equal sign?
• To maintain equality, an operation performed on one side of an equation
must be performed on the other side.
• Understand that physical objects can be used to represent and solve
algebraic equations.
• Understand that in an equation, the equal sign indicates that the value on
the left side of the sign is the same as the value on the right side.
• Understand that to maintain equality an operation performed on one side
of an equation must be performed on the other side.
Essential Knowledge and Skills
• Represent and solve a one-step equation, using a variety of concrete
materials such as colored chips, algebra tiles, or weights on a balance
scale.
• Solve a one-step equation by demonstrating the steps algebraically.
• Identify and use the following algebraic terms appropriately: equation,
variable, expression, term, and coefficient.
• Write verbal expressions as algebraic expressions. Expressions will be
limited to no more than two operations.
• Write verbal sentences as algebraic equations. Equations will contain no
more than one variable term.
• Translate algebraic expressions and equations to verbal expressions and
sentences. Expressions will be limited to no more than two operations.
Teacher Notes
• A one-step linear equation is an equation that requires one operation to
solve.
• A mathematical expression contains a variable or a combination of
variables, numbers, and/or operation symbols and represents a
mathematical relationship. An expression cannot be solved.
on the diagonal will yield the magic number.
• Use flashcards with equations on one side and the solution on the other.
• Have students circle or highlight the variable they are solving for.
• Use manipulatives such as Algebra Tiles and balance scales to help
students build a conceptual understanding of solving linear equations.
Model Lessons:
Enhanced Scope and Sequence, Grade 6
“Equation Vocabulary,”
“Balanced,”
Enhanced Scope and Sequence, Grade 5
“Variables and Open Sentence.” SOL 5.18
ARI Curriculum Companion
“Using Balance Mats and Counters to Solve One-step Equations”, p. 49-53
“Solving One-step Equations using Equation Mats”, p. 81-88
“Solving One-step Equations and Word Problems”, p. 89-92
Resources:
Course 1: 1-7, 9-2, 9-3, 9-4, 9-5
Understanding Math Software
Glencoe Teacher ‘s Resource Kit
Virginia SOL Mathematics Coach Grade 6
they would solve an addition/subtraction
or multiplication/division equation for a
student who was absent and missed the
lesson on solving equations.
Have students describe the process of
solving equations using a balance scale
or mat. Students write a story/narrative
using key mathematical vocabulary and
giving an example of each vocabulary
term.
SOL-like Multiple Choice:
VDOE Released SOL items (6.18)
Pretests, Posttest, Formative
assessments, Bellwork, Classwork, and
Homework
Page 14
Curriculum Pacing Guide
6th grade
2011 - 2012
• A term is a number, variable, product, or quotient in an expression of
sums and/or differences. In 7x2 + 5x – 3, there are three terms, 7x
2, 5x,
and 3.
• A coefficient is the numerical factor in a term. For example, in the term
3xy2, 3 is the coefficient; in the term z, 1 is the coefficient.
• Positive rational solutions are limited to whole numbers and positive
fractions and decimals.
• An equation is a mathematical sentence stating that two expressions are
equal.
• A variable is a symbol (placeholder) used to represent an unspecified
member of a set.
• A verbal expression is a word phrase (e.g., “the sum of two consecutive
integers”).
• A verbal sentence is a complete word statement (e.g., “The sum of two
consecutive integers is five.”).
• An expression is a name for a number.
• An algebraic expression is a variable expression that contains at least one
variable (e.g., 2x – 5).
• An algebraic equation is a mathematical statement that says that two
expressions are equal (e.g., 2x + 1 = 5).
• Key words in translating verbal expressions/ sentences to algebraic
expressions/equations may include words and their translations such as: is
to =, of to multiplication, more than to +, less than to –, increased by to +,
and decreased by to -.
• An expression that contains only numbers is called a numerical expression.
• An expression that contains a variable is called a variable expression.
Quarter
2
Week 2
Patterns, Functions, and Algebra
SOL 6.20
The student will graph inequalities on a number line.
Essential Understandings
Instructional Strategies:
• Match inequality with graph of inequality cards.
• Put inequalities on the board and give students a card with a number on
it. Students stand if their car is a solution to the given inequality.
Open response:
Write inequality statements given a
representation on a number line.
Use real life examples – What time
would you need to get to beat the
school’s 400 m record? Long jump
record? Graph your results on a number
Page 15
Curriculum Pacing Guide
6th grade
2011 - 2012
• In an inequality, does the order of the elements matter?
Yes, the order does matter. For example, x > 5 is not the same relationship
as 5 > x. However, x > 5 is the same relationship as 5 < x.
Essential Knowledge and Skills
• Given a simple inequality with integers, graph the relationship on a
number line.
• Given the graph of a simple inequality with integers, represent the
inequality two different ways using symbols (<, >, <, >).
Teacher Notes
• Inequalities using the < or > symbols are represented on a number line
with an open circle on the number and a shaded line over the solution set.
Ex: x < 4
• When graphing x ≤ 4 fill in the circle above the 4 to indicate that the 4 is
included.
• Inequalities using the or≤ ≥ symbols are represented on a number line
with a closed circle on the number and shaded line in the direction of the
solution set.
• The solution set to an inequality is the set of all numbers that make the
inequality true.
• It is important for students to see inequalities written with the variable
before the inequality symbol and after. For example x > -6 and 7 > y.
• Emphasize the definition of inequality: A mathematical sentence that
contains (<, >, ≥ , ≤ ).
• Only graph inequalities that are already solved (the variable is isolated on
one side of the inequality).
• Look at Guinness Book of World Records website and choose a record.
Write an inequality to beat that record.
Model Lessons:
Enhanced Scope and Sequence, Grade 6
“Give or Take a Few,”
Resources:
Course 2: 4-2a, 4-2, 4-3, 4-5
Glencoe Teacher ‘s Resource Kit
Understanding Math Software
Virginia SOL Mathematics Coach Grade 6
line.
Writing prompts:
Explain the difference between x > 7 and
7 > x. Explain how to verify a solution to
an inequality.
SOL-like Multiple Choice:
Which number is a solution to the
inequality 6 >x?
A 6
B 8
C 5
D 12
SOL-like Multiple Choice:
VDOE Released SOL items (6.20)
Pretests, Posttest, Formative
assessments, Bellwork, Classwork, and
Homework
Page 16
Curriculum Pacing Guide
6th grade
2011 - 2012 Quarter
2 Week
3
Geometry
SOL 6.11
The student will
a) identify the coordinates of a point in a coordinate plane;
and
b) graph ordered pairs in a coordinate plane.
Essential Understandings
• Can any given point be represented by more than one ordered pair?
The coordinates of a point define its unique location in a coordinate plane.
Any given point is defined by only one ordered pair.
• In naming a point in the plane, does the order of the two coordinates
matter? Yes. The first coordinate tells the location of
the point to the left or right of the y-axis and the second point tells the
location of the point above or below the x-axis. Point (0, 0) is at the origin.
• Understand that the coordinates of a point define its location in a
coordinate plane.
Essential Knowledge and Skills
• Identify and label the axes of a coordinate plane.
• Identify and label the quadrants of a coordinate plane.
• Identify the quadrant or the axis on which a point is positioned by
examining the coordinates (ordered pair) of the point.
• Graph ordered pairs in the four quadrants and on the axes of a coordinate
plane.
• Identify ordered pairs represented by points in the four quadrants and on
the axes of the coordinate plane.
• Relate the coordinate of a point to the distance from each axis and relate
the coordinates of a single point to another point on the same horizontal
or vertical line.
Teacher Notes
• In a coordinate plane, the coordinates of a point are typically represented
Instructional Strategies:
• Give students graph paper and ordered pairs which result in a picture
(i.e., rocket, fish, etc.) or have students draw a picture on a coordinate
graph and label the coordinates of specific points and list the ordered
pairs.
• Create a foldable showing the axes, quadrants and coordinates.
• Give students cards with an ordered pair or the graph of the ordered
pair and have them find their match.
• Use two large coordinate plans displayed in the front of the room. Pick
two students to come up at time and graph an ordered pair. Winner is
the one who plots the point correctly first..
• Teach vocabulary associated with graphing points on a coordinate plane:
Axes, origin, ordered pair, coordinate plane and quadrant.
Model Lessons:
Enhanced Scope and Sequence, Grade 6
“What’s the Point?”
ARI Curriculum Companion
“Patterns, Functions, and Algebra”, p. 63-67
Resources:
Course 1: 8-6
Course 2: 3-3
Understanding Math Software
Glencoe Teacher ‘s Resource Kit
Virginia SOL Mathematics Coach Grade 6
Open response:
Explain how the points (7, -10) and
(-10, 7) are different on a coordinate
plane.
Writing prompts:
Explain how to graph the point (-3, 6).
Have pairs of students draw a coordinate
grid complete with positive and negative
numbers. Ask them to plot any point in
quadrant II, III, and IV. Have them
explain
the meaning of any negative sign
associated with the ordered pair that
they plotted.
SOL-like Multiple Choice:
VDOE Released SOL items (6.11)
Pretests, Posttest, Formative
assessments, Bellwork, Classwork, and
Homework
Page 17
Curriculum Pacing Guide
6th grade
2011 - 2012 by the ordered pair (x, y), where x is the first coordinate and y is the
second coordinate. However, any letters may be used to label the axes
and the corresponding ordered pairs.
• The quadrants of a coordinate plane are the four regions created by the
two intersecting perpendicular number lines. Quadrants are named in
counterclockwise order. The signs on the ordered pairs for quadrant I are
(+,+); for quadrant II, (–,+); for quadrant III, (–, –); and for quadrant IV, (+,–
).
• In a coordinate plane, the origin is the point at the intersection of the x-
axis and y-axis; the coordinates of this point are (0,0).
• For all points on the x-axis, the y-coordinate is 0. For all points on the y-
axis, the x-coordinate is 0.
• The coordinates may be used to name the point. (e.g., the point (2,7)). It is
not necessary to say “the point whose coordinates are (2,7)”.
Quarter
2
Week 4
Measurement
SOL 6.10 (c only)
The student will
c) solve practical problems involving area and perimeter
Essential Understandings
• What is the difference between area and perimeter? Perimeter is the
distance around the outside of a figure while area is the measure of the
amount of space enclosed by the perimeter.
• Understand the attributes of polygons and the use of measures to
determine area and perimeter.
• Understand the derivation of formulas related to area and perimeter of
polygons; and how to determine which is used in problem situations.
• Understand how to apply area or perimeter in real-life situations.
Essential Knowledge and Skills
• Apply formulas to solve practical problems involving area and perimeter of
triangles and rectangles.
• Determine if a problem situation involving polygons of four or fewer sides
Instructional Strategies:
• Draw rectangles on coordinate plane and determine area and perimeter.
Use ordered pairs in ALL quadrants.
• Have students use manipulatives such as tiles, one-inch cubes, adding
machine tape, graph paper, geo-boards, or tracing paper with real world
applications to develop a deeper understand of the formulas for area
and perimeter.
• Give students blocks. Ask them to create shapes with a certain area and
perimeter (ex. An area of 8 and a perimeter of 12).
• For real world application of area and perimeter, use tools to measure
items in and around classroom.
• Give students situations like building a fence, putting in new carpet,
painting a wall adding baseboard to the floor of a room, etc… and have
them state whether they would find area or perimeter.
• Use the Shade Game, Build Perimeter , Area/Perimeter, activity to
engage students.
Model Lessons:
Enhanced Scope and Sequence, Grade 6
“Out of the Box,”
Open response:
Draw and label two different triangles
that each have an area of 24 square feet.
Find an object that has an area of ____.
Explain how you know.
Area and Perimeter: Word Problems
Writing prompts:
Describe the relationship between the
area of a parallelogram and the area of a
triangle with the same base and height.
Explain. If you were given the area of a
square, explain how you would find the
length of one side and the perimeter.
SOL-like Multiple Choice:
VDOE Released SOL items (6.10.c)
Pretests, Posttest, Formative
assessments, Bellwork, Classwork, and
Homework
Page 18
Curriculum Pacing Guide
6th grade
2011 - 2012 represents the application of perimeter or area.
• Subdivide a polygon into rectangles and right triangles, estimate the area
of the rectangles and/or right triangles to estimate the area of the
polygon, and find the area of the rectangles and/or right triangles to
determine the area of the polygon.
Teacher Notes
• Experiences in deriving the formulas for area, perimeter, and volume using
manipulatives such as tiles, one-inch cubes, adding machine tape, graph
paper, geoboards, or tracing paper, promote an understanding of the
formulas and facility in their use.†
• The perimeter of a polygon is the measure of the distance around the
polygon.
• The perimeter of a square whose side measures s is 4 times s (P = 4s), and
its area is side times side (A = s2).
• The perimeter of a rectangle is the sum of twice the length and twice the
width [P = 2l + 2w, or
P = 2(l + w)], and its area is the product of the length and the width (A =
lw).
• An estimate of the area of a polygon can be made by subdividing the
polygon into rectangles and right triangles, estimating their areas, and
adding the areas together.
• The area of a triangle is one half of the measure of the base times the
height: A = ½ bh, or A = bh ÷ 2.
• Experiences in deriving the formulas for area and perimeter, using
manipulatives such as tiles, one inch cubes, adding machine tape, graph
paper, geoboards, or tracing paper, promote an understanding of the
formulas and facility in their use.
ARI Curriculum Companion
“2-D Measurement,” p. 10-21
Resources:
Course 1 : 1-8, 4-5, 12-1b, 14-1, 14-2
Course 2 : 6-8, 11-4, 11-5
Understanding Math Software
NCTM Illuminations 6-8
“Area Triangles”
Glencoe Teacher ‘s Resource Kit
Virginia SOL Mathematics Coach Grade 6
Page 19
Curriculum Pacing Guide
6th grade
2011 - 2012 Quarter
2
Week 5
& 6
Measurement
SOL 6.10 (D only)
The student will
d) describe and determine the volume and surface area of a
rectangular prism.
Essential Understandings
• What is the relationship between area and surface area?
Surface area is calculated for a three-dimensional figure. It is the sum of
the areas of the two-dimensional surfaces that make up the three-
dimensional figure.
• How are volume and surface area related? Volume is the measure of the
amount a container holds while surface area is the sum of the areas of the
surfaces on the container.
• How does the volume of a rectangular prism change when one of the
attributes is increased? There is a direct relationship between the volume
of a rectangular prism increasing when the length of one of the attributes
of the prism is changed by a scale factor.
• Understand the attributes of polygons and the use of measures to
determine area and perimeter.
• Understand the derivation of formulas related to area and perimeter of
polygons and how to determine which is used in problem situations.
• Understand how to apply volume and surface area in real-life situations.
• Understand the derivation of formulas related to volume and surface area
of polygons.
Essential Knowledge and Skills
• Solve problems that require finding the surface area of a rectangular
prism, given a diagram of the prism with the necessary dimensions
labeled.
• Determine if a practical problem involving a rectangular prism represents
the application of volume or surface area.
• Apply formulas to solve problems involving area and perimeter for
triangles and rectangles.
Instructional Strategies:
• Use nets to develop and understand formula application.
• Review and practice algebraic, fraction, and decimal skills by using
formulas.
• Draw a 7 x 10 cm rectangle on a sheet of paper and find the perimeter.
Determine how the perimeter is affected when: length and width are
doubled; length and width are halved.
• Draw as many rectangles as you can with a perimeter of 24.
• Give students an object (i.e., school playground, number of tiles on the
floor, etc.) and a description of an attribute to be measured. Students
should determine whether area or perimeter should be measured. For
example, fence around a playground (perimeter), grass for playground
(area), and number of tiles covering the floor (area).
• Suggested manipulatives: 3-dimensional hollow figures with rice or sand
to fill, wooden cubes, sugar cubes, linker or snap cubes, polydron
shapes, card stock paper, rulers, and scissors.
• Use 3-dimensional figures that are hollow; then fill with sand, rice,
water, etc. to determine the volume.
• Have students bring in assorted 3-dimensional figures to determine
surface area by covering the figures with centimeter paper.
Model Lessons:
Enhanced Scope and Sequence, Grade 6
“Out of the Box”
Enhanced Scope and Sequence, Grade 7
“Volume of a Rectangular Prism,” SOL 7.5
“Surface Area of a Rectangular Prism,” SOL 7.5
“Attributes of a Rectangular Prism,” SOL 7.5
Resources:
Course 1: 14-5, 14-6
Course 2: 12-2, 12-4a, 12-4,
Understanding Math Software
Glencoe Teacher ‘s Resource Kit
Writing prompts:
Write a paragraph explaining real-life
situations, which apply to area and
perimeter.
Have students discuss the difference
between surface area and volume or
explain in written form how to calculate
surface area and volume.
SOL-like Multiple Choice:
VDOE Released SOL items (6.10d)
Pretests, Posttest, Formative
assessments, Bellwork, Classwork, and
Homework
Page 20
Curriculum Pacing Guide
6th grade
2011 - 2012
• Develop a procedure and formula for finding the surface area and volume
of a rectangular prism.
• Solve problems that require finding the volume of the rectangular prism
given a diagram of the prism with the necessary dimensions labeled.
• Describe how the volume or surface area of a rectangular prism is affected
when one measured attribute is multiplied by a scale factor. Problems will
be limited to changing attributes by scale factors only.
Teacher Notes
• The surface area of a rectangular prism is the sum of the areas of all six
faces ( 2 2 2SA lw lh wh= + + ).
• The volume of a rectangular prism is computed by multiplying the area of
the base, B, (length x width) by the height of the prism (V lwh Bh= = ).
• There is a direct relationship between changing one measured attribute of
a rectangular prism by a scale factor and its volume. For example,
doubling the length of the prism will double its volume. This direct
relationship does not hold true for surface area.
• Experiences in using a variety of measuring devices and making real
measurements promote an understanding of measurements and the
formula associated with measurements.
• Experiences in deriving the formulas for area and perimeter, using
manipulatives such as tiles, one-inch cubes, adding machine tape, graph
paper, geoboards, or tracing paper, promote an understanding of the
formulas and facility in their use.
Virginia SOL Mathematics Coach Grade 6
Quarter
2
Week 7
& 8
Measurement
SOL 6.10 (a & b only)
The student will
a) define pi (π) as the ratio of the circumference of a circle
to its diameter;
b) solve practical problems involving circumference and
area of a circle, given the diameter or radius;
Essential Understandings
• What is the relationship between the circumference and diameter of a
Instructional Strategies:
• Give students a circular object (i.e., plastic lids, cups, etc.) two different
colors of strings, and a centimeter ruler. Students will work in groups.
The students will measure the distance around the object and the
diameter using the strings and then measuring the string with the ruler.
Regardless of the lid size used, if the students have been careful
wrapping the string, they should get three diameters out of the string
length with a little string left over. After all groups have finished their
measurements and calculations for the circles, have them write the ratio
of circumference/diameter, for their circle and use a calculator to
convert the ratio into decimal form. Record decimal forms on the
Open response:
Compare and contrast the circumference
and area of a circle. What is the
relationship between the radius and
diameter of a circle? If you know the
circumference of a circle, can you figure
out the area? Explain why or why not.
Circle Word Problems: Circles
Writing prompts:
Ask students to write a description of a
Page 21
Curriculum Pacing Guide
6th grade
2011 - 2012 circle?
The circumference of a circle is about 3 times the measure of the diameter.
• Select the approximation for pi (π) when solving problems.
• Understand the derivation of pi and formulas for finding circumference
and area of a circle.
Essential Knowledge and Skills
• Derive an approximation for pi (3.14 or 22
7 ) by gathering data and
comparing the circumference to the diameter of various circles, using
concrete materials or computer models.
• Find the circumference of a circle by substituting a value for the diameter
or the radius into the formula C = πd or C = 2πr.
• Find the area of a circle by using the formula
A = πr2.
• Determine the circumference and/or area of a circle, using various tools.
• Create and solve problems that involve finding the circumference and area
of a circle when given the diameter or radius.
Teacher Notes
• Circumference is the distance around or perimeter of a circle.
• The area of a closed curve is the number of non-overlapping square units
required to fill the region enclosed by the curve.
• The value of pi (π) is the ratio of the circumference of a circle to its
diameter.
• The ratio of the circumference to the diameter of a circle is a constant
value, pi (π), which can be approximated by measuring various sizes of
circles.
• The fractional approximation of pi generally used is 22
7 .
• The decimal approximation of pi generally used is 3.14.
overhead or chalkboard. Ask the student to find the average of all ratios
found. When students have measured carefully, the average is usually
close to 3.14.
• Using a compass, have students construct a circle and then draw the
diameter and the radius. With a ruler have students measure the
diameter and radius and then find the circumference and area of the
circle they drew using the appropriate formula.
• Use the Bubble Mania, Circle Investigation, Parallelogram, and Pi
Investigation to engage students.
• Connect to literacy with “Sir Cumference and The Dragon of Pi” story
helping students understand how pi was derived.
Model Lessons:
Enhanced Scope and Sequence, Grade 6
“Going the Distance,”
ARI Curriculum Companion
“Circles”, p. 10-21
Resources:
Course 1: 4-6, 14-3, 11-6
Course 2: 11-6
Understanding Math Software
Glencoe Teacher ‘s Resource Kit
Virginia SOL Mathematics Coach Grade 6
diameter’s relationship to its
circumference (i.e. a circumference of a
circular object equals about 3.14 as long
as its diameter).
If the radius of the larger circle is twice
that of the smaller circle;
Explain how you can find the area
of the larger circle when you are
given the radius of the smaller circle.
Find the area of the larger circle.
SOL-like Multiple Choice:
VDOE Released SOL items (6.10a, b)
Pretests, Posttest, Formative
assessments, Bellwork, Classwork, and
Homework
5cm
Page 22
Curriculum Pacing Guide
6th grade
2011 - 2012
• The circumference of a circle is computed using C dπ= or 2C rπ= ,
where d is the diameter and r is the radius of the circle.
• The area of a circle is computed using the formula2
A rπ= , where r is
the radius of the circle.
Quarter
2
Week 9
Review for Benchmarks Use old release test from past years revised to higher level of thinking
Use Virginia SOL Coach
Benchmark 2 Assessment
(Jan. 22 – 28)
Quarter
3
Week 1
Measurement
SOL 6.9
The student will make ballpark comparisons between measurements in the
U.S. Customary System of measurement and measurements in the metric
system.
Essential Understandings
• What is the difference between weight and mass? Weight and mass are
different. Mass is the amount of matter in an object. Weight is the pull of
gravity on the mass of an object. The mass of an object remains the same
regardless of its location. The weight of an object changes dependent on
the gravitational pull at its location.
• How do you determine which units to use at different times? Units of
measure are determined by the attributes of the object being measured.
Measures of length are expressed in linear units, measures of area are
expressed in square units, and measures of volume are expressed in cubic
units.
• Why are there two different measurement systems? Measurement
systems are conventions invented by different cultures to meet their
needs. The U.S. Customary System is the preferred method in the United
States. The metric system is the preferred system worldwide.
• Understand that there is a structured relationship between and among
units of measure for length, area, weigh/mass, and volume in the metric
and U.S. Customary systems.
• Understand that weight and mass are different.
Instructional Strategies:
• The metric system and conversions between the systems will be
taught/reviewed in the third nine weeks.
• Use the Real World Intro to get students excited about the concept.
• Give students real life objects to measure using tools like measuring
tape, pan balance scale, measuring cups…
• Have them convert the measurements they find into other compatible
units. (i.e. 1 cup of Kool-aide could be 8 oz of Kool-aide or ½ pint).
• Give students pictures of items and have them match the picture to it
appropriate measurement unit. (i.e. Gorilla would go with ton or feet…)
• Use graphic organizers like G-man and Big G, to help students convert
liquid measures.
• Use Bingo to engage students.
• Take students outside to measure and compare objects and/or items
around the school. Take rulers, yard sticks, and meter sticks to use for
measuring.
• Students measure height, width, and length of classroom. Find the
number of cubic yards of air in the room. Make a model using cubes to
show that 27 cubic feet = one cubic yard. Suggested manipulatives:
straws, sticks, cubes, string, rulers, yardsticks, trundle wheel, measuring
cups, meter sticks, and scales.
• Students will use a variety of objects for measuring parts of the body
(fingers, arms, legs, waist to top of head, etc.) using things such as
Open response:
A recipe for macaroni and cheese calls
for
2 quarts of milk. I only have a pint
measuring tool. How can I use this tool
to make sure I used 2 quarts?
Fuji apples are $1.49 a pound. If the
apple I buy weighs 10 oz, how would I
figure the price of my apple?
Writing prompts:
Detrick is from Germany and has only
used the metric system. Explain to
Detrick
how the U.S. Customary system is similar
but different than the metric system.
SOL-like Multiple Choice:
VDOE Released SOL items (6.9)
Pretests, Posttest, Formative
assessments, Bellwork, Classwork, and
Homework
Page 23
Curriculum Pacing Guide
6th grade
2011 - 2012
• Understand that measures are determined by quantitative comparison to
a standard unit.
• Understand that units of measure are determined by the attributes of the
object being measured.
• Understand that measures of length are expressed in linear units,
measures of area are expressed in square units, and measures of volume
are expressed in cubic units.
Essential Knowledge and Skills
• Estimate the conversion of units of length, weight/mass, volume, and
temperature between the U.S. Customary system and the metric system
by using ballpark comparisons. Ex: 1 L ≈ 1qt. Ex: 4L ≈ 4 qts.
• Estimate measurements by comparing the object to be measured against
a benchmark.
• Compare and convert units of measure for length, area, weight/mass, and
volume within the U.S. Customary and metric system.
• Determine the most appropriate unit of measure for a given situation.
• Estimate measurements by comparing the object to be measured against
a benchmark.
• Solve measurement problems by estimating and determining length, using
standard and nonstandard units of measure.
• Solve measurement problems by estimating and determining
weight/mass, using standard and nonstandard units of measure.
• Solve measurement problems by estimating and determining area, using
standard and nonstandard units of measure.
• Solve measurement problems by estimating and determining liquid
volume/capacity, using standard and nonstandard units of measure.
Teacher Notes
• Making sense of various units of measure is an essential life skill, requiring
reasonable estimates of what measurements mean, particularly in relation
to other units of measure.
straws, cubes, books, and whatever else is readily available.
• Solve measurement problems by estimating and determining length,
using standard and nonstandard units of measure (i.e., rulers, tape
measures, trundle wheels, etc,).
Model Lessons:
Enhanced Scope and Sequence, Grade 6
“Measuring Mania,”
ARI Curriculum Companion
“Working with Units”, p. 2-18
Resources:
Course 1: 12-1, 12-2, 12-4, 12-5
Understanding Math Software
Glencoe Teacher ‘s Resource Kit
Virginia SOL Mathematics Coach Grade 6
Page 24
Curriculum Pacing Guide
6th grade
2011 - 2012 – 1 inch is about 2.5 centimeters.
– 1 foot is about 30 centimeters.
– 1 meter is a little longer than a yard, or about 40 inches.
– 1 mile is slightly farther than 1.5 kilometers.
– 1 kilometer is slightly farther than half a mile.
– 1 ounce is about 28 grams.
– 1 nickel has the mass of about 5 grams.
– 1 kilogram is a little more than 2 pounds.
– 1 quart is a little less than 1 liter.
– 1 liter is a little more than 1 quart.
– Water freezes at 0°C and 32°F.
– Water boils at 100°C and 212°F.
– Normal body temperature is about 37°C and 98°F.
– Room temperature is about 20°C and 70°F.
• Mass is the amount of matter in an object. Weight is the pull of gravity on
the mass of an object. The mass of an object remains the same regardless
of its location. The weight of an object changes dependent on the
gravitational pull at its location. In everyday life, most people are actually
interested in determining an object’s mass, although they use the term
weight, as shown by the questions: “How much does it weigh?” versus
“What is its mass?”
• The degree of accuracy of measurement required is determined by the
situation.
• Whether to use an underestimate or an overestimate is determined by the
situation.
• Physically measuring objects along with using visual and symbolic
representations improves student understanding of both the concepts and
processes of measurement.
• Multiple experiences with using nonstandard and standard units of
measure to measure physical objects help students develop an intuitive
understanding of size.
• Chunking or benchmarks are strategies used to make measurement
estimates.
• Chunks of length such as a window’s length can be used to estimate the
length of classroom wall.
• Benchmarks such as the two-meter height of a standard doorway can be
used to estimate height.
Page 25
Curriculum Pacing Guide
6th grade
2011 - 2012 Quarter
3
Week 2
Number and Number Sense
SOL 6.2
The student will
a) investigate and describe fractions, decimals and percents
as ratios;
b) identify a given fraction, decimal or percent from a
representation;
c) demonstrate equivalent relationships among fractions,
decimals, and percents; and
d) compare and order fractions, decimals, and percents.
Essential Understandings
• What is the relationship among fractions, decimals and percents?
Fractions, decimals, and percents are three different ways to express the
same number. A ratio can be written using fraction form ( 2
3 ), a colon
(2:3), or the word to (2 to 3). Any number that can be written as a fraction
can be expressed as a terminating or repeating decimal or a percent.
• Understand how the magnitude of a fraction compares to another number
represented by a fraction.
• Understand how to represent the same fraction in multiple ways, using
concrete material, a drawing, a symbol, or a statement.
• Develop strategies to compare, order, and determine equivalency among
fractions and decimals.
• Understand that a percent is a way of representing fractions and decimals.
• Understand that a number can be written as a fraction, decimal, or
percent.
• Understand that percent is a method of standardization that is efficient
because each number is always based on 100ths.
• Understand that percents are used in real-life applications to compare or
describe data.
• Select appropriate methods for computing with rational numbers
according to the context of the problem.
Essential Knowledge and Skills
Instructional Strategies:
• At this point students are working with fractions only – decimals and
percents will come later.
• Comparisons using pictorial representations.
• Construct as many true fractions sentences as possible using 4 digits.
Using the digits 5, 6, 7, and 8:
• Suggested manipulatives: base ten blocks, fraction bars, fraction circles,
decimal squares.
• Examples of real-life situations using estimation strategies include
shopping for groceries, buying school supplies, budgeting allowance,
deciding what time to leave for school or the movies, and sharing a pizza
or the prize money from a contest.
• Have students solve problems involving doubling recipes and/or figuring
out the amount of an ingredient needed in more than one recipe calling
for the same ingredient.
• Students will write problems using manipulative (like compare 5/8 and
0.6) then switch problems with a neighbor to solve.
• Change decimals to fractions by putting the decimal part over the
corresponding place value and reducing.
• Use newspapers and magazines to find equivalent fractions and
decimals.
• Divide students into groups of about 8. Give each student a card with a
decimal on it. Have them order themselves from least to greatest.
Teacher should check. Results can be displayed on a string by attaching
the cards with clothes pins. After they order decimals repeat with just
fractions. Then do with both decimals and fractions together.
• Create a card game. Students should match the equivalent fraction and
decimal.
• Compare equivalent fraction method and proportion method of
conversion.
• Use spreadsheet template to represent fractions on a 10x10 grid and
express fractions as equivalent decimals.
• Use newspapers and magazines to find equivalent fractions, decimals,
and percents.
Open response:
Jarred has two cakes that are the same
size. The first cake was chocolate, which
he cut into 12 equal parts. The second
cake was marble, which he cut into 6
equal parts. His family eats 5 slices of
chocolate cake and 3 slices of marble
cake. Did they eat more chocolate or
marble cake?
Show the decimal 0.8 as a picture
representation and write in fraction
form.
Explain your steps.
Order the numbers 4/5, 0.4, and 3/4
from least to greatest. Explain how you
got your answer. My mom said I could
eat 3/8 of my holiday candy or 0.4 of it.
Which option should I choose and why?
Writing prompts:
John said 5/8 was closer to a half and
Jenny said it was closer to a whole. Who
is correct? Draw a picture and write 3
sentences to support your answer.
For each situation, decide whether the
best estimate is more or less than one
half.
Record your conclusions and reasoning.
1. When pitching, Alan struck out 9 of
the 19 batters.
2. Sidney made 7 out of 17 free throws
3. Steven made 8 field goals out of 11
attempts
4. Kyle made 8 hits in 15 times at bat.
5. Maria only responded to 4 of her 35
text messages.
Have students explain in writing their
process for representing a fraction on a
10x10 grid and how they represent the
same fraction as an equivalent decimal.
Have students explain how to find the
sales tax and tip on a restaurant meal.
Page 26
Curriculum Pacing Guide
6th grade
2011 - 2012
• Identify the decimal and percent equivalents for numbers written in
fraction form including repeating decimals.
• Represent fractions, decimals, and percents on a number line.
• Describe orally and in writing the equivalent relationships among
decimals, percents, and fractions that have denominators that are factors
of 100.
• Represent, by shading a grid, a fraction, decimal, and percent.
• Compare two decimals through thousandths using manipulatives, pictorial
representations, number lines, and symbols (<, ,, ≥≤ >, or =).
• Compare two fractions with denominators of 12 or less using
manipulatives, pictorial representations, number lines, and symbols
(<, ,, ≥≤ >, or =).
• Compare two percents using pictorial representations and symbols
(<, ,, ≥≤ >, =).
• Order no more than 3 fractions, decimals, and percents (decimals through
thousandths, fractions with denominators of 12 or less), in ascending or
descending order.
• Identify, compare, order, and determine equivalent relationships among
fractions and decimals. Decimals are limited to the thousandths place.
• Recognize that percent means “out of 100” or hundredths, using the
percent symbol (%).decimals, and percents. Decimals are limited to the
thousandths place.
• Draw a shaded region on a 10-by-10 grid to represent a given percent.
• Represent in decimal, fraction, and/or percent form a given shaded region
of a 10-by-10 grid.
• Represent a number in fraction, decimal, and percent forms. Fractions will
have denominators of 12 or less.
Teacher Notes
• Percent means “per 100” or how many “out of 100”; percent is another
name for hundredths.
• Use statistics from baseball cards to make comparisons.
• Have students calculate sales tax, tips, and discounts.
• Students bring to class newspaper and magazine clippings which express
the discount on sale items in a variety of ways, including percent off,
fraction off, and dollar amount off. For items chosen from the clippings,
the students discuss which form is the easiest form of expression of
discount, which is most understandable to the consumer, and which
makes the sale seem the biggest bargain.
• Students obtain menus from their favorite restaurants. In groups,
students record what they would like to order and the cost of each item.
Afterwards they are to determine the tax and the tip that they should
leave (using 20%) and the total cost of their meal.
Model Lessons:
Enhanced Scope and Sequence, Grade 6
“Rational Speed Matching”
Enhanced Scope and Sequence, Grade 5
“Order Up!” SOL 5.2
ARI Curriculum Companion
“Comparing and ordering”, p. 9-13
Resources:
Course 1: 3-1, 3-2, 5-5, 5-6, 5-7, 10-4, 10-5, 10-6, 10-7
Course 2: 5-4, 5-5, 5-6, 5-8, 7-5
Understanding Math Software
NCTM Illuminations 6-8
“Fraction Model” I, II, III
Glencoe Teacher’s Resource Kit
Virginia SOL Mathematics Coach Grade 6
SOL-like Multiple Choice:
VDOE Released SOL items (6.2)
Pretests, Posttest, Formative
assessments, Bellwork, Classwork, and
Homework
Page 27
Curriculum Pacing Guide
6th grade
2011 - 2012
• A number followed by a percent symbol (%) is equivalent to that number
with a denominator of 100 (e.g., 30% = 30
100 =
3
10 = 0.3).
• Percents can be expressed as fractions with a denominator of 100 (e.g.,
75% = 75
100 =
3
4 ).
• Percents can be expressed as decimal (e.g., 38% = 38
100 = 0.38).
• Some fractions can be rewritten as equivalent fractions with
denominators of powers of 10, and can be represented as decimals or
percents
(e.g., 3
5 =
610
= 60
100 = 0.60 = 60%).
• Decimals, fractions, and percents can be represented using concrete
materials (e.g., Base-10 blocks, number lines, decimal squares, or grid
paper).
• Percents can be represented by drawing shaded regions on grids or by
finding a location on number lines.
• Percents are used in real life for taxes, sales, data description, and data
comparison.
• Fractions, decimals and percents are equivalent forms representing a
given number.
• The decimal point is a symbol that separates the whole number part from
the fractional part of a number.
• The decimal point separates the whole number amount from the part of a
number that is less than one.
• The symbol • can be used in Grade 6 in place of “x” to indicate
multiplication.
• Fractions may be represented and compared by using fraction
manipulatives, drawings, pictures, or symbols.
• Rational number is the set of numbers that can be written as a ratio or
fraction. Percents, and numbers represented in scientific notation with
positive exponents.
Page 28
Curriculum Pacing Guide
6th grade
2011 - 2012
• Equivalent relationships among fractions and decimals can be determined
by using manipulatives (e.g., fraction bars, base-ten blocks, fraction circles,
graph paper, and calculators).
• Strategies using 0, 1
2 and 1 as benchmarks can be used to compare
fractions.
• When comparing two fractions, use 1
2 as a benchmark. Example: Which
is greater, 4
7 or
3
9?
4
7 is greater than
1
2 because 4, the numerator, represents more than
half of 7, the denominator. The denominator tells the number of parts that
make the whole. 3
9 is less than
1
2 because 3, the numerator, is less than
half of 9, the denominator, which tells the number of parts that make the
whole. Therefore,
4
7 >
3
9.
• When comparing two fractions close to 1, use distance from 1 as your
benchmark. Example: Which is greater, 6 8
?7 9
or 6
7 is
1
7away from 1
whole. 8 1
9 9is away from 1 whole. Since
1 1
7 9> , then
6
7 is a greater
distance away from 1 whole than 8
9so
8 6
9 7> .
• Students should have experience with fractions such as
1
8 , whose
decimal representation is a terminating decimal (e. g.,
1
8 = 0.125) and
Page 29
Curriculum Pacing Guide
6th grade
2011 - 2012
with fractions such as
2
9 , whose decimal representation does not end but
continues to repeat (e. g.,
2
9 = 0.222…). The repeating decimal can be
written with ellipses (three dots) as in 0.222… or denoted with a bar above
the digits that repeat as in 0.2 .
Quarter
3
Week 3
Number and Number Sense
SOL 6.1
The student will describe and compare data, using ratios, and will use
appropriate notations, such as a
b , a to b, and a:b.
Essential Understandings
• What is a ratio?
A ratio is a comparison of any two quantities. A ratio is used to represent
relationships within a set and between two sets. A ratio can be written
using fraction form
( 2
3 ), a colon (2:3), or the word to (2 to 3).
• What is a ratio? A ratio is a comparison of any two quantities. A ratio is
used to represent relationships within a set and between two sets. A ratio
can be written using fraction form, (2/3), a colon (2:3), or the word to (2 to
3).
• What makes two quantities proportional? Two quantities are proportional
when one quantity is a constant multiple of the other.
• Understand that a ratio is a comparison of two quantities.
• Understand that ratios can be represented in more than one way.
Essential Knowledge and Skills
• Describe a relationship within a set by comparing part of the set to the
entire set.
Instructional Strategies:
• Include rates and unit rates.
• Have students in the classroom collect and compare data. For example,
boys to girls, students to teacher, colors of shoes, hair color, eye color,
etc.
• Survey classmates on favorite color and write ratios from results.
• Use ratio tables to solve word problems.
• Working in pairs, have students draw four cards. Use the numbers on
cards to write two different ratios.
• Students will exchange ratios and find equivalent ratios.
• Repeat the activity using different cards.
• Relate proportions to cooking recipes and other everyday things
(doubling, halving, etc.)
Model Lessons:
Enhanced Scope and Sequence, Grade 6
“Field Goals, Balls, and Nets”
ARI Curriculum Companion
“ Ratios and Proportions”, p. 21 – 26
Resources:
Course 1: 10-1, 10-2
Understanding Math Software
Glencoe Teacher ‘s Resource Kit
Virginia SOL Mathematics Coach Grade 6
SOL-like Multiple Choice:
VDOE Released SOL items (6.1)
Pretests, Posttest, Formative
assessments, Bellwork, Classwork, and
Homework
Page 30
Curriculum Pacing Guide
6th grade
2011 - 2012
• Describe a relationship between two sets by comparing part of one set to
a corresponding part of the other set.
• Describe a relationship between two sets by comparing all of one set to all
of the other set.
• Describe a relationship within a set by comparing one part of the set to
another part of the same set.
• Represent a relationship in words that makes a comparison by using the
notations a
b, a:b, and a to b.
• Create a relationship in words for a given ratio expressed symbolically.
• Write proportions that represent equivalent
Teacher Notes
• A ratio is a comparison of any two quantities. A ratio is used to represent
relationships within and between sets.
• A ratio can compare part of a set to the entire set (part-whole
comparison).
• A ratio can compare part of a set to another part of the same set (part-
part comparison).
• A ratio can compare part of a set to a corresponding part of another set
(part-part comparison).
• A ratio can compare all of a set to all of another set (whole-whole
comparison).
• The order of the quantities in a ratio is directly related to the order of the
quantities expressed in the relationship. For example, if asked for the ratio
of the number of cats to dogs in a park, the ratio must be expressed as the
number of cats to the number of dogs, in that order.
• A ratio is a multiplicative comparison of two numbers, measures, or
quantities.
• All fractions are ratios and vice versa.
• Ratios may or may not be written in simplest form.
Page 31
Curriculum Pacing Guide
6th grade
2011 - 2012
• Ratios can compare two parts of a whole.
• Rates can be expressed as ratios.
• A ratio is used to represent a variety of relationships within a set and
between two sets.
• A ratio can be written using a fraction form (2/3), a colon 2:3, or the word
to (2 to 3).
• A proportion can be written as a/c is to b/d, a:b = c:d, or a is to b as c is to
d.
• A proportion can be solved by finding the product of the means and the
product of the extremes. For example, in the proportion a:b = c:d. a and d
are the extremes and b an c are the means. If values are substituted for a,
b, c, and d such as 5:12= 10:24, then the product of extremes (5 x 24) is
equal to the product of the means (12 x 10).
• In a proportional situation, both quantities increase or decrease together.
• In a proportional situation, two quantities increase multiplicatively. Both
are multiplied by the same factor.
• A proportion can be solved by finding equivalent fractions.
Quarter
3
Week 4
Number and Number Sense
SOL 6.4
The student will demonstrate multiple representations of multiplication and
division of fractions.
Essential Understandings
• When multiplying fractions, what is the meaning of the operation?
When multiplying a whole by a fraction such as 3 x 1
2 , the meaning is the
same as with multiplication of whole numbers: 3 groups the size of 1
2 of
the whole. When multiplying a fraction by a fraction such as 2 3
3 4⋅ , we are
asking for part of a part. When multiplying a fraction by a whole number
Instructional Strategies:
• Non-calculator section of Math 6 SOL test includes questions from all
standards within the Computation and Estimation reporting category.
• Students, working in groups, explore fraction multiplication and division.
They use fraction circles and fraction bars to solve problems, such as,
“What is the fairest way to divide four cakes among five people?” Next,
they write in their math journal about the methods they used and the
reasons they believe their answers to be correct.
Model Lessons:
Enhanced Scope and Sequence, Grade 6
“Modeling Multiplication of Fractions,”
“Modeling Division of Fractions.”
Resources:
Course 1: 7-2a, 7-4a
Understanding Math Software
Open response:
A factory used 3/5 of a barrel of almonds
to make 6 batches of granola bars. How
many barrels of almonds did the factory
put in each batch? Sara’s lemon cookie
recipe calls for 2 2/3 cups of sugar. How
much sugar would Sara need to make
1/3 of a batch of cookies? Jan is baking.
She needs 4 cups of sugar. Her problem
is that she only has a ½ measuring cup
and a ¾ measuring cup. What is the least
number of scoops that she could make in
order to get 4 cups?
Writing prompts:
Explain why the product of two fractions,
such as ½ x ½ is less than each fraction.
Draw a picture and use at least 3
sentences to explain your answer.
SOL-like Multiple Choice:
Page 32
Curriculum Pacing Guide
6th grade
2011 - 2012
such as 1
2 x 6, we are trying to find a part of the whole.
• What does it mean to divide with fractions?
For measurement division, the divisor is the number of groups and the
quotient will be the number of groups in the dividend. Division of fractions
can be explained as how many of a given divisor are needed to equal the
given dividend. In other words, for 1 2
4 3÷ the question is, “How many
2
3 make
1
4?”
For partition division the divisor is the size of the group, so the quotient
answers the question, “How much is the whole?” or “How much for one?”
• How are multiplication and division of fractions and multiplication and
division of whole numbers alike? Fraction computation can be approached
in the same way as whole number computation, applying those concepts
to fractional parts.
• What is the role of estimation in solving problems? Estimation helps
determine the reasonableness of answers.
• Understand that fraction computation uses the same ideas a whole-
number computation, applying those concepts to fractional parts.
Essential Knowledge and Skills
• Demonstrate multiplication and division of fractions using multiple
representations.
• Model algorithms for multiplying and dividing with fractions using
appropriate representations.
• Multiply and divide with fractions and mixed numbers. Answers are
expressed in simplest form.
• Solve single-step and multistep practical problems that involve
multiplication and division with fractions and mixed numbers that include
denominators of 12 or less. Answers are expressed in simplest form.
Teacher Notes
Glencoe Teacher’s Resource Kit
Virginia SOL Mathematics Coach Grade 6
VDOE Released SOL items (6.4)
Pretests, Posttest, Formative
assessments, Bellwork, Classwork, and
Homework
Page 33
Curriculum Pacing Guide
6th grade
2011 - 2012
• Using manipulatives to build conceptual understanding and using pictures
and sketches to link concrete examples to the symbolic enhance students’
understanding of operations with fractions and help students connect the
meaning of whole number computation to fraction computation.
• Multiplication and division of fractions can be represented with arrays,
paper folding, repeated addition, repeated subtraction, fraction strips,
pattern blocks and area models.
• When multiplying a whole by a fraction such as 3 x 1
2 , the meaning is
the same as with multiplication of whole numbers: 3 groups the size of 1
2
of the whole.
• When multiplying a fraction by a fraction such as 2 3
3 4⋅ , we are asking for
part of a part.
• When multiplying a fraction by a whole number such as 1
2 x 6, we are
trying to find a part of the whole.
• For measurement division, the divisor is the number of groups. You want
to know how many are in each of those groups. Division of fractions can
be explained as how many of a given divisor are needed to equal the given
dividend. In other words, for 1 2
4 3÷ , the question is, “How many
2
3
make1
4?”
• For partition division the divisor is the size of the group, so the quotient
answers the question, “How much is the whole?” or “How much for one?”
• Using an area model assists with students’ developing understanding of
multiplication and division of fractions.
• Simplifying fractions to simplest form assists with uniformity of answers.
• It is helpful for students to simplify before they multiply fractions, using
the commutative property of multiplication to reduce fractions to simplest
form before multiplying.
Page 34
Curriculum Pacing Guide
6th grade
2011 - 2012 Quarter
3
Week 5
Computation and Estimation
SOL 6.6
The student will
a) multiply and divide fractions and mixed numbers; and
b) estimate solutions and then solve single-step and
multistep practical problems involving addition,
subtraction, multiplication, and division of fractions.
Essential Understandings
• How are multiplication and division of fractions and multiplication and
division of whole numbers alike? Fraction computation can be approached
in the same way as whole number computation, applying those concepts
to fractional parts.
• What is the role of estimation in solving problems? Estimation helps
determine the reasonableness of answers.
• Understand that fraction computation uses the same ideas as whole-
number computation, apply those concepts to fractional parts.
Essential Knowledge and Skills
• Multiply and divide with fractions and mixed numbers. Answers are
expressed in simplest form.
• Solve single-step and multistep practical problems that involve addition
and subtraction with fractions and mixed numbers, with and without
regrouping, that include like and unlike denominators of 12 or less.
Answers are expressed in simplest form.
• Solve single-step and multistep practical problems that involve
multiplication and division with fractions and mixed numbers that include
denominators of 12 or less. Answers are expressed in simplest form.
• Convert fractions to equivalent forms to perform the operations of
addition and subtraction.
• Simplify fractional answers to simplest form.
Teacher Notes
Instructional Strategies:
• Have students solve problems involving doubling recipes and/or figuring
out the amount of an ingredient needed in more than one recipe calling
for the same ingredient. (Example: How much flour will be needed to
make to batches of chocolate chip cookies and one batch of oatmeal
cookies?)
• Give students a recipe and have them make enough for different
number of servings. (Ex. The recipe makes 4 servings. Ask them to make
enough for 12 people.)
• Non-calculator section of Math 6 SOL test includes questions from all
standards with the Computation and Estimation reporting category.
• Use the area model to introduce concept.
• Work with fraction computation is divided into two weeks to allow more
time for mastery.
• Using manipulatives such as circle diagrams, pattern blocks grid paper,
and fraction bars help to build conceptual understanding and using
pictures and sketches to link concrete examples to the symbolic enhance
students’ understanding of operations with fractions and help students
connect the meaning of whole-number computation to fraction
computation.
Model Lessons:
Enhanced Scope and Sequence, Grade 6
“Modeling Multiplication of Fractions,”
“Modeling Division of Fractions.”
Resources:
Course 1: 5-3, 6-3, 6-4, 6-5, 6-6, 7-2, 7-3, 7-4, 7-5
Understanding Math Software
Glencoe Teacher’s Resource Kit
Virginia SOL Mathematics Coach Grade 6
Open response:
List 3 different fraction pairs that can be
combined to produce a whole number.
Explain how you know they will result in
a whole number. To design an outfit, you
need 5 ½ yards of fabric, but you only
have 2 2/3 yards. How do you know how
much fabric to buy, and what special
considerations should you take into
account? Compare adding and
subtracting fractions to adding and
subtracting whole numbers. Give several
examples to support your comparison.
A recipe for cookies calls for 2/3 cups of
sugar. If I want to make three batches of
cookies, should I double or triple the
recipe? Explain.
Writing prompts:
What are some instances that an exact
sum or difference is needed rather than
an estimate?
On the 2007 SOL test, 12 year olds were
given the following question:
Estimate the answer to 14/15 + 9/10.
A 1
B 2
C 23
D 25
27% of the students answered correctly,
with approximately equal numbers of
students choosing each of the wrong
answers. Explain what the thinking was
behind each of the choices.
I have a board that is 2 ¾ feet long. I
need to cut it so it will make a shelf that
is 1 4/5 feet long. I cut off 1 foot. Did I
cut off too much or too little? Explain
and include the correct amount to cut
off.
SOL-like Multiple Choice:
VDOE Released SOL items (6.6)
Page 35
Curriculum Pacing Guide
6th grade
2011 - 2012
• Simplifying fractions to simplest form assists with uniformity of answers.
• Addition and subtraction are inverse operations as are multiplication and
division.
• It is helpful to use estimation to develop computational strategies. For
example,
7 32
8 4⋅ is about
3
4 of 3, so the answer is between 2 and 3.
• When multiplying a whole by a fraction such as 1
32
⋅ , the meaning is the
same as with multiplication of whole numbers: 3 groups the size of 1
2 of
the whole.
• When multiplying a fraction by a fraction such as 2 3
3 4⋅ , we are asking for
part of a part.
• When multiplying a fraction by a whole number such as 1
62
⋅ , we are
trying to find a part of the whole.
• Equivalent forms are needed to perform the operations of addition and
subtraction of fractions.
• Rewriting an improper fraction as a mixed numeral assists with uniformity
of answers and concepts.
• There is an implied addition of the whole number part and the fractional
part in mixed numerals.
• Using manipulatives to build conceptual understanding and using pictures
and sketches to link concrete examples to the symbolic enhances
students’ understanding of operations with fractions and helps students
connect the meaning of whole-number computation of fraction
computation.
Pretests, Posttest, Formative
assessments, Bellwork, Classwork, and
Homework
Page 36
Curriculum Pacing Guide
6th grade
2011 - 2012 Quarter
3
Week 6
Computation and Estimation
SOL 6.7
The student will solve single-step and multistep practical problems involving
addition, subtraction, multiplication, and division of decimals.
Essential Understandings
• What is the role of estimation in problem solving? Estimation gives a
reasonable solution to a problem when an exact answer is not required. If
an exact answer is required, estimation allows you to know if the
calculated answer is reasonable.
• Understand how mathematics relates to problems in daily life.
• Understand how to represent problems within various contexts.
• Understand the importance of planning and maintaining a budget.
Essential Knowledge and Skills
• Solve single-step and multistep practical problems involving addition,
subtraction, multiplication and division with decimals expressed to
thousandths with no more than two operations.
• Determine essential information necessary, including the operations
required to solve consumer application problems.
• Solve one step and multi-step consumer application problems involving
whole numbers, fractions with denominators not greater than 12 and
decimals.
• Represent the solution as a data table or graph.
• Present and justify the solution orally or in writing.
Teacher Notes
• Estimation and checking the reasonableness of a result enhances
computational proficiency.
• Various estimation strategies, such as front-end, compatible numbers, or
rounding, are effective for various operations and situations.
• Understanding the placement of the decimal point is very important when
Instructional Strategies:
• Teach students to look for compatible numbers as an estimation
strategy. Using a grocery store ad, find two items whose total is about
$2, $3, or $5.
• Students imagine they are in line at a checkout counter at a grocery
store. Give students a $25.00 spending limit and a list of items which has
a cost that is over the limit. Students estimate the total cost and, then,
determine which products to drop from the list to get below the limit by
rounding the prices to the nearest dollar.
• Use grid paper to make decimal models to show division of decimals.
• Use grid paper when solving decimal division to help students line up
decimal.
• Using catalogs or newspaper ads have students estimate the cost of
buying a certain number of items, including some multiple items (i.e. 3
gallons of milk, 2 boxes of cereal, and a half gallon of orange juice).
• Solving multi-step problems in the context of all real-life situations
enhances interconnectedness and proficiency with estimation strategies.
• Use simple fractions (1/2, 1/3, 1/4) in consumer applications, i.e., ½ off
of a $90.00 coat, ¼ of a budgeted amount, etc.
• Examples of practical situations solved by using estimation strategies
include shopping for groceries, buying school supplies, budgeting an
allowance, deciding what time to leave for school or the movies, and
sharing a pizza or the prize money from a contest.
• Include real-life application problems involving money, travel, work,
recreation, and home life.
• Give students catalogs and get them to make their own two-step
decimal problem. (Ex. Choose school supplies that you need for the
semester for a $20 budget.)
• Make sure to include real world problems displayed in charts graphs and
tables.
• Students should display their answers in many different forms (charts,
graphs, tables, and paragraph).
Model Lessons:
Enhanced Scope and Sequence, Grade 6
Open response:
You want to purchase three items at a
store for $4.43, $5.42, and $6.45. You
have $16. Estimate the total cost by
rounding the cost of each item to the
nearest dollar. Will you have a problem
making this purchase? Explain. Compare
to the actual cost of the three items.
How are the steps similar/different when
dividing by a whole number verses a
decimal?
How much money will you need to bring
to the movies if you plan to buy a ticket
for you and your friend, drinks, and
snacks? Research online to find current
prices.
You and two friends sold lemonade
during a yard sale and made $47.35.
Your expenses were $12.85. About how
much money will each friend get if you
share your earnings equally? Explain
your results.
Writing prompts:
Sally has $7.45 to spend on crayons for
his class. If each box of crayons cost 25
cents, how many boxes can he buy?
Justify your answer.
When are estimates more useful or
descriptive than exact answers?
Use grocery store advertisements to
estimate a budget for food for a birthday
party. Spend less than $5 per person.
Explain your choices.
SOL-like Multiple Choice:
VDOE Released SOL items (SOL 6.7)
Pretests, Posttest, Formative
assessments, Bellwork, Classwork, and
Homework
Page 37
Curriculum Pacing Guide
6th grade
2011 - 2012 finding quotients of decimals. Examining patterns with successive decimals
provides meaning, such as dividing the dividend by 6, by 0.6, by 0.06, and
by 0.006.
• Solving multistep problems in the context of real-life situations enhances
interconnectedness and proficiency with estimation strategies.
• Examples of practical situations solved by using estimation strategies
include shopping for groceries, buying school supplies, budgeting an
allowance, deciding what time to leave for school or the movies, and
sharing a pizza or the prize money from a contest.
• A consumer application problem is defined as the type of problem that is
normally encountered in daily living, such as, but not limited to, money,
travel, work, recreation, and home life.
• A budget may be kept for short or long periods of time. Students may
keep a short-term budget to enable the purchase of an expensive item or
a long-term budget to facilitate a long-term spending plan.
“Practical Problems Involving Decimals,”
Understanding Math Software
Resources:
Glencoe Course 1: 1-1, 1-7a, 3-4, 3-5, 3-5b, 4-2, 4-4
Glencoe Teacher’s Resource Kit
Virginia SOL Mathematics Coach Grade 6
Quarter
3
Week 7
Number and Number Sense
SOL 6.3
The student will
a) identify and represent integers;
b) order and compare integers; and
c) identify and describe absolute value of integers.
Essential Understandings
• What role do negative integers play in practical situations?
Some examples of the use of negative integers are found in temperature
(below 0), finance (owing money), below sea level. There are many other
examples.
• How does the absolute value of an integer compare to the absolute value
of its opposite? They are the same because an integer and its opposite are
the same distance from zero on a number line.
• Understand how to identify, represent, order and compare integers.
• Understand that an integer and its opposite are the same distance from
zero.
Instructional Strategies:
• Whole numbers may be represented and compared by using whole
number manipulatives, drawings, pictures, and symbols.
• Suggested manipulatives: laminated number lines showing -20 to +20,
game markers
• Have students work in groups to investigate integers. Give each group a
number line showing -20 to +20 and a deck of cards with the face cards
removed. Each student places a different color marker on zero. As the
student is dealt a card face up, the student moves that number of
places: red is negative, black is positive. The first student to reach -20 or
+20 wins.
• Students create a Celsius thermometer naming the temperature as
positive and negative integers. Give students diagrams of thermometers
with missing negative and positive integers, and have them fill it in.
• Suggestions for curriculum integration are: Health- body temperatures,
Geography- longitude and latitude, elevation, Physical Science- electrical
charges.
• Students are assigned an integer value from -20 to +20 and create a
human number line. Ask questions about absolute value, opposites,
greater than/less than or equal to, etc.
Open response:
Explain why any negative integer is less
than any positive integer.
Writing prompts:
Dan went on a diving trip. He dove 20
feet below sea level to the top of a
sunken ship. He then floated up towards
a fish that was five feet above the
sunken ship. Finally he dove down to the
floor of the lake which was fifteen feet
below the fish. Draw a picture, using
integers, to display his dive. Extension:
How many feet below sea level is the
bottom of the lake?
Compare a number line to a
thermometer. How are they alike? How
are they different?
SOL-like Multiple Choice:
VDOE Released SOL items (6.3)
Pretests, Posttest, Formative
assessments, Bellwork, Classwork, and
Page 38
Curriculum Pacing Guide
6th grade
2011 - 2012 Essential Knowledge and Skills
• Identify an integer represented by a point on a number line.
• Represent integers on a number line.
• Order and compare integers using a number line.
• Compare integers, using mathematical symbols (<, >, =).
• Identify and describe the absolute value of an integer.
• Demonstrate absolute value using a number line.
• Determine the absolute value of a rational number.
Teacher Notes
• Integers are the set of whole numbers, their opposites, and zero.
• Positive integers are greater than zero.
• Negative integers are less than zero.
• Zero is an integer that is neither positive nor negative.
• A negative integer is always less than a positive integer.
• When comparing two negative numbers, the negative number that is
closer to zero is greater.
• An integer and its opposite are the same distance from zero on a number
line. For example, the opposite of 3 is -3.
• On a conventional number line, a smaller number is always located to the
left of a larger number (e.g., –7 lies to the left of –3; thus –7 < –3; 5 lies to
the left of 8 thus 5 is less than 8).
• Comparison between integers can be made by using the mathematical
symbols: < (less than), > (greater than), or = (equal to).
• The absolute value of a number is the distance of a number from zero on
the number line regardless of direction. Absolute value is represented as
|-6| = 6.
Model Lessons:
Enhanced Scope and Sequence, Grade 6
“Ground Zero”
Enhanced Scope and Sequence, Grade 8
“Organizing Numbers”, SOL 8.2
ARI Curriculum Companion
“Integers”, p. 13-19
Resources:
Course 1: 8-1
Course 2: 3-1
Venn Diagram Example
NCTM Illuminations 6-8
“Pan Balance Shapes”
Glencoe Teacher’s Resource Kit
Understanding Math Software
Virginia SOL Mathematics Coach Grade 6
Homework
Integers
Whole
Natural
Page 39
Curriculum Pacing Guide
6th grade
2011 - 2012 Quarter
3
Week 8
Number and Number Sense
SOL 6.5
The student will investigate and describe concepts of positive exponents and
perfect squares.
Essential Understandings
• What does exponential form represent?
Exponential form is a short way to write repeated multiplication of a
common factor such as
5 x 5 x 5 x 5 = 54
.
• What is the relationship between perfect squares and a geometric square?
A perfect square is the area of a geometric square whose side length is a
whole number.
• How is taking a square root different from squaring a number? Squaring a
number and taking a square root are inverse operations.
• Understand that a power of a number is repeated multiplication of that
number by itself.
Essential Knowledge and Skills
• Recognize and describe patterns with exponents that are natural numbers
by using a calculator.
• Recognize and describe patterns of perfect squares, not to exceed 202, by
using grid paper, square tiles, tables, and calculators.
• Recognize and describe patterns with square roots and squares by using
squares, grid paper, and calculators.
• Recognize powers of ten by examining patterns in a place-value chart: 104
= 10,000, 103 = 1000, 10
2 = 100, 10
1 = 10, 100 = 1.
• Determine the square root of a perfect square less than or equal to 400.
• Write scientific notation for a number greater than 10.
Teacher Notes
Instructional Strategies
• Have students explore the exponent key, the x^ 2 key, and the square
root key on a calculator. Students are encouraged to define the function
of each key.
• Students will work in groups using a number cube, and a 0-9 spinner to
express numbers in exponent form. One student will toss the cube to get
a number that all students will use as an exponent. Another student will
spin the spinner to get three different numbers. Each student will then
use any combination of the numbers with the exponent to write the
largest possible number. The student(s) to write the largest possible
number wins a point.
• Create a 9 or 16 square puzzle. The matching edges of the individual
squares should represent exponent form, standard form, and square
roots, and perfect squares. Give students the pieces of the puzzle cut
apart and ask them to arrange the pieces so that edges are equivalent.
• Apply prior knowledge of patterns to: powers of 10, exponents, and
square roots.
• Play BINGO. Students find numbers on the card that are equal to the
power called by the teacher.
• Write square and square root problems on a beach ball. Students catch
the ball and evaluate the problem under their right thumb.
• Have students use an almanac, astronomical chart, internet, or other
source to find and create a chart listing numbers, in both standard form
and scientific notation, such as, population, distances to planets, etc.
Model Lessons:
Enhanced Scope and Sequence, Grade 6
“Perfecting Squares,”
ARI Curriculum Companion
“Patterns, Functions, and Algebra”, p. 38-42(powers of
10, exponents)
“Patterns, Functions, and Algebra”, p. 43-48(squares and
square roots)
“Patterns, Functions, and Algebra”, p. 54-58(scientific notation)
Resources:
Course 1: 1-4, 4-1
Course 2: 1-9, 11-1
Open Response
Evaluate 10³, 104, 10
5, and 10
6. Explain
how you can evaluate 1020 without
using a calculator.
Explain how finding the square of a
number is like finding the area of a
square.
Writing prompts:
Write a short paragraph to explain why
expressions like 107 are written with
exponents.
Explain how finding the square of a
number is like finding the area of a
square.
SOL-like Multiple Choice:
VDOE Released SOL items (6.5)
Pretests, Posttest, Formative
assessments, Bellwork, Classwork, and
Homework
Page 40
Curriculum Pacing Guide
6th grade
2011 - 2012
• In exponential notation, the base is the number that is multiplied; the
exponent represents the number of times the base is used as a factor. In
83, 8 is the base and 3 is the exponent.
• A power of a number represents repeated multiplication of the number
(e.g., 83 = 8 · 8 · 8 and is read “8 to the third power”).
• Any real number (other than zero) raised to the zero power is 1. Zero to
the zero power (0) is undefined.
• Perfect squares are numbers that result from multiplying any whole
number by itself, i.e. 36 = 6 x 6.
• Perfect squares may be represented geometrically as the areas of squares
the length of whose sides are whole numbers, i.e., 1 x 1, 2 x 2, or 3 x 3.
This can be modeled with grid paper, tiles, geoboards, and virtual
manipulatives.
• A square root of a number is a number which, when multiplied by itself,
produces the given number, i.e., the square root of 49 is 7 since 7 x 7 = 49.
• The square root of a number can be represented geometrically as the
length of a side of the square.
• Patterns in place-value charts provide visual meaning of exponents: 103 =
1000, 102 = 100, 10
1 = 10.
• Scientific notation for a number is expressed by writing the number as a
number greater than or equal to 1 but less than 10 times a power of 10,
e.g., 3.2 x 103 is scientific notation for 3,200.
Understanding Math Software
Glencoe Teacher’s Resource Kit
Virginia SOL Mathematics Coach Grade 6
Quarter
3
Week 9
Review SOLs for Benchmark Use old Release tests from past years Benchmark 3 (SIMS) Assessment
(March 22 – 28)
Quarter
4
Week 1
Computation and Estimation
SOL 6.8
The student will evaluate whole number numerical expressions, using the order
of operations.
Essential Understandings
• What is the significance of the order of operations? The order of
Instructional Strategies:
• Non-calculator section of Math 6 SOL test includes questions from all
standards within the Computation and Estimation reporting category.
• Use whole numbers and benchmark decimals only at this point.
• Mnemonic devices (i.e. PEMDAS)
• Create a list of real-life situations where order matters (i.e., cooking, car
Open response:
Using each of the numbers 1, 2, 3, and 4
only once, any or all of the four
operations and grouping symbols if
necessary, write expressions that equal
1, 2, 3 and 4.
SOL-like Multiple Choice:
VDOE Released SOL items (6.8)
Page 41
Curriculum Pacing Guide
6th grade
2011 - 2012 operations prescribes the order to use to simplify expressions containing
more than one operation. It ensures that there is only one correct answer.
• Understand that the order of operations describes the order to use to
simplify expressions containing more than one operation.
• Select appropriate strategies and tools to simplify expressions.
• Understand that whole numbers, fractions, and decimals are rational
numbers.
• Simplify expressions with whole numbers by using the order of operations
in a demonstrated sep-by-step approach. The expressions should be
limited to positive values and not include braces { } or absolute value | |.
• Find the value of numerical expressions, using order of operations, mental
mathematics, and appropriate tools. Exponents are limited to positive
values.
Essential Knowledge and Skills
• Simplify expressions by using the order of operations in a demonstrated
step-by-step approach. The expressions should be limited to positive
values and not include braces { } or absolute value | |.
• Find the value of numerical expressions, using order of operations, mental
mathematics, and appropriate tools. Exponents are limited to positive
values.
Teacher Notes
• An expression, like a phrase, has no equal sign.
• Expressions are simplified by using the order of operations.
• The order of operations is a convention that defines the computation
order to follow in simplifying an expression.
• The order of operations is as follows:
� First, complete all operations within grouping symbols. If there are
grouping symbols within other grouping symbols, do the innermost
operation first.
� Second, evaluate all exponential expressions.
repair work, structural designs, getting ready for school).
Model Lessons:
Enhanced Scope and Sequence, Grade 6
“Order Up!”
ARI Curriculum Companion
“Order of operations and Properties”, p. 2
Resources:
Course 2: 1-3
Glencoe Teacher’s Resource Kit
Virginia SOL Mathematics Coach Grade 6
Pretests, Posttest, Formative
assessments, Bellwork, Classwork, and
Homework
Page 42
Curriculum Pacing Guide
6th grade
2011 - 2012
� Third, multiply and/or divide in order from left to right.
� Fourth, add and/or subtract in order from left to right.
• Parentheses ( ), brackets [ ], braces {}, and the division bar – as in
3 4
5 6
+
+
should be treated as grouping symbols.
• The power of a number represents repeated multiplication of the number
(e.g., 83 = 8 · 8 · 8). The base is the number that is multiplied, and the
exponent represents the number of times the base is used as a factor. In
the example, 8 is the base, and 3 is the exponent.
• Any number, except 0, raised to the zero power is 1. Zero to the zero
power is undefined
Quarter
4 Week
2
Geometry
SOL 6.12
The student will determine congruence of segments, angles, and polygons.
Essential Understandings
• Given two congruent figures, what inferences can be drawn about how the
figures are related? The congruent figures will have exactly the same size
and shape.
• Given two congruent polygons, what inferences can be drawn about how
the polygons are related? Corresponding angles of congruent polygons
will have the same measure. Corresponding sides of congruent polygons
will have the same measure.
• How do polygons that are similar compare to polygons that are
congruent?
• Congruent polygons are the same size and shape.
• Similar polygons have the same shape, and corresponding angles between
the similar figures are congruent. However, the lengths of the
corresponding sides are proportional. All congruent polygons are
considered similar with the ratio of corresponding sides being 1:1.
• Understand the meaning of congruence.
• Understand that similar geometric figures have the same shape but have
Instructional Strategies:
• Review proportions and ratios.
• Indirect measurement should be incorporated.
• Suggested manipulatives: rulers, cards stock paper for cutting out similar
shapes, grid paper for dilations, tracing paper, compass, and protractors.
• Using magazines have students look for examples of congruent figures
that are the same size and shape.
• Students use a straightedge to draw a picture (e.g., houses, books,
boxes, etc.). Only straight line segments that connect to form angles may
be used. Next, students exchange pictures with each other and, then,
attempt to duplicate their partner’s drawing. The compass is used to
construct line segments and angles that are congruent to those in their
partner’s drawing. Each student tries to make the drawing as close to the
original as they can. Finally students compare the copy with the original
to see how well they did.
• Create and compare scale drawings.
• Give each student two rectangular cards of different size to see if they
are similar. Have the students measure the cards in inches and compare
the two ratios to see if they are equal. If they are not similar, have
students cut one of the cards so they are similar. This can also be done
with triangles.
Writing prompts:
Compare and contrast various segments.
Compare and contrast various angles.
SOL-like Multiple Choice:
VDOE Released SOL items (6.12)
Pretests, Posttest, Formative
assessments, Bellwork, Classwork, and
Homework
Page 43
Curriculum Pacing Guide
6th grade
2011 - 2012 different sizes.
• Understand how ratios and proportions can be used to determine the
length of something that cannot be measured directly.
Essential Knowledge and Skills
• Characterize polygons as congruent and noncongruent according to the
measures of their sides and angles.
• Determine the congruence of segments, angles, and polygons given their
attributes.
• Draw polygons in the coordinate plane given coordinates for the vertices;
use coordinates to find the length of a side joining points with the same
first coordinate or the same second coordinate. Apply these techniques in
the context of solving practical and mathematical problems.
• Identify corresponding sides and corresponding angles of similar figures
using the traditional notation of curved lines for the angles.
• Determine if quadrilaterals or triangles are similar by examining the
congruence of corresponding angles and proportionality of corresponding
sides.
• Write proportions to express the relationships between the lengths of
corresponding sides of similar figures.
• Given two similar figures, write similarity statements using symbols such
as ΔABC ≈ ΔDEF, angle A corresponds to angle D, and AB corresponds to
DE.
Teacher Notes
• Congruent figures have exactly the same size and the same shape.
• Noncongruent figures may have the same shape but not the same size.
• The symbol for congruency is ≅ .
• The corresponding angles of congruent polygons have the same measure,
and the corresponding sides of congruent polygons have the same
measure.
• The determination of the congruence or noncongruence of two figures can
Model Lessons:
Enhanced Scope and Sequence, Grade 6
“Side to Side”
Resources:
Course 1: 13-3a, 13-6
Glencoe Teacher’s Resource Kit
Understanding Math Software
Virginia SOL Mathematics Coach Grade 6
Page 44
Curriculum Pacing Guide
6th grade
2011 - 2012 be accomplished by placing one figure on top of the other or by comparing
the measurements of all sides and angles.
• Construction of congruent line segments, angles, and polygons helps
students understand congruency.
• Two polygons are similar if corresponding (matching) angles are congruent
and the lengths of corresponding sides are proportional.
• Congruent polygons are a special type of similar polygons; the ratio of the
corresponding sides is 1:1.
Page 45
Curriculum Pacing Guide
6th grade
2011 - 2012 Quarter
4
Week 3
Geometry
SOL 6.13
The student will describe and identify properties of quadrilaterals.
Essential Understandings
• Can a figure belong to more than one subset of quadrilaterals?
• Any figure that has the attributes of more than one subset of
quadrilaterals can belong to more than one subset. For example,
rectangles have opposite sides of equal length. Squares have all 4 sides of
equal length thereby meeting the attributes of both subsets.
• Understand that plane figures are identified and described by their
similarities, differences, and defining properties.
• Understand that plane figures are classified by their defining properties.
• Understand that quadrilaterals can be classified according to the attributes
of their sides and/or angles.
• Understand that a quadrilateral can belong to one or more subsets of the
set of quadrilaterals.
• Understand that every quadrilateral in a subset has all of the defining
attributes of the subset. (If a quadrilateral is a rhombus, it has all the
attributes of a rhombus.)
• Understand the meaning of prefixes associated with the number of sides
of a polygon.
Essential Knowledge and Skills
• Sort and classify polygons as quadrilaterals, parallelograms, rectangles,
trapezoids, kites, rhombi, and squares based on their properties.
Properties include number of parallel sides, angle measures and number
of congruent sides.
• Identify the sum of the measures of the angles of a quadrilateral as 360°.
• Classify and draw triangles, quadrilaterals, pentagons, hexagons,
heptagons, octagons, nonagons, and decagons, using a variety of tools.
• Identify by the number of sides or number of angles the following
polygons: pentagon, hexagon, heptagon, octagon, nonagon, and decagon.
Instructional Strategies:
• Emphasize key vocabulary.
• Emphasize deductive reasoning. (Given what you know, what does that
tell you?)
• Use Venn Diagrams and concept maps for classification.
• Have students work with a partner. Each partner describes a triangle or
quadrilateral according to its characteristics. The other partner must
model the figure described using a rubber band and a geo-board.
• Students take turns describing and modeling.
• Suggested manipulatives: A selection of quadrilateral shapes that can be
sorted by characteristics, geo-strips, geo-boards.
• Use a variety of manipulatives to construct examples of polygons.
• Have students make mobiles displaying polygons from 3 to 10 sides.
They may use any resources that they want including poster board,
wood, string, etc.
Model Lessons:
Enhanced Scope and Sequence, Grade 6
“Exploring Quadrilaterals,”
ARI Curriculum Companion
“Polygons” p. 2-11, 80-92
“Classifying Angles” p. 41-50
Resources:
Course 1: 13-4
Understanding Math Software
Glencoe Teacher’s Resource Kit
Virginia SOL Mathematics Coach Grade 6
Writing prompts:
Compare and contrast various
quadrilaterals.
Compare and contrast various plane
figures.
SOL-like Multiple Choice:
VDOE Released SOL items (6.13)
Pretests, Posttest, Formative
assessments, Bellwork, Classwork, and
Homework
Page 46
Curriculum Pacing Guide
6th grade
2011 - 2012
• Classify and describe the similarities and differences in sets of triangles by
sorting.
• Classify a triangle based on the size of its angles and/or its sides.
• Determine that the sum of the measures of the angles of a triangle is 180°.
• Identify the classification(s) to which a quadrilateral belongs. (Include
classification by pairs of parallel sides.)
• Classify quadrilaterals, using deductive reasoning and inference.
Teacher Notes
• A quadrilateral is a closed planar (two-dimensional) figure with four sides
that are line segments.
• A parallelogram is a quadrilateral whose opposite sides are parallel and
opposite angles are congruent.
• A rectangle is a parallelogram with four right angles.
• Rectangles have special characteristics (such as diagonals are bisectors)
that are true for any rectangle.
• To bisect means to divide into two equal parts.
• A square is a rectangle with four congruent sides or a rhombus with four
right angles.
• A rhombus is a parallelogram with four congruent sides.
• A trapezoid is a quadrilateral with exactly one pair of parallel sides. The
parallel sides are called bases, and the nonparallel sides are called legs. If
the legs have the same length, then the trapezoid is an isosceles
trapezoid.
• A kite is a quadrilateral with two pairs of adjacent congruent sides. One
pair of opposite angles is congruent.
• Quadrilaterals can be sorted according to common attributes, using a
variety of materials.
• Quadrilaterals can be classified by the number of parallel sides: a
parallelogram, rectangle, rhombus, and square each have two pairs of
parallel sides; a trapezoid has only one pair of parallel sides; other
Page 47
Curriculum Pacing Guide
6th grade
2011 - 2012 quadrilaterals have no parallel sides.
• Quadrilaterals can be classified by the measures of their angles: a
rectangle has four 90° angles; a trapezoid may have zero or two 90°
angles.
• Quadrilaterals can be classified by the number of congruent sides: a
rhombus has four congruent sides; a square, which is a rhombus with four
right angles, also has four congruent sides; a parallelogram and a rectangle
each have two pairs of congruent sides.
• A square is a special type of both a rectangle and a rhombus, which are
special types of parallelograms, which are special types of quadrilaterals.
• The sum of the measures of the angles of a quadrilateral is 360°.
• A chart, graphic organizer, or Venn Diagram can be made to organize
quadrilaterals according to attributes such as sides and/or angles.
Page 48
Curriculum Pacing Guide
6th grade
2011 - 2012 Quarter
4
Week 4-
8
Review SOLs for end of year SOL Testing Instructional Strategies:
• Give students a recently past release test to complete. Identify areas of
weakness (include those from past benchmark tests). Review all class
weaknesses in whole group. Address individual weaknesses in small
groups.
• Utilize Glencoe Virginia Standards of Learning Assessment Practice for
SOL skills using old SOL numbers and crosswalk.
• Utilize Virginia SOL Mathematics Coach for practice of weak skills in
small groups by identified students based on past performance on
Benchmarks.
Posttest, 2009/2010 Release test,
Formative assessments, Bellwork,
Homework, Classwork
Final SOL Test in May