Language Arts Curriculum Guide … Curriculum Guides files... · Web viewSolve simple addition word problems Write number sentences using addition Determine what operation is needed
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For Learning; Given a die, or number spinner. The student will make 5 random 5-digit numbers. The student will then write, read, and order the numbers from the greatest to least.
When students are discussing math they will be assessed on their appropriate use of vocabulary.
Of Learning: RIT 181-190RIT 191-200RIT 201-210
A group of 4 students will use a 5 digit flip chart to read write and compare whole numbers to ten thousands. Students will write the numbers in expanded form.
Students will write math vocabulary words and definitions down in math journal. Appropriate vocabulary includes: numerator, denominator, ones, tens, hundreds, thousands, decimal point, place value, greatest and least, expanded notation.
287.01.b Learning
Continuum
Math BenchmarkTeacher
For Learning:Using colored markers the student will high light the thousands place in red, the hundreds place in yellow, the tens place in green, and the ones in blue.
Using a 5 number flip chart the student will create a 5-digit number and then write the number in expanded form.
Students will write math vocabulary words and definitions down in math journal. Appropriate vocabulary includes: numerator, denominator, ones, tens, hundreds, thousands, decimal point, place value, greatest and least, and expanded notation.Using the vocabulary words students will create flash cards.
287.01.a
287.01.f
Ordering, Equalities,
and Inequalities
Learning Continuum
Math BenchmarkTeacher Observable
For Learning:Given two numbers students will decide which symbol to use for less than, greater than or equal to.
When students are discussing math they will be assessed on their appropriate use of vocabulary.
Of Learning:RIT 181-190RIT 191-200RIT 201-210
The students will place a marker on their hundreds board by following the teachers instructions: What number is 7 greater than 43? What number is 10 less than 55? What number comes between 47 and 49?
Students will write math vocabulary words and definitions down in math journal.Using the vocabulary words students will create flash cards.
287.01.d
287.01.f
Fractions / Ratio /
Learning Continuum
Math BenchmarkTeacher Observable
For Learning:Ask the students to draw pictures to show the following fractional parts:2/5 of a set of circles is shaded.4/5 of the squares are red.3/4 of the triangles are blue.1/3 of the balls are footballs.4/9 of the fruit are apples.
Using a Hershey candy bar the student will practice, identify, and make equivalent fractions.
Students will write math vocabulary words and definitions down in math journal. Appropriate vocabulary includes: numerator, denominator, ones, tens, hundreds, thousands, decimal point, place value, greatest and
About Teaching Mathematics A K-8 Resource, 2000.By Marilyn Burns
ProportionWhen students are discussing math, they will be assessed on their appropriate use of vocabulary.
Given 3 fractions with the same denominator students will be able to order them from least to greatest.
When students are discussing math they will be assessed on their appropriate use of vocabulary.
Of Learning:RIT 181-190RIT 191-200 RIT 201-210
least, expanded notation Using the vocabulary words students will create flash cards.
Students will use fraction bars made from different colored strips of construction paper, to create bars that are equal to ½, ¼, 1/8, and 1 whole. Compare fractions to each other and to a whole.
Students will write math vocabulary words and definitions down in math journal.Using the vocabulary words students will create flash cards.
287.01.e
287.01.c
287.01.f
Money
Learning Continuum
Math BenchmarkTeacher Observable
For Learning:Given a collection of coins and bills, students will accurately count the amount of money (0-$10.00)
When students are discussing math they will be assessed on their appropriate use of vocabulary.
Of Learning:RIT 181-190RIT 191-200RIT 201-210
Students are given a list of items and their cost. Students need to purchase items and determine how much change they will receive from $5.00.
Students will write math vocabulary words and definitions down in math journal.Using the vocabulary words students will create flash cards.
290.03.a
Factorization / Divisibility
Learning Continuum
Math BenchmarkTeacher Observable
For Learning:
Learning For Learning: Add the cost of school supplies using
For Learning:Given 5 addition and 5 subtraction problems with regrouping, students will correctly complete the problems.
When students are discussing math they will be assessed on their appropriate use of vocabulary.
Of Learning:RIT 181-190RIT 191-200RIT 201-210
With a partner, students will use a spinner to obtain 3 numbers and then spin again for three more numbers to add. The student with the highest answer wins. This can be done with subtraction also and the student with the lowest answer wins.
Students will write math vocabulary words and definitions down in math journal. Appropriate vocabulary includes: addends, difference, operation, number sentence, subtraction, minus, equals, addition, sum, zero, and fact family.Using the vocabulary words students will create flash cards.
287.01.e287.01.f
Learning Continuum
Math
For Learning:Students will be able to order a series of numbers with decimals from least to greatest, and add or subtract those
Read Alexander Who Used to be Rich Last Sunday to the class. Ask students to figure out how much money each of Alexander’s brothers had when the
numbers when given a worksheet.Another assessment is to have students spend $1 in two, three, four, and five transactions instead of a week's transactions. A different amount of money should be spent each time. Example: 2 transactions. $.60, $.40, or $.26, $.74.
When students are discussing math, they will be assessed on their appropriate use of vocabulary. Of Learning:RIT 181-190RIT 191-200RIT 201-210
story started. Then reread the story. During reading stop so that students can write the amount of money being used at each place in the story. The important part of this activity is that students use decimals and understand the value being represented by the decimals.
Students will write math vocabulary words and definitions down in math journal. Appropriate vocabulary includes: decimal point, place value, greatest, least, expanded notation. Using the vocabulary words students will create flash cards.
By Bonnie Tank and Lynne Zolli
Math Solutions Publication 2001
287.01
Fractions
Learning Continuum
Math BenchmarkTeacher Observable
For Learning:Given 3 fractions with the same denominator students will be able to order them from least to greatest.
When students are discussing math they will be assessed on their appropriate use of vocabulary.
Of Learning:RIT 181-190RIT 191-200RIT 201-210
Students will use fraction bars made from different colored strips of construction paper, to create bars that are equal to ½, ¼, 1/8, and 1 whole. Compare fractions to each other and to a whole.
Students will write math vocabulary words and definitions down in math journal. Appropriate vocabulary includes: decimal point, place value, greatest, least, expanded notation. Using the vocabulary words students will create flash cards.
Mathematical Reasoning and Problem Solving Return to Top
288.01288.01.a288.01.b288.01.c
288.02288.02.a
290.03.a
288.03288.03.a288.03.b
288.04288.04a288.04b
Reasoning and Problem
Solving
Learning Continuum
Math BenchmarkTeacher Observable
For Learning:Think about a situation where you might compare two amounts. Write and solve a story problem that compares two numbers. Show your thinking using words, numbers, or pictures.
Students will be given information to insert into a graph. Then using, that information students will, add, subtract, and multiply the information according to directions.
Give students a worksheet with problems and answers where some of the answers are incorrect. Students must use a calculator to check and correct the worksheet.
When students are discussing math they will be assessed on their appropriate use of vocabulary.
Of Learning:RIT 181-190
RIT 191-200
RIT 201-210
Show how you solve the problem. Use words, pictures, or numbers: Kira and Jake are playing marbles. Kira has 40 marbles and Jake has 26. How many more marbles does Kira have than Jake?
Students will be given a package of M & M’s. ( mini’s work great) They will make predictions, estimate, add, subtract, multiply, compare (less than, greater than, or equal to) and graph the assorted colors according to teacher direction.
Given a set of 6 double-digit numbers, students will use any two numbers to complete an addition problem and check their work with a calculator.
Students will write math vocabulary words and definitions down in math journal. Appropriate vocabulary includes: Add, plus, minus, less, equals, is the same as, sum and difference. Using the vocabulary words students will create flash cards.
Putting Together and Taking ApartTERC- A Dale Seymour Publications
Lane County Mathematics Project- Alternative Problem Solving in Mathematics
Concepts and Principles of Measurement Return to Top
289.01289.01.a289.01.b289.01.c289.01.d
289.01.g
Length, Weight, Volume
Learning Continuum
Math BenchmarkTeacher Observable
For Learning:While students are using the string of beads to measure and record measurements of the different items, the teacher will assess each student’s abilities.
Given a worksheet with pictures of objects, students will correctly measure the objects using both a centimeter and inch ruler.
When students are discussing math they will be assessed on their appropriate use of vocabulary.
Of Learning:RIT 181-190RIT 191-200RIT 201-210
Students string 4 same colored beads on a string, each bead representing ¼ of an inch. Repeat with different colored beads for increased inches. Students then measure different items in the classroom and record their measurements.
Students estimate the length of their hand, feet, arm, ear, and thumb and record their estimations.Students will then use a standard inch ruler, and a metric ruler to measure their hands, feet, arm, ear, and thumb. Students will then determine how far off their estimation was.
Students will write math vocabulary words and definitions down in math journal. Appropriate vocabulary includes: hour, half hour, quarter hour, minute, second, hour hand, minute hand, year, month, week, inch, foot, yard, cups, measure meter, centimeter, and liter. Using the vocabulary words students will create flash cards.
289.01289.01.e
Learning Continuum
Math BenchmarkTeacher Observable
For Learning:The teacher will use on- going assessments to ask different students questions such as: If PE is going to be at 11:00, how many minutes do we have until we go to PE.?
Students will create a chart for a week. They will enter times on the chart that they get up, eat, attend school, and do special things. Students will record what time it would be 15 min. later or earlier according to teacher direction.
Students will be given a real calendar, donated by a business, and asked to identify specific days, and dates on the calendar.
When students are discussing math they will be assessed on their appropriate use of vocabulary.
Of Learning:RIT 181-190RIT 191-200RIT 201-210
calendar and put assignments, birthdays, holidays, and special class events on appropriate dates. As the year and calendars progress, discussions will take place about months in a year, days in a week, weeks in a year, and days in a year.
Students will write math vocabulary words and definitions down in math journal. Appropriate vocabulary includes: hour, half hour, quarter hour, minutes, second hour hand, minute hand, year, month, week, inch, foot, yard, cup, measure, meter, centimeter and liter.Using the vocabulary words students will create flash cards.
291.01.c
291.01.e
Area, Perimeter, Circum-ference
Learning Continuum
Math BenchmarkTeacher Observable
For Learning:Students will work in pairs to measure the area and perimeter of the 4-square outline, basketball free-throw key, and hopscotch outline on the playground. Students may use calculators.
When students are discussing math they will be assessed on their appropriate use of vocabulary.
Of Learning:RIT 181-190RIT 191-200RIT 201-210
Using graph paper, students will draw different sizes of squares and rectangles. Students will then determine the perimeters and areas of each shape.
Students will write math vocabulary words and definitions down in math journal. Appropriate vocabulary includes: rectangle, circle, square, triangle, sphere, cube, cone, cylinder, rectangular prism, pyramid, perimeter, and area. Using the vocabulary words students will create flash cards.
Algebra, Functions, and Mathematical Models Return to Top293.01.a293.01.b
Learning Continuum
Math
For Learning:Draw a picture of a tricycle on the board. Have student predict how many wheels different numbers of tricycles
Have one child stand up. Ask the class how many eyes one child has. Have another child come up also. Count how many eyes two have. Continue.
will have. (3,5,7) Record explanations in words, pictures or numbers that describe your strategies.
When students are discussing math, they will be assessed on their appropriate use of vocabulary.
Of Learning:RIT 181-190RIT 191-200RIT 201-210
Children can make records of the pattern by recording on individual sheets. Have children predict beyond the information provided.
Students will write math vocabulary words and definitions down in math journal.Using the vocabulary words students will create flash cards.
A K-8 Resource1992By Marilyn BurnsMath Solutions Publications
290.01.a
290.01.b
290.01.d
Solving Equations
and Inequalities, Simplifying
Expressions, Order of
Operations
Learning Continuum
Math BenchmarkTeacher Observable
For Learning:
Given a set of five problems with missing numbers, students will be able to determine the missing number.Also teacher observation of the game.
Students look at these equations (4 x5=20, 20÷4= 5) Do you agree? Use words, numbers or pictures to help explain your thinking.
Of Learning:RIT 181-190RIT 191-200RIT 201-210
In a group of 3 students 2 will hold a playing card up to their forehead ( they will not look at their own card)The 3rd person adds the 2 cards together and tells the answer to the 2 students. They must then guess their own card number by knowing the answer and seeing the other person’s number. This can be done with addition, subtraction, or multiplication.
Students will use rainbow cubes to make 3 groups with five cubes in each group. Then students will write a multiplication number sentence for 3 groups of five (3x5=15). Then students will take the 15 rainbow cubes and make 5 groups with 3 in each group. Students will write a division number sentence to represent this. (15 ÷3 =5) Students do repeated groupings.
For Learning:Students will write related addition or multiplication facts when presented with a set of numbers that are related.
Of Learning:RIT 181-190RIT 201-210
Working in pairs, students will use dominos to write related addition or multiplication facts.
Concepts and Principles of Geometry Return to Top291.01291.01.a
291.01.e
Shapes and Figures, 2- &
3-dimensional
Learning Continuum
Math BenchmarkTeacher Observable
For Learning:On paper list the attributes of different shapes. For example 4 corners 4 sides. Students will draw and identify the different shapes. ( 2 D) At the bottom of the paper have students label 3 D figures.
Of Learning:RIT 181-190RIT 191-200RIT 201-210
Students will be given a paper with the picture of one of the following: circle, triangle, rectangle, square sphere, pyramid, cube, cone, cylinder, and rectangular prism. Students will go to a certain place in the room after the teacher gives a description of different objects (4 corners, no points, 3 sides, etc.). After students gather according to their shape they must work together to come up with a definition and vocabulary word for their shapes.
291.01.b
Congruency and Similarity
Learning Continuum
Math BenchmarkTeacher Observable
For Learning:In small groups students will match shapes that are congruent and identify those that are not. The teacher will use observation and note taking for the assessment.
Of Learning:RIT 181-190RIT 201-210
Pass out shapes of same and different sizes to students. (squares, triangles, etc) The students will stand in front of the class. The rest of the class members will decide which pairs of students should be together because their shapes are congruent.
291.01.bLearning Continuum
For Learning:Assessment will be teacher observation of a symmetrical design on the soccer
Students will be given an outline of a plain soccer shirt. Students will create a design for the shirt using a
In small groups students will slide, flip or rotate objects using the correct vocabulary. Of Learning:RIT 181-190RIT 191-200RIT 201-210
symmetrical design. Students will need to draw the line of symmetry on their shirt.
Explore slides, flips and turns using animal crackers to show position after sliding, flipping, or rotating.
291.02.a
Coordinate
Learning Continuum
Math BenchmarkTeacher Observable
For Learning: Given a map students will be able to locate places when given the correct coordinates.
Of Learning:RIT 181-190 (Ordered Pairs)
RIT 181-190 (Graphing)RIT 191-200 (Graphing)RIT 201-210 (Graphing)
Using grid paper students will number down the side and add letters across the bottom. Then by teacher directions they will draw an object at point 3-f, 4-d etc.
291.01.e
GeometricProperties
and Terminology
Learning Continuum
Math BenchmarkTeacher Observable
For Learning:When students are discussing math they will be assessed on their appropriate use of vocabulary.
Of Learning:RIT 181-190RIT 191-200RIT 201-210
Students will write math vocabulary words and definitions down in math journal. Appropriate vocabulary includes: Rectangle, circle, square, triangle, sphere, cube, cone cylinder, rectangular prism, pyramid, perimeter, area, flip, slide and turn.Using the vocabulary words students will create flash cards.
Data Analysis, Probability, and Statistics Return to Top
292.01292.01.a292.01.b292.01.c
Learning Continuum
Math BenchmarkTeacher Observable
For Learning:Interpret information found in a table, chart or graph. Students will write about the information that they derived from the table, chart or graph.
When students are discussing math
Given a table of monthly temperatures, determine the highest and lowest temperature in a desert.
Students will write math vocabulary words and definitions down in math journals. Appropriate vocabulary
they will be assessed on their appropriate use of vocabulary.
includes: tables, charts, graphs, legends or key symbols. Using the vocabulary words, students will create flash cards.
292.03292.03.a
292.04292.04.a292.04.b
Probability & Prediction
Learning Continuum
Math BenchmarkTeacher Observable
For Learning:Students will write predictions about the dice game. Then write the reasons for the occurrences.
Of Learning: RIT 181-190RIT 191-200RIT 201-210
What’s the Record?Need a pair of dice.Who can set a record for the most of rolls of two dice without getting doubles? Try the challenge. Roll two dice and tally the number of rolls you make before getting doubles.
Approved by the State Board of Education March 6, 2003
ADVANCED: Exceeds Standards Back to Top
The student demonstrates thorough knowledge and mastery of skills that allows him/her to function independently above their current educational level.
The student demonstrates a comprehensive understanding of all relevant information relevant to the topic at level.
The student demonstrates comprehension and understanding of knowledge and skills above his/her grade level.
The student can perform skills or processes independently without any significant errors.
PROFICIENT: Meets Standards Back to Top
The student demonstrates mastery of knowledge and skills that allow them to function independently on all major concepts and skills related to their educational level.
The student demonstrates a comprehensive understanding of all information relevant to the topic, at level.
The student can perform skills or processes independently without any significant errors.
The student demonstrates basic knowledge and skills usage but cannot operate independently on concepts and skills related to his/her educational level. Requires remediation and assistance to complete tasks without significant errors.
The student has an incomplete knowledge of the topic and/or misconceptions about some information.
The student requires assistance and coaching to complete tasks without errors.
BELOW BASIC: Critically Below Standards Back to Top
The student demonstrates significant lack of skills and knowledge and is unable to complete basic skills or knowledge sets without significant remediation.
The student has critical deficiencies of relevant knowledge of topic and/or misconceptions about some information.
The student cannot complete any skill set without significant assistance and coaching.
Idaho State Standards: 3rd Grade MathematicsReturn to Top
286. MATHEMATICS STANDARDS – GRADE 3, SECTIONS 287 THROUGH 293.The samples associated with the content standards are meant to illustrate meaning and to represent possible areas of application. They are not intended to be an exhaustive list, but are samples of applications that would demonstrate learning.
287. BASIC ARITHMETIC, ESTIMATION, AND ACCURATE COMPUTATIONS.Rationale: An understanding of numbers and how they are used is necessary in the everyday world. Computational skills and procedures should be developed in context so the learner perceives them as tools for solving problems.
Standard – The student will: Content Knowledge and Skills: Samples of Applications:01. Understand and
use numbers.
Return to Ordering
Return to Fractions
a. Read, write, order, and compare whole numbers to 10,000.
Return to Whole Numbers
i. When given a set of whole numbers, order them from least to greatest and greatest to least.
Return to Place Valueb. Demonstrate the knowledge of
place value through 9,999.i. Identify each place value up to the
thousands place.ii. Identify the value of a given digit in a
number; for instance, 9,630: 6 = 600.iii. From a newspaper or magazine, find
examples of 4 in the hundreds place.iv. Use expanded notation (9000 + 600 +
i. Round to the nearest ten and/or to the nearest hundred: 52 to 50; 65 to 70; 450 to 500; 108
to 100.ii. Estimate the number of half-gallon
containers of milk needed for a class of 20 if each student receives 1cup.
iii. Estimate the number of cars needed for a class field trip if each car holds 6 people (not including the driver).
b. Evaluate the reasonableness of an answer.
i. Is the reasonable height of a 3rd grader 4 inches, 4 feet, or 4 yards?
Return to Whole Numbersc. Use appropriate vocabulary. i. Appropriate vocabulary: round and
estimate.
288. MATHEMATICAL REASONING AND PROBLEM SOLVING.Rationale: These processes are essential to all mathematics and must be incorporated in all other mathematics standards.
Standard – The student will:
Content Knowledge and Skills: Samples of Applications:
01. Understand and use a variety of problem-solving skills.
Return to Reasoning & Problem Solving
a. Select strategies appropriate to solve a problem.
i. Strategies: logical reasoning making chart or table act it out draw a picture guess and check working backwards
b. Select and use appropriate operations.
i. Given a variety of story problems, select and use the appropriate operation.
c. Make predictions and decisions based on information.
i. Predict the next two days’ temperatures based on information from the previous two days.
02. Use reasoning skills to recognize problems and express them mathematically.
Return to Reasoning & Problem Solving
a. Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain mathematical reasoning and concepts.
i. Graph favorite ice cream flavors of students. Write results in a mathematical equation such as # of students choosing chocolate is greater than # of students choosing strawberry written as: c > s; # students choosing chocolate plus # students choosing strawberry equals 20 students is written as: c + s = 20.
03. Apply appropriate technology and models to find solutions to problems.
Return to Reasoning & Problem Solving
a. Appropriately use a 4-function calculator to solve complex grade-level problems.
i. Check computation.
b. Select appropriate models to represent mathematical ideas.
04. Communicate results using appropriate terminology and methods.
Return to Reasoning & Problem Solving
Return to Statistics
a. Use a variety of methods, such as words, numbers, symbols charts, graphs, tables, diagrams, and models, to communicate mathematical information.
i. Convert a story problem to a number sentence using appropriate notations, terms, and labels.
ii. Classroom presentation of mathematical information obtained from research such as a chart – compare and contrast the average temperatures or rainfall in the desert and forest.
b. Use appropriate vocabulary to communicate mathematical information.
289. CONCEPTS AND PRINCIPLES OF MEASUREMENT.Rationale: The first step in scientific investigation is to understand the measurable attributes of objects.
Standards - The student will:
Content Knowledge and Skills: Samples of Applications:
01. Understand and use U.S. customary and metric measurements.
Return to Length, Weight, Volume
Return to Time / Temperature
a. Select and use appropriate units and tools to make formal measurements in both systems (time, length, temperature, perimeter).
i. Introduce clocks (digital, analog), rulers, yardsticks (standard and metric), scales, thermometers (F/C), containers.
ii. What tool would you use to measure a carpet?
Return to Length, Weight, Volume
b. Apply estimation of measurement to real-world and content problems using actual measuring devices.
i. Use a reasonable measure to determine: distance from school to home capacity of containers of various
sizes (pool versus bath tub).c. Explore relationships within the
U.S. customary system.i. Use a reasonable measure to
determine: distance from school to home capacity of containers of various
size (pool versus bathtub)
Return to Length, Weight, Volume
d. Explore relationships within the metric system.
i. Use a reasonable measure to determine: distance from school to home capacity of containers of various
size (pool versus bathtub)
Return to Time / Temperature
e. Tell time using both digital and analog clocks, using 5-minute intervals.
i. The student will make a chart listing the time of certain events during the day to the nearest 5 minutes.
ii. During the school day the student will write the time on a piece of paper to the correct 5-minute interval.
If a movie is 2 hours long, how many minutes would that be?
ii. 24 hours in a day.iii. 7 days a week.iv. 12 months in a year.v. 52 weeks in a year.vi. 365 days in a year.
Return to Length, Weight, Volume
Return to Time / Temperature
g. Use appropriate vocabulary. i. Appropriate vocabulary: hour, half-hour, quarter hour, minute, second, hour hand, minute hand, year, month, week, inch, foot, yard, cups, measure, meter, centimeter, liter.
290. CONCEPTS AND LANGUAGE OF ALGEBRA.Rationale: Algebra is the language of mathematics and science. Through the use of variables and operations, algebra allows students to form abstract models from contextual information.
Standard – The student will:
Content Knowledge and Skills: Samples of Applications:
01. Use algebraic symbolism as a tool to represent mathematical relationships.
a. Represent vertical notation in horizontal form.
Return to Solving Equations
i. 21 + 38 = 59ii. 21 + 38 59
Return to Solving Equationsb. Write a number sentence using
symbols (boxes or letters) to represent an unknown number.
i. 12ٱ = - 42 ii. x + 7 = 10
c. Use symbols (<, >, =) to express relationships.
i. Use the correct symbol to make the number sentence true. 52ٱ 71ٱ 14ٱ
Return to Solving Equationsd. Explore inverse (reversal) of
operations with multiplication and division.
i. 3 x 6 = 18, so 18÷ 6 = 3.
02. Evaluate algebraic expressions.
Return to Properties
a. Explore and use the commutative properties of addition and multiplication.
i. a + b = b + a. a x b = b x a.
03. Solve algebraic equations and inequalities.
a. Solve missing addends and missing factor problems using inverse operations.
291. CONCEPTS AND PRINCIPLES OF GEOMETRY.Rationale: The study of geometry helps students represent and make sense of the world by discovering relationships and developing spatial sense.
Standard – The student will:
Content Knowledge and Skills: Samples of Applications:
01. Apply concepts of size, shape, and spatial relationships.
Return to Shapes and Figures
a. Identify, compare, and analyze attributes of two- and three-dimensional shapes and develop vocabulary to describe the attributes.
i. Draw a circle, triangle, rectangle, and square. Identify and label sphere, pyramid, cube, cone, cylinder, rectangular prism, and list the similarities.
Return to Congruency & Similarity
Return to Symmetry and Transformations
b. Explore congruence, similarity, and symmetry.
i. Find examples in the classroom and on the playground of objects that are congruent, similar, and symmetrical.
ii. Use letters of the alphabet and paper folding to demonstrate congruence, similarity and symmetry.
Return to Area, Perimeterc. Investigate perimeters in real-
world situations.i. Find the perimeter of three objects in
your classroom. ii. Given a triangle puzzle piece (or a
rectangle puzzle piece) add the lengths of the sides to find the perimeter.
Return to Symmetry and Transformations
d. Predict and describe the results of sliding, flipping, and turning two-dimensional shapes.
i. Slide, flip, and turn a pentomino.
Return to Area, Perimeter
Return to Shapes and Figures
Return to Geometric Properties and Terminology
e. Use appropriate vocabulary. i. Appropriate vocabulary: rectangle, circle, square, triangle, sphere, cube, cone, cylinder, rectangular prism, pyramid, perimeter, area.
292. DATA ANALYSIS, PROBABILITY, AND STATISTICS.Rationale: With society’s expanding use of data for prediction and decision-making, it is important that students develop an understanding of the concepts and processes used in analyzing data.
Standard – The student
will:Content Knowledge and Skills: Samples of Applications:
01. Understand data analysis.
Return to Data Analysis
a. Interpret information found in tables, charts, and graphs.
i. Given a table of monthly temperatures, determine the highest and lowest temperature in a desert.
ii. Create a legend or key to explain the value of the symbols used.
b. Explain and justify conclusions drawn from tables, charts, and graphs.
c. Understand and use appropriate vocabulary.
02. Collect, organize, and display data.
Return to Data Analysis
a. Collect, organize, and display data in tables, charts, or graphs in order to answer a question and/or test a hypothesis.
i. Given the question: How much time is spent to the nearest hour doing homework (including reading), playing, and watching TV in a 24-hour period? Gather data and display information on a graph.
03. Understand basic concepts of probability.
Return to Probability & Prediction
a. Predict, perform, and record results of simple probability experiments.
i. Given four socks: 2 blue, 2 brown, and the fact that its dark, what is the least number of socks needed to make sure there is a matched pair.
04. Make predictions or decisions based on data.
Return to Probability & Prediction
a. Make predictions or decisions based on probable results or past experiences.
i. There are 5 crackers and 2 cookies in a sack. The cookie drawn out of the sack must be eaten. Make a decision on whether or not to draw from the bag. Explain your decision.
b. Understand and use appropriate vocabulary.
i. Appropriate vocabulary: compare, tables, graphs, and charts.
293. FUNCTIONS AND MATHEMATICAL MODELS.Rationale: One of the central themes of mathematics is the study of patterns, relationships, and functions. Exploring patterns helps students develop mathematical power.
Standard – The student will:
Content Knowledge and Skills: Samples of Applications:
01. Understand the concept of functions.
Return to Patterns, Sequences, Functions
a. Extend patterns and identify the rule (function) that creates the pattern.
i. Identify, describe, and extend geometric and numeric patterns, including growing and shrinking patterns. 2, 5, 8, 11, ___ , ___, ___. __, __, __, 50, 60, 70, __, __, __.
Return to Patterns, Sequences, Functions
b. Discover, describe, and extend patterns by using manipulatives and pictorial representations.
commutative, solve, square numbers, input, output, number sequence
absolute value, evaluate, quotient
o square root symbol, %, absolute value symbol
RIT 231-240 RIT 241-250 RIT 251-260 RIT 261-300
inequality, if-then statement, term in sequence, square numbers, negative coefficient
o I = p x r x t
regression equation, varies inversely as the square, slope of parallel lines, solution to system, factor (used with equations)
parabola, intercepts, number of solutions, simultaneous equations, counterexample, solution set, sin A, cosine, tangent, discriminant, imaginary solutions, difference of two squares, read solution set from graph, factor completely
transformation, hypotenuse, edge, isosceles, scalene triangle, similar trapezoids, alternate interior angles, sum of angles in triangle
symmetrical halves, diameter, radius, angle bisector, tangent, corresponding parts of congruent triangles, Pythagorean theorem, corresponding angles, complementary angles, construction
o sign for parallel lines
slope, non-vertical and non-horizontal, midpoint, endpoint, rotational symmetry, reflected, perpendicular bisector, similar triangles, similar trapezoids, similar cylinders, conditional, counterexample, conclusion of in-then statement, interior of angle, exterior angle of regular polygon, interior angle of regular polygon, sum of angles in triangle equals 180 degrees, congruent angles, adjacent angles, vertical angles
o ” = inches, yd = yards, b = base, h = height, r = radius, s = side, angle symbol, - for negative, + for positive, d = distance, tsp = teaspoon, pt = pint, gal = gallon, qt = quart, c = cup
missing number, pentagon, simplest fraction, biggest, hundredths, one less, decimal numeral, squared, divisible, inequality, expanded numeral, equivalent, point, standard numeral, sequence
o + used as positive symbol, - used as negative symbol
counting number, portion, fractional part, lowest terms, reciprocal, order, scientific notation, prime factorization, not prime, factor tree, common multiples, greatest common denominator, equivalent, nearest dollar
o square root symbol
always true, proportion, multiply, between, tens digit, standard numeral, ratio
RIT 231-240 RIT 241-250 RIT 251-260 RIT 261-300
Base ten, prime factors infinite non-repeating decimal (261-270)
ISAT “Sub-Goal” RIT Below 150-160 RIT 161-170 RIT 171-180 RIT 181-190
Reasoning and Problem Solving
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how many, not, in all, altogether
product, number sentence, problem, how many more, multiples, greater than, left, how much, money, answer, about, outside, inside, shape, calendar, picture
add, subtract, multiply, divide, rate, kilometers, hours, between, equals, cost, time, less than, closest to, equation, weigh, minutes, pieces, dozen, cups, inches, pounds, miles, sum, dime, nickel, pennies, quarter
o tally marks, =, - as an integer sign, %, °C, € for answer
equation, product, increased, number line, information not needed, division, estimate, odd, prime, cube, pattern, geometric patterns, extra information
ISAT “Sub-Goal” RIT 181-190 RIT 191-220 RIT 201-210
Understand the properties of integers: commutative, associative, identity, zero property of multiplication, distributive property of multiplication over addition, and inverse property of addition
Data Analysis, Probability, and StatisticsData Analysis
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Solve simple word problems based on data from picture and bar graphs
Solve problems using information from a bar graph
Construct and interpret line graphs involving problem solving
Solve problems using information from a bar graph
Solve multi-step word problems with pictographs, bar graphs, or line graphs
Construct, and solve word problems involving line graphs
Construct and solve word problems involving circle graphs
Construct and solve word problems involving information from a table
Read and interpret dual bar graphs and dual broken-line graphs
Solve problems using information from a picture graph (symbol may represent more than one)
Interpret data given in percent form on a circle graph and broken line graph
Probability and Prediction
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Predict whether common events are certain, likely, unlikely, possible, impossible, fair or unfair
Investigate experimental probability of an event using a coin or spinner
Develop concept of chance and make predictions for events (ex. rolling a number dice)
Compute simple probability outcomes
Determine the probability of an outcome (multiple events)
Use the counting principle to determine probability
Statistics
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Use tallies to record data Compute averages with a given set of
data
Solve practical problems involving the mean (average) of a set of numbers
ISAT “Sub-Goal” RIT 181-190 RIT 191-220 RIT 201-210Mathematical Reasoning and Problem SolvingMathematical Reasoning and Problem Solving
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Solve simple addition word problems Write number sentences using addition Determine what operation is needed to
solve a word problem (addition and subtraction)
Solve simple word problems using addition and subtraction
Solve one-step word problems involving addition or subtraction of four or fewer digits
Solve one-step word problems involving division
Identify extra information or missing information that is necessary to solve word problems
Choose and apply an appropriate problem solving strategy: Draw a picture, Make a model, Guess and test, Make a list, Make a table, or Find a pattern
Identify the correct information to solve addition and subtraction word problems
Solve one-step word problems involving multiplication and division, including money
Estimate the answers to word problems Determine what operation is needed to solve a
word problem (all four operations) Choose and apply an appropriate problem
solving strategy: Draw a picture, Make a model, Guess and test, Make a list, Make a table, Find a pattern, Work backwards, Solve a simpler problem, or Draw a diagram
Solve word problems involving any combination of basic operations on whole numbers (one-step problems)
Write a number sentence to solve one-step word problems involving the operations of addition, subtraction, and multiplication of fractions and decimals
Use a number line to write number sentences using subtraction
Solve multi-step word problems involving any combination of basic operations
Solve one- and two-step word problems involving any combination of basic operations on whole numbers, decimals, and fractions
Translate verbal statements into equations (all four operations; several operations)
Estimate the answers to word problems
Solve written word problems involving the addition or subtraction of monetary amounts
Solve word problems involving customary and metric measurement
Solve word problems involving distance, rate and time
Use logic to solve problems Solve word problems using
proportional reasoning Solve geometry problems by
making a drawing or diagram Choose and use an appropriate
problem solving strategy: Draw a picture, Make a model, Guess and test, Make a list, Make a table, Find a pattern, Work backwards, Solve a simpler problem, Draw a diagram, Write an equation, or Logical Deduction