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1Idaho State Expanded Curriculum Guide Mathematics 3rd Grade ©State of Idaho 2003

Number Sense Algebra, Functions, & Mathematical Models State StandardsEstimation/Accurate Computation Geometry ISAT Cut ScoresReasoning/Problem Solving Data Analysis, Probability, & Statistics Sample Test Items Measurement McRel Alignment

New VocabularyNumber Sense Estimation/Accurate

ComputationReasoning/Problem Solving

MeasurementAlgebra, Functions, & Mathematical Models

GeometryData Analysis, Probability, & Statistics

State Standard

and Benchmark

Local Curriculum

Learning Continuum and other

Performance Objectives

Sample Assessment and Sample Quizzes

Sample Sequence

Minimum Hours

Allotted

Sample TeachingStrategy

Sample Resources

Number Sense Return to Top

287.01.a

287.01.f

Whole Numbers

Learning Continuum

Math BenchmarkTeacher Observable

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.


State

Standard and

Benchmark

Local Curriculum




Sample Sequence

Minimum Hours

Allotted


Sample Resources

287.01.f

Place Value, Expanded

and Standard Notation

Observable


Of Learning:RIT 181-190 (Place Value)RIT 191-200 (Place Value)RIT 201-210 (Place Value)

RIT 191-200 (Exponents)RIT 201-210 (Exponents)

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


For Learning:Given two numbers students will decide which symbol to use for less than, greater than or equal to.


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


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


State

Standard and

Benchmark

Local Curriculum




Sample Sequence

Minimum Hours

Allotted


Sample Resources

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.


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.


287.01.e

287.01.c

287.01.f

Money

Learning Continuum


For Learning:Given a collection of coins and bills, students will accurately count the amount of money (0-$10.00)



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.


290.03.a

Factorization / Divisibility

Learning Continuum


For Learning:

Learning For Learning: Add the cost of school supplies using


State

Standard and

Benchmark

Local Curriculum




Sample Sequence

Minimum Hours

Allotted


Sample Resources

287.01.eDecimals

Continuum(Decimals)

Learning Continuum(Percents)


Given an amount of money with a cent sign, change to dollar sign and decimal point format (56 cents to $0.56)

Of Learning:RIT 181-190 (Decimals)RIT 191-200 (Decimals)RIT 201-210 (Decimals)

RIT 191-200(Percents)RIT 201-210 (Percents)

dollar sign and decimal point.

Estimation and Computation Return to Top

287.02287.02.a287.02.b 287.02.c287.02.d287.02.e287.02.f287.02.g

287.03287.03.a287.03.b 287.03.c

Whole Numbers

Learning Continuum


For Learning:Given 5 addition and 5 subtraction problems with regrouping, students will correctly complete the problems.



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

Lessons For Addition And Subtraction


State

Standard and

Benchmark

Local Curriculum




Sample Sequence

Minimum Hours

Allotted


Sample Resources

DecimalsBenchmarkTeacher Observable

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


For Learning:Given 3 fractions with the same denominator students will be able to order them from least to greatest.



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.

Percents Math BenchmarkTeacher Observable

For Learning:

Of Learning:RIT 191-200RIT 201-210


State

Standard and

Benchmark

Local Curriculum




Sample Sequence

Minimum Hours

Allotted


Sample Resources

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


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.


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


State

Standard and

Benchmark

Local Curriculum




Sample Sequence

Minimum Hours

Allotted


Sample Resources

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


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.



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


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.

Each month students will create a


State

Standard and

Benchmark

Local Curriculum




Sample Sequence

Minimum Hours

Allotted


Sample Resources

289.01.f

289.01.g

Time, Temperature

Students will be given a real calendar, donated by a business, and asked to identify specific days, and dates on the calendar.



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


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.



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.

About Teaching Mathematics-


State

Standard and

Benchmark

Local Curriculum




Sample Sequence

Minimum Hours

Allotted


Sample Resources

293.01.c

Patterns, Sequences, Functions

BenchmarkTeacher Observable

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.


Children can make records of the pattern by recording on individual sheets. Have children predict beyond the information provided.


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


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.


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.


State

Standard and

Benchmark

Local Curriculum




Sample Sequence

Minimum Hours

Allotted


Sample Resources

290.02.a290.03.a

Properties

Learning Continuum


For Learning:Students will write related addition or multiplication facts when presented with a set of numbers that are related.


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


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.


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


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.


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


State

Standard and

Benchmark

Local Curriculum




Sample Sequence

Minimum Hours

Allotted


Sample Resources

291.01.dSymmetry

and Transform-

ations


shirt.

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


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


For Learning:When students are discussing math they will be assessed on their appropriate use of vocabulary.


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


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


State

Standard and

Benchmark

Local Curriculum




Sample Sequence

Minimum Hours

Allotted


Sample Resources

292.02292.02.a

Data Analysis

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


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.

288.04.a

Statistics

Learning Continuum


For Learning:


13Idaho State Expanded Curriculum Guide Mathematics 3rd Grade ©State of Idaho

2003

APPROVED ISAT PROFICIENCY SCORESReturn to Top

Approved by the State Board of Education March 6, 2003

READING 2 3 4 5 6 7 8 9 10Basic 174 185 192 198 203 207 210 213 216Proficient 182 193 200 206 211 215 218 221 224Advanced 193 204 211 217 222 226 229 232 235

LANGUAGE 2 3 4 5 6 7 8 9 10Basic 176 186 193 200 204 207 211 213 214Proficient 184 194 201 208 212 215 219 221 222Advanced 197 207 214 221 225 228 232 234 235

MATH 2 3 4 5 6 7 8 9 10Basic 174 185 194 202 208 214 222 229 231Proficient 185 196 205 213 219 225 233 240 242Advanced 201 212 221 229 235 241 249 256 258

PROFICIENCY LEVELS DEFINITIONS

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.


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BASIC: Below Standards Back to Top

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 +


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30 + 0).

Return to Moneyc. Determine, by counting, the value

of a collection of bills and coins up to $10.00.

i. Count and write the value of a collection of coins and bills.

Return to Fractions, Ratio, Proportion

d. Use concrete materials to recognize and represent commonly used fractions.

i. When given a set of fraction materials, select and identify parts of the whole.

ii. Fold a paper to show 1/2 and 1/4.

Return to Money

Return to Decimals –Number Sense

Return to Decimals –Estimation and Computation

e. Explore decimals using money through hundredths.

i. Add the cost of school supplies using dollar sign and decimal point.

ii. Given an amount of money with a cent sign, change to dollar sign and decimal point format (56¢ to $0.56).


Return to Place Value

Return to Ordering

Return to Fractions, Ratio, Proportion

Return to Money

Return to Decimals –Estimation and Computation

f. Understand and apply appropriate vocabulary.

i. Begin to use terms: numerator, denominator, ones, tens, hundreds, thousands, decimal point, place value, greatest and least, expanded notation.

02. Perform computations accurately.


a. Add and subtract whole numbers with and without regrouping through 999.

i. Know basic facts through 18.ii. Subtract your age from the principal’s

age.

b. Instantly recall basic addition and subtraction facts through 18.

i. Play Bingo.

Return to Whole Numbersc. Add three addends with 1 and 2

digits.i. Add the lunch count from 3

classrooms.ii. Change the format from horizontal to

vertical.d. Multiply whole numbers through

10 x 10. i. Use concrete materials to model

multiplication facts.ii. Determine how many days are in 5

weeks.

Return to Whole Numberse. Explore the relationship between

multiplication and division.i. 3 x 6 = 18, 18 ÷ 6 = 3.ii. Work with dimes, nickels, and

pennies, to explore multiples of tens, fives, and ones.

iii. Explore multiplication work with arrays, looking for 3 groups 2 or 3


2003

groups of 5.iv.

Return to Whole Numbersf. Select and use an appropriate

method of computation from mental math, paper and pencil, calculator, or a combination of the three.

i. Choose the best method: If someone has a dollar, is there

enough money to buy a candy bar and soda?

Find the total number of students in 1st, 2nd, and 3rd grade.

Given that 43 out of 100 students ride the bus, determine how many do not.

Return to Whole Numbersg. Use appropriate vocabulary. i. Appropriate vocabulary: addends,

difference, operation, number sentence, subtraction, minus, equals, addition, sum, zero, fact family.

03. Estimate and judge reasonableness of results.


a. Use estimation to predict computation results.

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.


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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.


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.


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 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.


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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:


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?


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)


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)


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.


2003


f. Explore the relationship among units of time.

i. Elapsed time: If you went on vacation for 3

weeks, how many days would you be gone?

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.



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.



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.


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Return to Factorization / Divisibility


Return to Properties

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.



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.

02. Apply graphing in two

a. Apply ideas about direction and distance.

i. Kick ball, foot ball.


2003

dimensions.

Return to Coordinate

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.


2003

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.



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, __, __, __.


b. Discover, describe, and extend patterns by using manipulatives and pictorial representations.

i. Describe the pattern and explain the rule.

ii. Skip counting with odd or even numbers.


c. Understand and use appropriate vocabulary.


New Vocabulary (l) and Symbols (¢)

ISAT “Sub-Goal”

RIT Below 150-160 RIT 161-170 RIT 171-180 RIT 181-190

Algebraic Concepts

Return to Top

o € for answer to equation (151-160)

o ( ) used in equations o <, > symbols signo – used as negative

RIT 191-200 RIT 201-210 RIT 211-220 RIT 221-230

if-then, product, sumo variables, exponents (signs /

symbols)

input, output, table, associative, equation

o £, ³

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



ISAT “Sub-Goal”


Compu-tation

Return to Top

(Below 150) ando +, =, -(151-160) equals, factso x (multiplication symbol)

o $, decimal point closest, how manyo division symbol (both

forms)

RIT 191-200 RIT 201-210 RIT 211-220 RIT 221-230

difference, not true, power of 10, rounded, thousands

o ¢, %

estimate, round, closest to, sum, of (used as in “½ of 36”)

o square root symbol

smallest, tentho – as a negative, + as a

positive

product, divide, most, if – then, compute, lowest terms

RIT 231-240 RIT 241-250 RIT 251-260 RIT 261-300

“Solve for n” decimal fractions, opposite sum of opposites



ISAT “Sub-Goal”


Geome-try

Return to Top

shape, circle, same as matches, triangle, square, corners, cone, closed, inside

congruent, figure symmetry, point, sides, rectangle, cube, straight, line segment, shortest

o line AB (with double arrow over AB), line segment AB (with segment line over AB)

RIT 191-200 RIT 201-210 RIT 211-220 RIT 221-230 symmetrical, parallel, intersecting,

diagonal, pair, angle, cylinder, outside, inside, sphere, faces, corresponding, point, intersect, outside, axis of symmetry, line segment, pentagon

o symbol for parallel lines

intersection, quadrilaterals, octagon, parallelogram, pyramid, isosceles, right angle, diameter, right angle, geometric, perpendicular, plane

o D for triangle, angle symbol

symmetrical, perpendicular, ray, vertex, rotation, triangular prism, corresponding parts, supplementary, acute angle, transformation

o @ - congruent symbol, « - double arrow symbol for similarity, p - pi symbol, DABC – to label triangle

radius, polygon, circumference, trapezoid, rectangular box, equilateral, similar, obtuse angle, straight angle, slide

o angle symbol, label for line – L1

RIT 231-240 RIT 241-250 RIT 251-260 RIT 261-300

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

postulate (261-270) HL (271-280)



ISAT “Sub-Goal” RIT Below 150-160 RIT 161-170 RIT 171-180 RIT 181-190

Measure-ment

Return to Top

longest, shortest, how tall, kilometer, meter, time (151-160)

o C for Celsius, cm for centimeter

how long, names of days of week, next, names of months, pennies, centimeter, inches

o degree symbol, : for time – 1:00, face of quarter, dime, penny, and nickel

line segment, area, square units, perimeter, days, week, set, coins, thermometer, temperature, pounds, ounces, pints, quarts

o $, decimal point for cents, F = Fahrenheit, lb = pounds, sq = square units, cent sign, recognize back of penny, nickel, dime, and quarter

about, length, estimate, perimeter, change, quarter, dollars, dozen, units, feet, yard, grams, meters, cups, gallons, nickel, pennies, dime, tablespoon, hours, minutes, degree

o m = meters, g = grams

RIT 191-200 RIT 201-210 RIT 211-220 RIT 221-230

height, width, parallelogram, square, rectangle, triangle, year, ton, seconds, kilogram, distance, miles, liter

o mm = millimeter, a.m. and p.m., hr = hours, min = minutes

right angle, circumference, minutes, decades, milligrams, gram, cubic feet, volume, liters, length, weight, kilometers, millimeters, mass

o ft for feet, mL = milliliters, right angle symbol, symbol for line segment, p

yards, measure of angle, degrees, protractor, centuries, below zero, Celsius, rectangular solid, rectangular prism, decades, ounces

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

reasonable, formula, segment BC, pi, radius squared, diameter, metric units, quarts, gallons, rectangular box, base, rate

o oz = ounces, C = circumference

RIT 231-240 RIT 241-250 RIT 251-260 RIT 261-300

rectangular house, height and base, algebraic expression, rows and columns, checking account, car purchase, commission, simple interest

o F = 9/5 C + 32, formula for finding volume of a pyramid

doubled and tripled, rectangular solid, cylindrical tank, algebra tiles, inscribed, time-and-a-half, sales tax, discount

circumscribed, distance formulao formula for finding volume of a cone,

formula for volume of a cube, formula for finding volume of a rectangular solid

rate of interest, successive discounts (271-280)



ISAT “Sub-Goal”


Number Sense

Return to Top

how manyo — for answer

ones, tens, hundreds, thousands, numeral, ordinal numbers through eleventh, counting

even numbers, same as, fewest

o < and > signs, = sign

first, second, third, etc., odd, one-fourth, one-half, reduce, fractions, order, divisible, round, smallest, largest, lowest terms, greatest common factor, least common multiple, closest, units, set, digit, greater than, greatest

RIT 191-200 RIT 201-210 RIT 211-220 RIT 221-230

thirds, fourths, rounded, thousands, exponential form, mixed number, improper fraction, lowest common denominator, percent, expanded form, prime, factor, proportion

o use of dot as a multiplication symbol

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

Return to Top

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 +, $, decimal point for cents, ¢

RIT 191-200 RIT 201-210 RIT 211-220 RIT 221-230

terms, meter, millimeters, kilogram, feet, yards, unit of measurement, height, thousands, hundreds, tens, table, graph, length, width, rectangular, area, square inches, exactly, coins, numeral, even, change, average, opposite, percent, subtrahend, addend, formula, circle, diameter, operation, total, fact, fraction, surfaces, cube, temperature, first – fifth (ordinal names), difference, equivalent

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

o r x t = d

decimals, fractions, what shape, hour, minutes, gallons, average, probability, graph, squares

o %

mortality, odometer, magic square, deducted, less than twice, addends, less than sum, rectangle, diameter, radius, label (units), area, perimeter

o I = prt

RIT 231-240 RIT 241-250 RIT 251-260 RIT 261-300

regression equation matrix



ISAT “Sub-Goal”


Data Analysis, Statistics and Probability

Return to Top

probability chance most often

RIT 191-200 RIT 201-210 RIT 211-220 RIT 221-230

average, bar graph, percentage

o %

least often, how many ways, ordered pairs, coordinates, distance formula

dice, arranged, highest mean

even numbers, mean, median, integer, intersection, table, frequency, origin, quadrant

RIT 231-240 RIT 241-250 RIT 251-260 RIT 261-300

vertex, fractional part, amount of sales, translation, matrix, possibility, mean salary, coordinates of points

coordinate, Venn diagram, greatest decrease, endpoints, midpoint


ISAT “Sub-Goal” RIT 181-190 RIT 191-220 RIT 201-210AlgebraSolving Equations, Simplifying Expressions, Order of Operations

Return to Guide

Solve for missing addends in an addition or subtraction sentence

Use inverse operations to find missing equation

Identify missing elements in number sentences

Identify and understand the greater or lesser of two numerals (use the symbols < and > through 999,999)

Use symbols of inequality, < and > to write and complete number sentences

Solve simple addition problems with “n” as an addend or sum

Solve simple multiplication problems with “n” as a multiple or product

Solve simple division problems with “n” as a quotient or divisor

Solve whole number equations with any operation

Evaluate an expression involving more than one operation (order of operations)

Use the basic properties of multiplication to write an algebraic expression that is equivalent to a given algebraic expression

Solve equations involving more than one operation

Multiply and divide polynomials Solve equations involving

rational numbers (addition and subtraction)

Patterns, Sequences, Functions

Return to Guide

Find and extend patterns, both increasing and decreasing

Complete a number pattern Complete a table according to a rule Choose and apply an appropriate

problem solving strategy: Find a pattern

Count and write by 4’s Find and extend patterns

Use of a function “machine” to determine input and output

Properties

Return to Guide

Identify the associative, commutative, identity and zero property of multiplication

Use strategies to develop computational fluency with multiplication: zero property, property of one, arrays, doubles, nine patterns

Use the basic properties of addition to write an algebraic expression equivalent to a given algebraic expression


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

Return to Guide

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

Return to Guide

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

Return to Guide

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 201-210Estimation and ComputationDecimals

Return to Guide

Subtract whole numbers and decimals to the hundredths place (same number of digits)

Add decimals to hundredths place using both horizontal and vertical format (not the same number of digits)

Subtract decimals to hundredths place (not the same number of digits)

Multiply a decimal by a whole number Divide a decimal by a whole number

and vice versa Compute simple addition or

subtraction problems involving monetary amounts up to $10.00

Compute and count change up to and including $5.00 (addition and subtraction only)

Add whole numbers and decimals to the hundredths place (not the same number of digits)

Subtract whole numbers and decimals to the hundredths place (not the same number of digits)

Compute basic operations with monetary amounts up to and including $20.00

Add decimals to thousandths, vertically and horizontally, with and without regrouping

Subtract decimals to thousandths, vertically and horizontally, with and without regrouping

Multiply a decimal by a decimal, vertical form (tenths or hundredths)

Compute simple addition or subtraction problems involving monetary amounts up to $10.00

Compute half price greater than $20.00

Add decimals to hundredths place using both horizontal and vertical format

Subtract decimals to hundredths place

Compute and count change greater than $20.00

Subtract decimals through hundred-thousandths with a calculator

Compute and count change up to and including $10.00 (addition and subtraction only)

Solve written word problems involving the addition or subtraction of monetary amounts

Fractions

Return to Guide

Subtract mixed numbers with like denominators with regrouping

Express 1 in many different ways (1/1, 2/2, 4/4)

Subtract fractions with like denominators

Add fractions having unlike denominators, answer in lowest terms

Add mixed numbers with like denominators with regrouping

Subtract mixed numbers with like denominators with regrouping

Subtract mixed numbers with unlike denominators with regrouping

Multiply a fraction by a fraction; answer in lowest terms

Multiply mixed numbers


ISAT “Sub-Goal” RIT 181-190 RIT 191-220 RIT 201-210Whole Numbers

Return to Guide

Subtract a 2-digit number from a 3-digit number with a single regrouping

Identify the division facts related to a multiplication fact with one factor as 1,2,3,4,5 and the other factor 0-9

Understand the concept of division using concrete objects

Subtract a 3- or 4-digit number from a 4-digit number with regrouping

Use strategies to develop computational fluency with multiplication: “zero property,” “property of one,” “arrays,” doubles,” “nine patterns”

Multiply a 3-digit by a 1-digit number with regrouping (including zero)

Multiply three 2-digit numbers (one is 10) Identify the division facts related to a

multiplication fact Divide a 2-digit number by a 1-digit number

with no remainder (basic facts to 9) Solve one-step word problems involving

division Add 2 or several multi-digit numbers with

regrouping Subtract multi-digit numbers with regrouping Divide a 3-digit or 4-digit number by a 1-digit

number Divide a 2-digit number by a 2-digit number

with no remainder Add multi-digit numbers without using a

calculatorMultiply multi-digit numbers

Solve one-step word problems involving multiplication

Subtract multi-digit numbers with regrouping

Multiply a 2-digit number by a 2-digit number with no regrouping

Multiply a 2-digit number by a 2-digit number with regrouping

Subtract multi-digit numbers without using a calculator

Multiply a 3-digit number by a 2-digit number with regrouping

Multiply a 3-digit number or 4-digit number by a 2-digit number or 3-digit number with zeros

Add whole numbers using place value

Understand the concept of division using pictorial representation

Use front-end estimation strategy for multiplication and division

Divide a 2-digit number by a 2-digit number with a remainder

Subtract multi-digit numbers without using a calculator

Multiply by multiples of 10 and 100 with an emphasis on mental math

Divide a 3-digit number by a multiple of 10

Divide a 3-digit number by a 2-digit number (no zeros)

GeometryCongruency and Similarity

Return to Guide

Identify congruent figures, angles, and line segments

Identify similar figures (same shape, may or may not be same size)

Identify congruent figures, angles and line segments



Coordinate

Return to Guide

Graph ordered pairs in the first quadrant

Geometric Properties and Terminology

Return to Guide

Identify points on a line Identify the correct label for a line

Identify position concepts: (over, under, inside, outside, in front, behind, top, middle, bottom)

Describe and measure right angles Identify right angles Identify intersecting, parallel lines Identify the diagonal of a circle

Identify points, lines, line segments, rays, planes, and angles

Identify the diameter of a circle Identify intersecting, parallel, and

perpendicular lines Calculate the surface area of a

rectangular prism Identify angles according to their

measure: right, obtuse, and acute

Shapes and Figures, 2- and 3-Dimensional

Return to Guide

Identify and name the plane figures: circle, triangle, square, and rectangle

Recognize solid figures: cube (box) Identify characteristics of plane figures

(sides and corners)

Recognize solid figures: sphere (ball) Identify and name solid figures: cube,

cylinder, cone, rectangular prism, and sphere

Identify characteristics of plane figures (sides and corners)

Identify faces, edges, and corners (vertices) on solid figures

Identify polygons: triangle, quadrilateral, pentagon, and octagon

Identify quadrilaterals: square, rectangle, and parallelogram

Identify, name, and analyze solid figures: cube, cylinder, triangular pyramid and square pyramid (faces, edges, and vertices)

Symmetry and Transfor-mations

Identify figures with line symmetry Recognize transformations of plane

figures (slides, flips, and turns)

Identify figures with line symmetry and symmetrical parts

Identify mirror-images



Return to Guide Identify types of transformations

(slides, flips, and turns)

MeasurementArea, Perimeter, Circumference

Return to Guide

Develop area readiness by counting squares and blocks

Estimate and verify the area of a figure using square units (counting)

Find the perimeter of a polygon with 5 or less sides (no formula)

Estimate and verify the area of a figure using square units (counting)

Find the area of irregular shapes; using square units

Find the perimeter of polygons

Find the perimeter of a square or rectangle using the formula

Solve practical word problems involving perimeter and area of a square, rectangle or triangle

Calculate the area of a triangle

Length, Weight, Volume

Return to Guide

Measure weight with metric measures with units provided (grams)

Measure length to the nearest inch, foot, and yard and do appropriate conversions between these units

Measure length to the nearest millimeter, centimeter, meter, and kilometer

Select the appropriate metric and customary unit to measure an object or distance

Perform conversions between linear units in the customary system; also as necessary in addition or subtraction problems

Perform conversions between units of capacity in the customary system; also as necessary in addition or subtraction problems

Find the volume of a figure using cubic units

Perform conversions between units of mass in the metric system; also as necessary in addition or subtraction problems

Select appropriate unit of measure for length and area

Find the volume of rectangular solids using the formula

Time, Temperature

Return to Guide

Tell time to the nearest one minute on analog and digital clocks

Compute word problems with time and calendars

Determine elapsed clock time (no remaining with addition and subtraction)

Identify time relationships: minutes in an hour, hours in a day, days in a week, weeks in a year

Compute basic operations with units of time (include basic concept of time zones)



Determine elapsed clock time (any operation with renaming)

Number SenseDecimals

Return to Guide

Identify the greater or lesser of two decimals

Write a decimal for a shaded region (to tenths place)

Round decimals to the nearest whole number

Identify and understand place value for decimals (tenths, hundredths, and thousandths)

Write a decimal for a shaded region (hundredths)

Write a terminating decimal as a fraction or mixed number

Round decimals to nearest whole number, tenth, hundredth, or thousandth

Multiply a decimal by multiples of 10, 100, or 1000

Factorization / Divisibility

Return to Guide

Apply rules of divisibility by 5 Identify the greatest common factor of

two whole numbers each of which is less than 100

List some common multiples of two whole numbers

Identify numbers as prime or composite

Apply rules of divisibility by 2’s Complete a factor tree for a number

(prime factorization) Understand and demonstrate that many

whole numbers break down in different ways (e.g., 12 = 4 x 3 = 2 x 6 = 2 x 2 x 3)

Identify the least common multiple of two whole numbers

Apply rules of divisibility Identify the greatest common

factor of two whole numbers each of which is less than 100

List the prime and composite numbers less than 50 in a word problem

Fractions, Ratio, and Proportions

Return to Guide

Separate regions into sub regions that are equivalent (halves, thirds, fourths)

Read, shade, and write fractional parts of a group

Change a fractional numeral to its simplest form (lowest terms)

Write equivalent fractions using pictorial representation

Write improper fractions from picture presentations

Find equivalent fractions using multiples and factors

Write mixed numbers as improper fractions and improper fractions as mixed numbers

Change a fractional numeral to its simplest form (lowest terms)

Write the missing number in two equivalent ratios

Use a number line to identify a fractional point



Identify the least (lowest) common denominator of two fractions

Express a fraction as a decimal and vice versa

Solve proportions using the cross product method

Understand the concept of ratio using concrete and pictorial models

Money

Return to Guide

Identify the coins: pennies, nickels, and dimes

Identify the value of a penny, nickel, dime, quarter, and one dollar bill

Combine and identify the value of a collection of coins and bills up to and including $1.00

Combine and identify equivalent values of coins and bills up to and including $1.00

Make change to $1.00 by “counting on” or subtracting

Combine and identify the value of a collection of coins and bills up to and including $100.00

Ordering

Return to Guide

Order sets of objects 0-20 Identify the greater or lesser of two

numerals Order numerals through 999 Identify the numeral that comes

before, between, or after any given numeral through 999

Compare and order fractions Compare and order decimals to the

hundredths place

Compare and order fractions and mixed numbers

Order numbers from least to greatest and greatest to least

Compare and order numbers through the billions

Order decimals and fractions to the hundred thousandths

Identify the greater or lesser of 2 integers

Ordering integers that include fractions and wholes

Ordering exponential values


ISAT “Sub-Goal” RIT 181-190 RIT 191-220 RIT 201-210Percents

Return to Guide

Model percents using a 10 x 10 grid Write a decimal or fraction as a

percent and vice versa

Write a decimal or fraction as a percent or vice versa

Place Value

Return to Guide

Match number words to numerals to the ten thousands place

Identify and understand the place value and value of each digit in numbers through the hundred thousands

Add whole numbers using place value Identify and understand place value

for decimals (tenths, hundredths, and thousandths)

Identify the number and written word for ordinal numbers

Write numerals in expanded form through the hundred thousands

Match word names to numerals through billions

Identify place value using model to count

Understand and identify the place value and value of each digit in numerals through the billions

Write the word name for a decimal and vice versa

Write numerals in expanded form through the hundred billions

Whole Numbers

Return to Guide

Identify one more and one fewer Count and write by 2’s and 3’s Round 2- and 3-digit numbers to the

nearest hundred and tens Identify the value of Roman Numerals

using I, V, and X

Order numerals through 9999 Count and convert to dozens Round 4- and 5-digit numbers to the

nearest hundred thousand, thousand, hundred or ten

Round to the nearest millions and billions

Write the Roman numeral equivalent of Arabic numbers 1-2000 and vice versa


ISAT “Sub-Goal” RIT 181-190 RIT 191-220 RIT 201-210Mathematical Reasoning and Problem SolvingMathematical Reasoning and Problem Solving

Return to Guide

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


2003

Sample Test ItemsReturn to Top

RIT 181-190: Algebraic Concepts

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RIT 181-190: Computation






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RIT 181-190: Geometry






RIT 181-190: Measurement





2003


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RIT 181-190: Number Sense and Numeration

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RIT 181-190: Problem Solving

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2003

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RIT 181-190: Statistics, Probability, & Graphing

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