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Idaho State Expanded Curriculum Guide Math 5th 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 Top307.01.a307.02.c

Whole Numbers

Learning Continuum

Math BenchmarkTeacher Observable

For Learning:Students will write, compare, and order whole numbers trough billions on math sheet given by the instructor.

Play Roman numeral Bingo

Of Learning:RIT 201-210RIT 211-220

Explain how to compare two numbers. (Compare the values of the same place, and always start with the greatest place value.)

Practice rounding numbers to a give place value up to billion

Students math roman numeral to it’s equivalent Arabic number

307.01.b

Place Value, Expanded

and Standard Notation

Learning Continuum


For Learning:Teacher will read a six to ten digit number to students and they will write that number using correct place value.

Students will be given a number in the billions and they will rewrite that number using expanded notation.


Demonstrate using place value neighborhood the relationship between units, thousands, millions and billions.

Show students how to write a 6 to 10 digit number using expanded notation.


State Standard

and Benchmark

Local Curriculum




Sample Sequence

Minimum Hours

Allotted


Sample Resources

307.01.b307.01.e

Ordering, Equalities,

and Inequalities

Learning Continuum


For Learning:Students will arrange a set of decimals and/or fractions in order from least to greatest

Of Learning:RIT 201-210RIT 211-220RIT 221-230

Demonstrate how to order a set of decimals from least to greatest. Follow the procedure for ordering whole numbers. Work from left to right. If number contains a whole number order it first then start at tenths place and work to the right in order to arrange decimals.

Give students a card with a fraction with a common denominator or a different denominator and have them line up in order.

307.01.e

Fractions / Ratio /

Proportion

Learning Continuum


For Learning:Given a set of 10 flash cards student will write down 20 proper fractions to be reduced. Student will also include a answer key for fraction set.

Show students 6 green cubes and 8 red cubes. Students will show on an answer sheet three different ways to write the ratio of green to red cubes.


Using unfix cubes demonstrate how to reduce fractions by grouping with sets of two, three, etc.

Demonstrate to students how you can use unfix cubes to write ratio problems. Have students create pictures to represent improper fractions

Review daily in Daily Oral Math type practice

Daily oral math

Mountain mathhttp://www.mountain-math.com/products_math.shtml

307.01.f307.02.a307.01.d

Factorization / Divisibility

Learning Continuum


For Learning:Students will use a factoring tree to factor a teacher given large number.

Students will divide a two or three digit number by a one or two digit number with zeros in the quotient.

Students will write down the answers to the 100 harder multiplication and division facts in a timed test.

Show students that in order to factor numbers we need to know both prime and composite numbers.Show students how to make a factor tree when factoring larger numbers.

Demonstrate the steps in dividing a three and four digit number by a one-digit number.

Demonstrate the steps in dividing a three and four digit number by a one-digit number.

http://www.mountain-math.com/products_math.shtml




State Standard

and Benchmark

Local Curriculum




Sample Sequence

Minimum Hours

Allotted


Sample Resources

307.01.c307.01.d307.01.e

Decimals

Learning Continuum


For Learning:Given a picture of a set of objects the student will write a fraction for the set, reduce the fraction to its lowest form, and then write its decimal form.

Given a list of decimals students will put the list in order from least to greatest.

Students will change a list of decimals to fractions and order them from greatest to least.


Demonstrate using a picture of a set of objects how to write a fraction for the set of objects, reduce the fraction and write its decimal form.

On the board write 3.21, 3.34, 3.05, and 3.29. Demonstrate how to compare the numbers by first rewriting them vertically with their decimal points aligned. Show students how the fraction equivalents would also be ordered.

Percents

Learning Continuum


For Learning: Create a quiz grid with numbers on the front. Each number represents a questions. Form teams. Players take turns picking numbers and answering questions.


Place a fraction, decimal, and percent on the wall in different places around the room. Give the students cards with equivalent fraction, decimal, or percent on it and have them go stand under the different form of their number.

Integers Learning Continuum


For Learning:

Of Learning:RIT 221-230

Exponents and Scientific

Learning Continuum

Math

For Learning:Given a list of number the student writes them in scientific notation.

Proxima Centauri, the closest star to our own, is still 39,900,000,000,000 km away. Write this on the board. Explain to the students that this

http://guinan.gsfc.nasa.gov/docs/cosmic/glossary.html#kilometer


State Standard

and Benchmark

Local Curriculum




Sample Sequence

Minimum Hours

Allotted


Sample Resources

Notation BenchmarkTeacher Observable


number is so large that we need to reduce it. We use scientific notation to do this. Explain how to move the decimal and write the number

Give the students a list of numbers to the power of ten. Practice ordering them. E.g. 2X10^2 is larger than 2x10^3)

Estimation and Computation Return to Top

307.03.a307.03.b307.03.c307.02.f

Whole Numbers

Learning Continuum


For Learning:Have students take turn coming to the board to “teach” the other students how to do a problem.


Divide a 3 or 4 digit number by a one or two digit number. Check by multiplication.

Use manipulatives to show division the why of division

Estimate the answer mentally and then do the work. Demonstrate using real life items, how to estimate the price of a group of items.

DecimalsLearning Continuum


For Learning:


RIT 201-210 (Money)RIT 211-220 (Money)

307.03.a307.03.b307.03.c307.02.b

Fractions

Learning Continuum


For Learning:Given a set of fractions and mixed numbers the student will round to the nearest whole number.


Use estimation to predict you answers before you solve:Adding fractions with like denominatorsAdding mixed numbers with regroupingUse manipulatives to explain the


State Standard

and Benchmark

Local Curriculum




Sample Sequence

Minimum Hours

Allotted


Sample Resources

RIT 211-220RIT 221-230

why’s

Percents

Listed in the RIT range

Learning Continuum


For Learning:


Integers

Learning Continuum


For Learning:Given a worksheet with thermometers showing different temperatures, students will write positive and negative numbers to tell the temperature.


Teacher uses a number line to define integers as positive and negative numbers. Students read a thermometer using positive and negative numbers.

Squares

Learning Continuum


For Learning:Have the students draw a picture or representation that explains the relationship between multiplying a number by itself and squaring a number.


Practice dividing a number by itself.Explain that a shorter way of writing this is to square the number

Use Manipulatives to show the relation of the two.

Mathematical Reasoning and Problem Solving Return to Top

308.02.a308.02.b308.02.c

Reasoning and Problem

Learning Continuum


For Learning:Students will be given a 1 – 100 number chart and working in cooperative learning groups, students will use the number chart to solve problems involving multiples, inequalities, properties of numbers, even, odd, sums, and products.

After reviewing problem solving strategies, Set the student up in groups. Give each group a different word problem. Have each group decide which strategy will work best for their type of problem. Once done the groups will come to the board and defend their choice.

Problem solver- creative publications


State Standard

and Benchmark

Local Curriculum




Sample Sequence

Minimum Hours

Allotted


Sample Resources

Solving (Equals, Lawrence Hall of Science, c. 1989, p. 16 - 21)


Figure out the perimeter and area of the classroom. How much carpet would you need to re-carpet the class.

Place test scores on the board and have the students figure the mean for the class

308.01.a308.01.b308.01.c

UsingProblemSolvingSkills


For Learning:Student write word problems for two of the problem solving strategies

Students use information from the calendar and logical reasoning to solve problems about dates in the future.Ask students:If there are 7 days in a week and today is Tuesday the 8th what will be the date in three weeks on Friday.

308.03.a308.03.b308.03.cApplyingTechnologyAnd Models to find Solutions


For Learning:Given a set of numbers in a short time frame, students will find the answer by moving the decimal point to the right or left.

Given a series of “story” problems, students will explain what problem solving strategy that they used to arrive at their answer.

Teacher will demonstrate how to use a calculator to explore the pattern when multiplying by multiples of 10. Students will see the relationship and learn how to move the decimal point when using multiples of 10.

Using individual white boards, each student will solve problems presented by the teacher. Problems will include different strategies: 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

308.04.a308.04.b308.04.cCommunicate results using appropriate terminology and methods


For Learning:Given an array of data, such as students’ favorite sports, they will make a bar graph, pie graph, or line graph.

Students will use a Venn diagram to show number of brothers and sisters in each student’s family.

Teacher will show how to construct a bar graph on the students’ favorite ice cream flavors.


State Standard

and Benchmark

Local Curriculum




Sample Sequence

Minimum Hours

Allotted


Sample Resources

Students will trace and cut out pre-measured strips of paper to make discoveries about triangles. Data is entered in a table and the information is used to evaluate the triangles.

Concepts and Principles of Measurement Return to Top309.01.a309.01.b309.01.d

Length, Weight, Volume

Learning Continuum


For Learning:Given a ruler, the students will measure the height of their desk from the floor and express it in inches and centimeters.

Given a worksheet with problems involving weight of objects, using pounds and ounces, students will write the answers. Additional problems include adding pounds and ounces and correctly carrying the ounces to pounds.


Length: Teacher will demonstrate to the class how to read a ruler, yardstick, and meter stick. Teacher will show how to make comparisons between units (for example a centimeter is about a half-inch, a yard is equivalent to a meter, a mile is equivalent to a kilometer). Students will measure the length of their textbook, work in groups to measure the length of the room using yards and meters.

Weight: Teacher discusses with the students that 1 pound = 16 ounces and 2,000 pounds = 1 ton. Teachers discusses when it is appropriate to use ounces (like in baking), pounds to weigh themselves, and tons to weigh an automobile. Students will complete worksheets using this information.

For Learning:Given a ruler, students will measure

Area: Teacher uses carpeting a room to show how to use area. Teacher


State Standard

and Benchmark

Local Curriculum




Sample Sequence

Minimum Hours

Allotted


Sample Resources

Area and Volume


the area of their desktop and express the answer in square inches and square centimeters.

Given a problem on the board with the dimensions of a container that is 8” high X 6” wide X 7” deep, students will compute the volume and express the answer in cubic inches.

presents the formula for area: length X width. Teacher explains that answers are in square units. Teacher gives students the measurements and students compute the area of a rectangle.

Volume: Teacher gives the formula for volume: length X width X height. Teacher explains that volume is expressed in cubic units. Teacher gives example of using volume to fill a fish tank with water or to fill a swimming pool with water. Teacher presents a problem with a tank and students compute the volume.

309.01.f

Time, Temperature

Learning Continuum


For Learning:Time: Given a clock with a time set by the teacher, teacher will ask students to add and subtract time. Students will write answers on paper.

Temperature: Teacher will put a drawing of a thermometer on the board and use increments of 1, 2, or 5. Teacher colors in the fluid and students read the temperature and write the answers on paper.


Temperature: Using a classroom set of thermometers, teacher has students go outside and find the warmest and coldest spot in the area around the school building. Teacher observes students and asks them to tell the reading. Teacher also discusses the way thermometers may use different increments of measurement.

Time: Teacher uses a model of a clock to set a clock time and then present problems to students involving addition and subtraction of time. For example: It’s 8:30 now, what time will it be in two hours.

309.01.e

ConvertingUnits of

Measurement


For Learning:Given the height of the room in feet and inches, students will convert the measurement to inches.

Teacher explains the relationship between inches, feet, yard, and miles and their metric equivalents. Teacher poses problems to the class such as: 78” of material is how many feet and inches; if we have 2.5 meters of yarn, how many centimeters does


State Standard

and Benchmark

Local Curriculum




Sample Sequence

Minimum Hours

Allotted


Sample Resources

that equal? Teacher poses more problems to students using real life situations, such as size of the room, students compute the problems and express answers in multiple forms.

309.02.aApply

DimensionalAnalysis


For Learning:Students solve the following problem: A student reads for 30 minutes a night for 4 nights a week. Students need 8 hours for an extra recess. How many nights will it take a student to earn a free recess?Of Learning:RIT 201-210 (Angle Measurement)RIT 211-220 (Angle Measurement)

Given real life situations and objects, students will choose an appropriate type of measurement and compute the answer. For example: A student reads 30 minutes a night for 4 nights a week. How many hours will the student read in a month?

309.01.cPerimeter,

area of rectangle, square, triangle

Learning Continuum


For Learning:Teacher draws rectangular and triangular shapes on the board with measurements provided. Students compute the perimeter and area and write answers on paper.


Perimeter: Teacher explains that perimeter is the distance around an object. Teacher may present the formula for perimeter of a square: perimeter = side squared and rectangle: perimeter = 2L + 2W. Students will measure perimeter of objects around the school, such as the pad for the basketball court.

Area: (rectangle and square, see above). Area of a triangle: Teacher presents the formula: area = ½ base X height. Teacher makes sure that students understand that you find the area of the triangle and divide by 2. Teacher draws triangles on the board and students compute the area and express the area in square units.

Algebra, Functions, and Mathematical Models Return to Top

310.01.a313.01.a313.01.b

Learning Continuum

Math Benchmark

For Learning:Given the sequence 2, 5, 11, ___, 47, ___, students will fill in the blanks.

Of Learning:

Teacher presents sequences of numbers, such as 6, 12, ___, 24, ___. Students identify the pattern and complete the sequence or fill in the blanks. Students create sequences


State Standard

and Benchmark

Local Curriculum




Sample Sequence

Minimum Hours

Allotted


Sample Resources

313.02.a

Patterns, Sequences, Functions

Teacher Observable

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

for their peers to solve. Can also use pattern blocks, skittles, pencils and pens, etc. To create a pattern.

310.01.c310.02.a310.02.b310.03.a307.02.e

Solving Equations

and Inequalities, Simplifying

Expres-sions, Order

of Operations

Learning Continuum


For Learning:Given the problem: 5(8 – 3) + 62 = ___ students will solve the problem.

Given a problem such as: 5 * 3 + X = 2 * 20Students will write the answer to the problem.


Order of operations: Teacher presents the saying: “please excuse my dear Aunt Sally” which stands for parentheses, exponents, multiply, divide, add, and subtract. Teacher explains that you work from left to right. Students complete sample problems.

Solving for X: Teacher presents a problem such as: 10 * 2 + X = 12 * 2 and demonstrates how to solve for X.

310.01.a310.01.b

Properties

Learning Continuum


For Learning:Students will be given a variety of equations, and they will solve for X using the inverse operation.

Given a variety of example problems, students will label the problem for the property that is shown: commutative, associative, distributive, and zero property.


Algebraic expressions involving addition: Teacher demonstrates how to solve addition problems with a variable, and to think of a related subtraction equation. Teacher demonstrates how to solve a subtraction problem with a variable and to think of a related addition problem. Students solve problems from the math book.

Properties of integers: Commutative, associative, distributive, and zero property. Teacher provides examples and explanations. Students complete problems.


State Standard

and Benchmark

Local Curriculum




Sample Sequence

Minimum Hours

Allotted


Sample Resources

Concepts and Principles of Geometry Return to Top

311.01.a311.01.e

Shapes and Figures, 2- &

3-dimensional

Learning Continuum


For Learning:Using a worksheet, students will identify and label solid and plane figures.


Solid objects: Students will make a model for rectangular prisms, triangular pyramids, square pyramids, cones, and cylinders. Using the models, the teacher explains the concepts of edges, faces, vertices (corners), and surface area.

Identifying polygons including quadrilaterals (square, rectangle, parallelograms, rhombus, trapezoid), pentagon, octagon, triangles (scalene, right, isosceles, equilateral). Students will find polygon shapes around the room. Teacher explains and discusses each shape and gives more examples.

Students find examples of shapes at home and brings them in

311.01.cCongruency

and Similarity

Learning Continuum


For Learning:Given a worksheet with pairs of lines, angles, and shapes, the student will label congruent and not congruent pairs.


Congruent: Teacher explains that congruent means a line, an angle, or a shape that is exactly the same size. Students identify congruent and not congruent shapes, lines, or angles.

Have the students cut lines form string. Move the lines around the page to see that they are the same.

Geometer’s Sketchpadhttp://www.keypress.com/sketchpad/product_info.html

311.01.cSymmetry

and Transform-

ations

Learning Continuum


For Learning:Teacher will fold paper in front of the class and ask if there is symmetry or more than one line of symmetry. Students will write the answers for each example.

Given a shape or image, students will create a symmetric image and then

Students use paper to fold plane figures. If it can be folded in half and both halves match, then the figure has symmetry. Examples are given showing more than one line of symmetry.Use mirror to project symmetric shapes and angles on a page

Interactive manipulatives

http://www.matti.usu.edu/nlvm/

nav/index.html


State Standard

and Benchmark

Local Curriculum




Sample Sequence

Minimum Hours

Allotted


Sample Resources

transform the imageOf Learning:RIT 201-210RIT 211-220

Students define Transformation as a rotation of a shape or imagePractice transformations using mires

311.01.b311.01.d311.01.f

GeometricProperties

and Terminology

Learning Continuum


For Learning:Students will draw and label a point, line, line segment, ray, parallel lines, perpendicular lines, and intersecting lines.

Teacher will draw three angles on the board and students will identify the type of angle.


Using the board the teacher will demonstrate and explain point, line, line segment, ray, parallel lines, perpendicular lines, and intersecting lines.

Angles: Using a protractor, the teacher will show right angles, acute, and obtuse angles. Students will practice making angles

Students learn appropriate symbols for line, point, line segment, ray, parallel lines, etc.

311.02.a

Coordinate

Learning Continuum


For Learning:Given a piece of graph paper with the X and Y-axis, students will use coordinates (ordered pairs) to draw a figure.

Of Learning:RIT 201-210 (Graphing)RIT 211-220 (Graphing)RIT 221-230 (Graphing)

Teacher introduces the concept of X and Y-axis and ordered pairs using graph paper. Teacher explains that the X-axis is horizontal and the Y-axis is vertical. Teacher explains that the first number in an ordered pair is X coordinate and the second number is the Y coordinate. Teacher explains negative numbers on the X and Y-axis.

Data Analysis, Probability, and Statistics Return to Top312.02.a312.01.a312.01.b312.01.c

Data Analysis

Learning Continuum


For Learning:Given a table of data, such as number of students in after school activities, students will construct a bar graph, a line graph, and a circle graph for the same information.

Teacher presents and explains how to use a various types of graphs made from data given in the text or collected by the students.

Students practice making graphs for different situations, i.e. Bar graph for favorite ice cream flavors


State Standard

and Benchmark

Local Curriculum




Sample Sequence

Minimum Hours

Allotted


Sample Resources

312.04.a312.04.b312.05.a312.05.b

Probability & Prediction

Learning Continuum


For Learning:Given a problem with socks.Sock drawer contains 1 pair of blue socks, 2 pairs of red socks, 3 pair of brown socks, and 6 pair of white socks. What is the probability of pulling a pair of white socks out of drawer without looking at the pair you draw.


Teacher uses a graph to show the favorite flavors of ice cream. Using probability, students predict the probability that someone will choose one of the favorites.

Using a spinner or coin, explain the chances of getting a 2. Give each student or pair of students a coin or spinner and have them test it.

Combina-tions and Permuta-

tions

Learning Continuum


For Learning:Given a list of numbers students will list all of the ways they can be put together


Give each student a bag with 4 green skittles, 2 red skittles, and three yellow skittles. Tell them they need to draw out two and write down what they get. Return to the bag and repeat until all combinations have been drawn. Discuss that this is an arrangement and then do two to three problems as a class.

312.03.a312.03.b

Statistics

This is not listed on the 5th

grade RIT but is on the one above and below

Learning Continuum


For Learning:Given a set of sample test scores the student will find the mean, median, and mode.


Teacher will introduce mean, median, and mode using classroom test scores. Explain the mean, or average, is the sum of the scores divided by the number of scores. The mean should be rounded to the nearest tenth. The mode is the score that occurs the most often. The median is the middle number when the items are arranged in order. The range is the difference between the greatest and least numbers.


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.

Idaho State Expanded Curriculum Guide Math 5th Grade ©State of Idaho 2003 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.


State Standards—5th Grade MathReturn to Top

306. MATHEMATICS STANDARDS – GRADE 5, SECTIONS 307 THROUGH 313.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.

307. 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 Number Sense—Whole Numbers

a. Read, write, order, and compare whole numbers through billions, commonly used fractions, and decimals through thousandths.

i. Read, write, and compare large numbers.

ii. Identify a digit’s value in whole numbers and decimals.

iii. Read, write, and compare decimal numbers.

iv. Write a number with a 4 in the thousandth place and a 3 in the thousandth place.

Return to Place Value

Return to Ordering, Equalities, and Inequalities

b. Demonstrate and apply the knowledge of whole numbers, decimal place value, and patterns of periods (thousandths to billions).

i. Use numbers, words, and pictures to explain how a tenth and a hundredth are related.

Return to Number Sense--Decimals

c. Explore the relationship between equivalent fractions.

i. Use numbers, words, and pictures to explain how 0.50 and 1/2 are related.

Return to Factorization/ Divisibility


d. Explore the relationship between decimals and simple fractions through thousandths.

Return to Ordering, Equalities, and Inequalities

Return to Fractions, Ratio, Proportion


e. Show a sense of magnitudes and relative magnitudes of whole numbers, decimals, and simple fractions.

i. Order a list of decimalsii. Order a list of simple fractions,

for instance, 1/4, 1/3, 1/2, or 2/3, 1/2, 3/4.


f. Explore and apply number theory concepts (prime, composite, multiples, factors).

i. What are the multiples of 12 and the factors of 12?

ii. Use composite numbers to discover the divisibility rules for 2 and 5.


02. Perform computations

accurately.


a. Multiply and divide whole numbers. i. Use basic arithmetic facts to solve more complex problems.

ii. Identify and use mathematical properties (zero property, associative, distributive, communicative, and identity property), for instance, 4 x 12 = (4 x 10) + (4 x 2).

Return to Estimation—Fractions

b. Add and subtract fractions with like denominators and simplify as necessary.

i. Add 1/4 + 1/4.ii. Subtract 3/4 - 1/4.

Return to Number Sense—Whole Numbers

c. Add and subtract decimals through thousandths.

i. Add 2.34 + 51.602.

d. Instantly recall basic multiplication and division facts up to 10s.

i. Complete 100 division facts with single-digit factors in 3 minutes.

Return to Solving Equations e. Evaluate numerical expressions that include parentheses.

i. Solve basic expressions that have parenthesis, for instance, 4 + (2 x 3).

Return to Est/Comp—Whole Numbers

f. Select and use an appropriate method of computation from mental math, paper and pencil, calculator, or a combination of the three.

g. Use appropriate vocabulary.

03. Estimate and judge reasonableness of results.

Return to Estimation—Whole Numbers


a. Use estimation to predict computation results.

i. Estimate all computation to determine if reasonable.

ii. Round to estimate reasonable solutions (11.436 - 6.1 = □).



b. Recognize when estimation is appropriate and understand the usefulness of an estimate as distinct from an exact answer.

i. Is $20 enough money to buy 2 CD’s? Do you need an exact sum or an estimate?



c. Determine whether a given estimate is an overestimate or underestimate.

i. Is your estimate greater or less than the actual answer? Explain.


d. Use appropriate vocabulary.

308. MATHEMATICAL REASONING AND PROBLEM SOLVING.Rationale: These processes are essential to all mathematics and must be incorporated in all other mathematics standards.



01. Understand and use a variety of problem-solving skills.

Return to Using Problem Solving Skills

a. Use a variety of strategies to compute problems drawn from real-world situations.

i. There were 31 wheels and 12 seats in a bike shop. The bike shop sold bicycles and tricycles. How many bicycles and how many tricycles were in the bike shop?

ii. Plan a party for the 5th grade. Estimate how many packages of plates you will need if plates come in packages of ten.

Return to Using Problem Solving Skills

b. Solve problems using the 4-step process of problem solving (explore, plan, solve, examine).

i. Identify when a problem has too much or too little information.

ii. Check for reasonable answers.Return to Using Problem Solving Skills

c. Make predictions and decisions based on information.

02. Use reasoning skills to recognize problems and express them mathematically.

Return to Reasoning and 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. Explain how to use the array model of multiplication to solve this problem, for instance, 27 x 42.ii.Explain how you know that 0.5 and 0.50 are equivalent.


b. Apply solutions and strategies to new problem situations.

i. Determine how many cubes will be needed to fill a box that is 3 centimeters wide, 2-centimeters long, and 2 centimeters high.


c. Formulate conjectures and discuss why they must be or seem to be true.

i. Formulate a conjecture about multiplying with multiples of ten and explain why it is true, for instance, 20 x 30 = 600.


03. Apply appropriate technology and models to find solutions to problems.

Return to Applying Technology

a. Understand the purpose and capabilities of appropriate technology use as a tool to solve problems.

i. Use a calculator to explore the pattern when multiplying with multiples of ten, for instance, 400 x 20 = 8,000.


b. Use computer applications to display and manipulate data.

i. Use computer applications to create a bar graph representing student collected data.


c. Select appropriate models to represent mathematical ideas.

i. Make a model to show 2/3 is equal to 4/6.

ii. Make a model of 4 x 25 in different ways.

04. Communicate results using appropriate terminology and methods.

Return to Communicate Results

a. Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to communicate mathematical information.

i. Use a bar graph to show favorite flavors of ice cream in the class.


b. Use appropriate vocabulary to communicate mathematical information.


c. Use appropriate notation. i. Convert a one-step story problem to a number equation using appropriate notations, terms, and labels.

309. CONCEPTS AND PRINCIPLES OF MEASUREMENT.Rationale: The step in scientific investigation is understanding the measurable attributes of objects.

Standard – 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 Perimeter, Area of Rectangle, Square

a. Select and use appropriate units and tools to make formal measurements in both systems.

i. Measure the length of your desk.ii. Draw a 6-centimeter line and a 6-

inch line.



b. Apply estimation of measurement to real-world and content problems using actual measuring devices.

Return to Perimeter, Area of Rectangle, Square

c. Explore the differences and relationships between perimeter and area in both systems.

i. Form 2 different rectangles, each with a perimeter of 50 centimeters.

ii. Form 2 different rectangles, each with an area of 100 centimeters.


d. Solve problems involving length, perimeter, area, weight, mass, and temperature.

i. Find the perimeter of your desk. ii. Look around the room and find an

obtuse, right and acute angle.

Return to Converting Units of Measurement

e. Convert unit of measurement within each system.

i. Each 5th grader in the classroom needs 1 foot of string for an art project. How many yards of string does the class need?

Return to Time/Temperature f. Apply understanding of relationships to solve real-world problems related to time.

i. If a student started reading at 10:55 a.m. and finished at 12:15 p.m., how much time has passed?

g. Use appropriate vocabulary.02. Apply dimensional

analysis.

Return to Apply Dimensional Analysis

a. Understand units and their relationship to one another and to real-world applications.

i. Each student reads 15 minutes a night. How many hours did each student read in a week?

310. 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.

Return to Patterns, Sequences, Functions

Return to Properties

a. Explore the meaning and use of variables in simple expressions and equations.

i. What is the value of n + 3 if n = 2?

ii. What is the value of n if n + 3 = 11?

Return to Propertiesb. Translate simple word statements and

story problems into algebraic i. Write an equation to match a

story problem.


equations.

Return to Solving Equations c. Use symbols (<, >, =) to express relationships.

i. Use the correct symbol to make this number sentence true: 24 + 6 18 + 9.

02. Evaluate algebraic expressions.

Return to Solving Equations

a. Explore and use the following properties as they relate to addition and multiplication: commutative, associative, identity, zero, and inverse.

i. Give an example or demonstrate the following properties: zero, identity, commutative, associative, distributive, and inverse.

Return to Solving Equations b. Investigate the order of operations (parentheses only).

i. Compare (2 + 3) x 4 and 2 + (3 x 4).

03. Solve algebraic equations and inequalities.

Return to Solving Equations

a. Solve missing addends and missing factor problems using inverse operations.

i. 3 x n = 9.ii. 5 + n = 16.iii. Give the family of facts for (6, 4,

10) and (6, 4, 24).

311. 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 & Figures

a. Identify, compare, and analyze attributes of two- and three-dimensional shapes and develop vocabulary to describe the attributes.

i. Find examples of these figures and objects in the real world: sphere/circle, rectangle/rectangular prism, triangle/triangular pyramid.

ii. Draw a trapezoid, parallelogram, and regular polygons.

iii. Explain the classification system of quadrilaterals.

Return to Geometric Properties and Terminology

b. Explore the fundamental concepts, properties, and relationships among points, lines, rays, angles, and shapes.

i. Construct and label an acute angle, right angle, and an obtuse angle.

ii. Construct and label a line, line segment, and ray.


Return to Congruency and Similarity

Return to Symmetry and Transformations

c. Explore congruence, similarities, and symmetry of shapes.

i. Find lines of symmetry by drawing or folding a variety of shapes.

ii. Divide a square into 4 congruent parts in more than 1 way.

Return to Geometric Properties and Terminology

d. Determine perimeters of polygons and area of rectangles/squares in real-world situations.

i. Find the perimeter of a variety of closed shapes.

Return to Shapes & Figures e. Predict and describe the results of sliding, flipping, and turning two-dimensional shapes.

i. Create a design by rotating a square around a fixed point.

ii. Identify shapes that will tessellate.iii. Create a design by reflecting your

name.Return to Geometric Properties and Terminology

f. Use appropriate vocabulary.

02. Apply graphing in two dimensions.

Return to Coordinate

a. Identify and plot points on a coordinate plane.

i. Play Battleship!ii. Plot a set of points on a

coordinate plane to form a picture.

312. 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.



01. Understand data analysis.

Return to Data Analysis

a. Read and interpret tables, charts, and graphs.

i. Find a graph in the social studies textbook and interpret it.

Return to Data Analysisb. Explain and justify conclusions drawn

from tables, charts, and graphs.

Return to Data Analysisc. Understand and use vocabulary.

02. Collect, organize, and display data.

Return to Data Analysis

a. Collect, organize, and display data with appropriate notation in tables, charts, and graphs.

i. Collect and display data from a class on their favorite sports.

03. Apply simple statistical measurements.

Return to Statistics

a. Find measures of central tendency - mean, median, and mode - with simple sets of data.

i. Given a set of data, identify the mean, median, and mode.

ii. Line up from shortest to tallest and find the “median”, or, if even number of students, find two students to “represent the median.”

Return to Statistics b. Determine the range of a set of data. i. Using the lengths of pencils in the classroom, determine the range.


04. Understand basic concepts of probability.

Return to Probability and Prediction

a. Predict, perform, and record results of simple probability experiments.

i. Using 1 dice, roll the dice thirty times and record the results.


b. Understand and use the language of probability.

i. Use outcome, probable, certain, likely, unlikely, and impossible when conducting a probability experiment.

05. Make predictions or decisions based on data.


a. Make predictions based on simple experimental probabilities.

i. Knowing the probability of a given outcome such as rolling dice, predict the likelihood of a future event.


b. Understand and use appropriate vocabulary.

313. 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.


a. Extend patterns and identify a rule (function) that generates the pattern using whole numbers and decimals.

i. Given a numerical pattern extend it and identify the rule in as many ways as possible.

ii. Create a numerical pattern.


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

i.Using toothpicks, create a geometric pattern that can be continued.

Return to Applying Technology and Models

c. Use mathematical models to show change in real context.

i.Create a graph showing how a candle’s height changes over time after being lit.

d. Understand and use appropriate vocabulary.

02. Apply functions to a variety of problems.


a. Use patterns to represent and solve simple problems.

i. Would you rather have 15-minutes recess each day for the next 2 weeks or would you rather have 1 minute the 1st day, 2 minutes the 2nd day, 4 minutes the 3rd day, and so on, through the 2 weeks. Explain your thinking using words, numbers, and pictures.


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


New Vocabulary (l) and Symbols (¢)

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


New Vocabulary (l) and Symbols (¢)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)




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)




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)


New Vocabulary (l) and Symbols (¢)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




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 201-210 RIT 211-220 RIT 221-230AlgebraSolving Equations, Simplifying Expressions, Order of Operations

Return to Guide

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)

Solve decimal equations (one step, addition and subtraction)

Solve integer equations (one step, multiplication and division)

Evaluate expressions using the order of operations (may include parentheses or exponents)

Solve quadratic equations

Solve for missing addends in an addition or subtraction sentence

Use boxes or other symbols to stand for any number in expressions or equations

Solve whole number equations with one variable (multiplication and division)

Solve integer equations (one step, all four operations)

Solve equations involving more than one operation

Solve one-step linear equations in one variable using addition, subtraction, multiplication, and division with integer solutions

Simplify numeric expressions by applying properties of rational numbers (e.g. identity, inverse, distributive, associative, commutative)

Patterns, Sequences, Functions

Return to Guide

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

Use logic to solve a problem involving a function table

Complete a function table according to a rule

Recognize and continue a number pattern and/or geometric representation (e.g. Fibonacci sequence, triangular numbers)

State a rule to explain a number pattern, including arithmetic progression

Investigate geometric patterns and relationships and describe them algebraically


ISAT “Sub-Goal” RIT 201-210 RIT 211-220 RIT 221-230Properties

Return to Guide

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

Understand the properties of integers: commutative, associative, identity, zero property of multiplication, distributive property of multiplication over addition, and inverse property of addition

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 StatisticsCombinations and Permutations

Return to Guide

Solve problems involving arrangements

Use a tree diagram to determine the number of possible outcomes of an event

Data Analysis

Return to Guide

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

Read and interpret information from a graph

Interpret Venn Diagrams Make predictions from a graph

Interpret data given in horizontal and vertical bar graphs to solve problems

Probability and Prediction

Return to Guide

Compute simple probability outcomes

Determine the probability of an outcome (multiple events)

Use the counting principle to determine probability

Investigate experimental probability of an event using a coin or spinner

Investigate experimental probability of an event using a coin or spinner

Predict outcomes using probability


ISAT “Sub-Goal” RIT 201-210 RIT 211-220 RIT 221-230Statistics

Return to Guide

Solve practical problems involving the mean (average) of a set of numbers

Know the concepts of mode, median, and mean; compute and compare them in simple examples to demonstrate that these measures of central tendency may differ for a given set of data

Estimation and ComputationDecimals

Return to Guide

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

Add decimals through hundred-thousandths with a calculator

Multiply a decimal by a decimal, factors to thousandths

Divide a decimal by a whole number and vice versa

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

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

Write a number sentence to solve one-step word problems involving the operations of addition, subtraction, and multiplication of fractions and decimals

Subtract decimals through hundred-thousandths with a calculator

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

Divide a whole number (or decimal) by a decimal to thousandths

Fractions

Return to Guide

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

Add fractions with like denominators, answer in lowest terms

Add mixed numbers with unlike denominators with regrouping

Multiply a whole number by a fraction

Divide a fraction by a fraction Divide a mixed number by a whole

number or a fraction

Add and subtract fractions with like denominators; change improper fractions to mixed numbers

Subtract fractions having unlike denominators, answer in lowest terms

Add and subtract whole numbers, fractions and mixed numbers

Use estimation to solve problems involving mixed numbers


ISAT “Sub-Goal” RIT 201-210 RIT 211-220 RIT 221-230 Divide a whole number, fraction or

mixed number by a mixed numberIntegers

Return to Guide

Add integers with like signs Add integers with unlike signs Add several integers Multiply integers with unlike signs Divide integers with unlike signs

Divide integers, like signs

Percents

Return to Guide

Find a percent of a number Find the percent one number is of another (20 is what % of 90)

Find a number from a percent (4 is 9% of what number)

Squares

Return to Guide

Calculate the square of any number less than 100

Whole Numbers

Return to Guide

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)

Divide a 3-digit or 4-digit number by a 1-digit number

Use multiplication as a check for division

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

Divide a 4-digit number by a 2-digit number

Develop computational fluency with division facts

Divide multi-digit numbers using a calculator

Introduce the math strategy of compatible numbers in estimating for all four operations


ISAT “Sub-Goal” RIT 201-210 RIT 211-220 RIT 221-230GeometryCongruency and Similarity

Return to Guide

Identify congruent figures, angles and line segments

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

Identify congruent polygons and their corresponding sides and angles

Identify congruent triangles according to corresponding parts (SSS, SAS, ASA)

Coordinate

Return to Guide

Graph ordered pairs in all four quadrants (coordinate geometry)

Geometric Properties and Terminology

Return to Guide

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

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

Identify angles: right, obtuse, and acute

Identify when two intersecting lines are perpendicular

Identify properties of similar figures

Measure angles using a protractor

Identify the center, radius and diameter of a circle

Measure angles using a protractor Classify angles: supplementary

and complementary Classify angles: adjacent, vertical,

corresponding, and supplementary Find the missing angle

measurement in a triangle when two angles are known

Analyze circles: center, chord, diameter, radius, arc, semicircle, and circumference

Shapes and Figures, 2- and 3-Dimensional

Return to Guide

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

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

Contrast open and closed figures Identify polygons: triangle,

quadrilateral, pentagon, hexagon, and octagon

Identify quadrilaterals: square, rectangle, parallelogram,

Analyze solid figures: rectangular prism, triangular prism, triangular pyramid, square, pyramid (faces, edges and vertices)

Classify polygons by sides and angles


ISAT “Sub-Goal” RIT 201-210 RIT 211-220 RIT 221-230figures: cube, cylinder, triangular pyramid and square pyramid (faces, edges, and vertices)

trapezoid, rhombus Analyze solid figures: triangular

pyramid and rectangular pyramid (faces, edges, and vertices)

Symmetry and Transformations

Return to Guide

Identify mirror-images Identify types of transformations (rotation)

MeasurementArea, Perimeter, Circumference

Return to Guide

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

Calculate the area of irregular shapes

Understand the effects of changing dimensions on perimeter and area

Length, Weight, Volume

Return to Guide

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

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

Measure length with metric measures (centimeter)

Measure length with customary measures (inch)

Select the appropriate unit of measure for length, area, and volume

Time, Temperature

Return to Guide

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

Compute word problems with time and calendars


ISAT “Sub-Goal” RIT 201-210 RIT 211-220 RIT 221-230

Number SenseDecimals

Return to Guide

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

Round monetary amounts to the nearest single coin or bill which could be used to pay for a purchase up to and including $20.00

Write the decimal equivalent of a fraction and label as repeating or terminating

Round decimals to nearest whole number, tenth, or hundredth

Write a terminating decimal as a fraction or mixed number

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

Identify and order decimal and fractional coordinates on a number line


Relate fractions to decimals Write a decimal or mixed decimal

for a fraction (2/3=0.66)

Exponents and Scientific Notation

Return to Guide

Write whole number in exponential form and compute the power of a number

Order of “powers” Write a whole number or a decimal

in scientific notation Write a number expressed in

scientific notation in standard form

Identify and use powers of 10

Factorization / Divisibility

Return to Guide

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

Understand and use rules of divisibility

Identify the greatest common factor of two whole numbers: list the factors or prime factorization

Identify the greatest common factor and least common multiple of two whole numbers

Identify the least common denominator for 3 or more fractions: list the multiples or prime factorization


ISAT “Sub-Goal” RIT 201-210 RIT 211-220 RIT 221-230Fractions, Ratio, and Proportions

Return to Guide

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

Write improper fractions from picture presentations


Compare and order fractions and mixed numbers


Model and write numerical fractions


Understand the concept of ratio using concrete and pictorial models

Determine if a pair of ratios is equal or not equal using the equivalent fractions method

Write the missing number in 2 equivalent ratios

Solve proportions using the cross product method

Integers

Return to Guide

Order integers on a number line Identify the greater or lesser of 2 integers

Order integers on a number line

Understand the meaning of integers

Ordering

Return to Guide

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

Compare and order fractions with the same denominator and with different denominators

Order decimals to thousandths; identify the greater or lesser of two decimals to thousandths

Order a set of integers from least to greatest

Place numbers in correct order on a number line

Percents

Return to Guide

Write a decimal or fraction as a percent or vice versa

Express a fraction as a decimal and as a percent

Write a ratio (fraction) as a percent and a percent as a ratio (fraction): denominators of 100


ISAT “Sub-Goal” RIT 201-210 RIT 211-220 RIT 221-230Place Value

Return to Guide

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

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

Match word names to numerals to the hundred thousands in decimals

Whole Numbers

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Round to the nearest millions and billions

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

Mathematical Reasoning and Problem SolvingMathematical Reasoning and Problem Solving

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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

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

Solve practical problems involving the mean (average) of a set of numbers

Solve one- and two-step word problems involving any combination of basic operations on whole numbers, decimals, and fractions

Determine the discount price and sale price

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, or Write an equation

Calculate the cost of one item or

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, or Write an equation

Write and solve an equation using ratios, given a word problem

Write and solve an equation for a word problem

Solve simple interest problems (amount x rate x time)

Use estimation to determine if solutions to word problems are reasonable


ISAT “Sub-Goal” RIT 201-210 RIT 211-220 RIT 221-230test, Make a list, Make a table, Find a pattern, Work backwards, Solve a simpler problem, Draw a diagram, Write an equation, or Logical Deduction

the unit cost using a proportion


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RIT 201-210: Algebraic Concepts

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RIT 201-210: Computation

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RIT 201-210: Geometry






RIT 201-210: Measurement

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RIT 201-210: Number Sense and Numeration

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RIT 201-210: Problem Solving

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RIT 201-210: Statistics, Probability, & Graphing



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