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For the Idaho State Department of Education

Assessments Mapped to the Idaho State Mathematics Standards for Grades 2-10

January 2003 by

KEY TO ABBREVIATIONS

Learning Continuum (RIT Scales):

N = Number Sense and NumerationC = ComputationP = Problem SolvingM = MeasurementA = Algebraic ConceptsG = GeometryS = Statistics/Probability and Graphing

DMA# = Direct Math Assessment, grade level

N# = NAEP, grade level

[dupl.] = an item description from the Learning Continuum that appears more than once, either at the same grade level or at the grade level below or above it

276. MATHEMATICS STANDARDS – GRADE 2 (AVERAGE SCORE: 187-197)

277. BASIC ARITHMETIC, ESTIMATION, AND ACCURATE COMPUTATIONS

Standard – The student will:

Content Knowledge and Skills:

Item Description: Item Source:

01. Understand and use numbers.

a. Demonstrate knowledge of our numeration system by counting a variety of ways.

Count and write by 10’s to 100 [dupl.]

Count and write by 2’s and 3’s [dupl.]

Count and write by 4’s [dupl.]

Identify the number and written word for ordinal numbers

Count and convert to dozens

N: 171-180

N: 181-190

N: 191-200

N: 191-200

N: 191-200

b. Read, write, order, and compare whole numbers to 1,000.

Identify the greater or lesser of two numerals

N: 181-190

1

Order sets of objects 0-20

Order numerals through 999

Identify the numeral that comes before, between, or after any given numeral through 999

Identify one more and one fewer

N: 181-190

N: 181-190

N: 181-190

N: 181-190

c. Demonstrate the knowledge of place value through 999.

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

Add whole numbers using place value

Identify place value using model to count [dupl.]

N: 161-170

N: 181-190N: 191-200

N: 191-200

d. Determine, by counting, the value of a collection of pennies, nickels, dimes, and quarters, up to $1.00.

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

M: 181-190

M: 181-190

M: 181-190

M: 181-190

2

e. Explore decimals using money through hundredths.

Identify the greater or lesser of two decimals

N: 181-190

f. Understand and apply appropriate vocabulary.

New Vocabulary in this Range: 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

New Vocabulary in this Range: thirds, fourths, rounded, thousands, exponential form, mixed number, improper fraction, lowest common denominator, percent, expanded form, prime, factor, proportion [dupl.]

N: 181-190

N: 191-200

02. Perform computations accurately.

a. Demonstrate proficiency with addition and subtraction facts through 18.

Identify fact families with sums 0-18 in horizontal format

Understand the concept of subtraction using symbols; subtract two numbers in vertical format

C: < 150

C: < 150

b. Add whole numbers with and without regrouping through 99.

Add a 2-digit number and a 2-digit number with no regrouping

Add 1- and 2-digit

C: 161-170

C: 171-180

3

numbers with regrouping

c. Add a series of one-digit addends.

Add three 1-digit numbers

C: 151-160

d. Explore double-digit subtraction of whole numbers with regrouping through 99.

Subtract a 1-digit number from a 2-digit number with regrouping

Subtract two 2-digit numbers with regrouping

C: 151-160

C: 171-180

e. Use appropriate vocabulary.

New Vocabulary in this range: difference, not true, power of 10, rounded, thousands [dupl.]

C: 191-200

03. Estimate and judge reasonableness of results.

a. Use estimation to predict computation results.

b. Evaluate the reasonableness of an answer.

Round 2- and 3-digit numbers to the nearest hundred and tens [dupl.]

Estimate the answers to word problems [dupl.]

N: 181-190

P: 191-200

c. Use appropriate vocabulary.

278. MATHEMATICAL REASONING AND PROBLEM SOLVING




01. Understand and use a variety of problem-solving

a. Select strategies appropriate to solve a problem.

Identify extra information or missing information

P: 181-190

4

skills. 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

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 [dupl.]


P: 181-190

P: 191-200

P: 191-200

b. Select and use appropriate operations.

Determine what operation is needed to solve a word problem (addition and subtraction)

Solve simple word problems using addition and subtraction

Solve simple addition word problems [dupl.]

P: 181-190

P: 181-190

C: 191-200

02. Use reasoning skills to recognize problems and express them

a. Generate a number sentence from a problem-solving situation.

Solve one-step word problems involving addition or subtraction of four or

P: 181-190

5

mathematically. fewer digits

Solve for missing addends in an addition and subtraction number sentence

P: 181-190

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

a. Select appropriate models to represent mathematical ideas.

Use a number line to write number sentences using subtraction [dupl.]

S: 191-200

04. Communicate results using appropriate terminology and methods.

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

b. Use appropriate vocabulary to communicate mathematical information.

New Vocabulary in this Range: 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

New Vocabulary in this Range: terms, meter, millimeters, kilogram, feet, yards, unit of measurement, height, thousands, hundreds, tens, table, graph, length, width, rectangular, area,

P: 181-190

P: 191-200

6

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 [dupl.]

279. CONCEPTS AND PRINCIPLES OF MEASUREMENT




01. Understand and use U.S. customary and metric measurements.

a. Explore the use of standard and non-standard tools for measuring time, length, volume, weight, and temperature.

Measure capacity to the nearest cup, pint, quart, and gallon and do appropriate conversions between these units

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

Compute word problems with time and calendars

Measure length to the nearest millimeter,

M: 171-180

M: 181-190

M: 181-190

M: 181-190

M: 191-200

7

centimeter, meter, and kilometer [dupl.]

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

Estimate and measure the length of an object to the nearest metric and customary measure using a picture of a ruler

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


M: 171-180

M: 191-200

P: 191-200

c. Tell time using both digital and analog clocks to the quarter hour.

Tell time to the quarter hour using analog and digital clocks

M: 171-180

d. Explore the relationship among units of time.

Order periods of time (days of the week, months of the year, etc.)

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

M: 161-170

M: 191-200


New Vocabulary in this Range: about, length, estimate, perimeter, change, quarter, dollars, dozen, units, feet, yard, grams, meters, cups, gallons, nickel, pennies, dime, tablespoon, hours, minutes, degree

M: 181-190

8

[dupl.]

New Vocabulary in this Range: height, width, parallelogram, square, rectangle, triangle, year, ton, seconds, kilogram, distance, miles, liter [dupl.]

M: 191-200

280. CONCEPTS AND LANGUAGE OF ALGEBRA




01. Use algebraic symbolism as a tool to represent mathematical relationships.

a. Represent vertical notation in horizontal form.

b. Write a number sentence given an addition or subtraction problem.

Write number sentences using addition

A: 181-190

c. Compare numbers using vocabulary (less than, greater than, equal to) and symbols (<, >, =).

Compare, group, and order whole numbers to 100 by using the symbols for “less than”, equal to”, and “greater than” (<, =, >)

Use > or < symbols to compare two numbers

N: 171-180

N: 171-180

d. Understand the relationship between addition and subtraction and demonstrate reversal of operations.

02. Evaluate algebraic a. Explore and use the Demonstrate the C: 191-200

9

expressions. commutative property of addition.

associative, commutative, and zero property of addition [dupl.]

281. CONCEPTS AND PRINCIPLES OF GEOMETRY




01. Apply concepts of size, shape, and spatial relationships.

a. Recognize, name, build, draw, compare, and sort two- and three-dimensional shapes.

Classify and sort solid figures

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

Identify characteristics of plane figures (sides and corners) [dupl.]

Recognize solid figures: cube (box)

Identify points on a line

Identify the correct label for a line

Recognize solid figures: sphere (ball)

Identify and name solid figures: cube, cylinder, cone, rectangular prism, and sphere [dupl.]

G: 171-180

G: 181-190

G: 181-190G: 191-200

G: 181-190

G: 181-190

G: 181-190

G: 191-200

G: 191-200

b. Recognize and create shapes that have symmetry.

Identify figures with line symmetry

Identify figures with

G: 181-190

G: 191-200

10

line symmetry and symmetrical parts [dupl.]

c. Explore slides, flips, and turns.

Recognize transformations of plane figures (slides, flips, and turns) [dupl.]

Identify types of transformations (slides, flips, and turns)

G: 181-190

G: 181-190

d. Understand appropriate vocabulary.

New Vocabulary in this Range: symmetry, point, sides, rectangle, cube, straight, line segment, shortest

New Vocabulary in this Range: symmetrical, parallel, intersecting, diagonal, pair, angle, cylinder, outside, inside, sphere, faces, corresponding, point, intersect, outside, axis of symmetry, line segment, pentagon [dupl.]

G: 181-190

G: 191-200

02. Apply graphing in two dimensions.

a. Apply ideas about direction and distance.

282. DATA ANALYSIS, PROBABILITY, AND STATISTICS




01. Understand data analysis.

a. Interpret information found in simple tables,

Solve simple word problems based on

S: 181-190

11

charts, and graphs. data from picture and bar graphs

Solve simple word problems based on data from picture and bar graphs

Solve problems using information from a bar graph

Solve problems using information from a bar graph [dupl.]

Solve multi-step word problems with pictographs, bar graphs, or line graphs [dupl.]

P: 181-190

P: 181-190

S: 191-200

S: 191-200

b. Understand and use appropriate vocabulary.

New Vocabulary in this Range: most often

New Vocabulary in this Range: average, bar graph, percentage [dupl.]

S: 181-190

S: 191-200

02. Collect, organize, and display data.

a. Gather and display data in tables, charts, and graphs in order to answer a question.

Use tallies to record data

S: 191-200

03. Understand basic concepts of probability.

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

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) [dupl.]

S: 181-190

S: 191-200

12

04. Make predictions or decisions based on data.

a. Make predictions or decisions based on probable results or past experiences.

Predict the likely number of times a condition will occur based on an analysis of data

Predict whether common events are certain, likely, unlikely, possible, impossible, fair or unfair

S: 171-180

S: 181-190

283. FUNCTIONS AND MATHEMATICAL MODELS




01. Understand the concept of functions.

a. Extend patterns and identify the rule (function) that creates the pattern.

Count and write by 10’s to 100 [dupl.]

Count and write by 2’s and 3’s [dupl.]

Complete a number pattern

Find and extend patterns, both increasing and decreasing [dupl.]

Complete a table according to a rule

Choose and apply an appropriate problem solving strategy: Find a pattern


Find and extend

N: 171-180

N: 181-190

N: 181-190

A: 181-190P: 181-190

A: 181-190

A: 181-190

A: 191-200

C: 191-200

13

patterns [dupl.]

b. Sort and classify objects by more than one attribute.

c. Understand and use appropriate vocabulary.

New Vocabulary in this Range: sign

New Vocabulary in this Range: if-then, product, sum [dupl.]

A: 181-190

A: 191-200

14

ASSESSMENTS MAPPED TO THE IDAHO STATE MATHEMATICS STANDARDS FOR GRADES 2-10







a. Read, write, order, and compare whole numbers to 10,000.

Order numerals through 9999

N: 191-200

b. Demonstrate the knowledge of place value through 9,999.

Write numerals in expanded form through the thousands place

Identify place value using model to count [dupl.]

N: 171-180

N: 191-200

c. Determine, by counting, the value of a collection of bills and coins up to $10.00.

Combine and identify the value of a collection of coins and bills up to and including $10.00

M: 191-200

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

e. Explore decimals using money through hundredths.

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

M: 191-200


New Vocabulary in this Range: thirds, fourths, rounded, thousands, exponential form, mixed number, improper fraction, lowest common denominator, percent,

N: 191-200


expanded form, prime, factor, proportion [dupl.]

New Vocabulary in this Range: missing number, pentagon, simplest fraction, biggest, hundredths, one less, decimal numeral, squared, divisible, inequality, expanded numeral, equivalent, point, standard numeral, sequence [dupl.]

N: 201-210


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

Add 2-and 3-digit numbers with no regrouping

Subtract a 1-digit number from a 2-digit number with no regrouping

Subtract a 2-digit number from a 2-digit number with no regrouping

Subtract 2-and 3-digit numbers with no regrouping

Add two 2-digit and 3-digit numbers with regrouping

Add 2 or several multi-digit numbers with regrouping [dupl.]

Add multi-digit numbers without using a calculator

C: 151-160

C: 161-170

C: 161-170

C: 161-170

C: 171-180

C: 181-190

C: 181-190


[dupl.]

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

Subtract multi-digit numbers with regrouping

Subtract multi-digit numbers without using a calculator [dupl.]

C: 181-190

C: 191-200

C: 191-200C: 201-210

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

c. Add three addends with 1 and 2 digits.

Add three 1-digit numbers [dupl.]

Add 2 or several multi-digit numbers with regrouping [dupl.]

C: 151-160

C: 181-190

d. Multiply whole numbers through 10 x 10.

Understand the concept of multiplication using symbols; recall multiplication facts with one factor as 1,2,3,4,5 and other factor 0-9

Multiply a 2- or 3-digit number by a 1-digit number with no regrouping

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

C: 151-160

C: 171-180

C: 191-200


e. Explore the relationship between multiplication and division.

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

Identify the division facts related to a multiplication fact

C: 181-190

C: 181-190

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.

New Vocabulary in this range: difference, not true, power of 10, rounded, thousands [dupl.]

New Vocabulary in this range: estimate, round, closest to, sum, of (used as in “½ of 36”) [dupl.]

C: 191-200

C: 201-210



Round 2- and 3-digit numbers to the nearest hundred and tens [dupl.]

Use front-end estimation strategy for multiplication and division [dupl.]

N: 181-190

C: 201-210

b. Evaluate the reasonableness of an answer.


P: 191-200







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



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 [dupl.]

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 [dupl.]

P: 191-200

P: 191-200

P: 201-210


Identify the correct information to solve addition and subtraction word problems

P: 191-200


Determine what operation is needed to solve a word problem (all four operations)

Solve word problems involving any combination of basic operations on whole numbers (one-step problems)

Solve multi-step word problems involving any combination of basic operations

Solve one-step word problems involving multiplication

Solve simple addition word problems [dupl.]

P: 191-200

P: 191-200

P: 191-200

C: 191-200

C: 191-200

c. Make predictions and decisions based on information.

Predict the likely number of times a condition will occur based on an analysis of data [dupl.]

S: 171-180

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.

Construct and interpret line graphs involving problem solving [dupl.]

P: 181-190


a. Appropriately use a 4-function calculator to solve complex grade-level problems.


b. Select appropriate models to represent mathematical ideas.

Use a number line to write number sentences using subtraction [dupl.]

S: 191-200


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


New Vocabulary in this Range: 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 [dupl.]

New Vocabulary in this Range: equation, product, increased, number line, information not needed, division, estimate, odd, prime, cube, pattern,

P: 191-200

P: 201-210


geometric patterns, extra information [dupl.]

289.CONCEPTS AND PRINCIPLES OF MEASUREMENT

Standards - The student will:




a. Select and use appropriate units and tools to make formal measurements in both systems (time, length, temperature, perimeter).

Choose the appropriate tool: clock to measure time, calendar to measure days and months, thermometer to measure temperature, ruler to measure length

Measure length to the nearest millimeter, centimeter, meter, and kilometer [dupl.]

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

Select appropriate unit of measure for length and area [dupl.]

M: 151-160

M: 191-200

M: 191-200

M: 201-210



Estimate and verify the area of a figure using square units (counting) [dupl.]

P: 191-200

M: 191-200


c. Explore relationships within the U.S. customary system.

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

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

M: 191-200

M: 191-200

d. Explore relationships within the metric system.

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

M: 201-210

e. Tell time using both digital and analog clocks, using 5-minute intervals.

Tell time to the nearest 5 minutes using analog and digital clocks

M: 171 – 180

f. Explore the relationship among units of time.

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

M: 191-200



New Vocabulary in this Range: height, width, parallelogram, square, rectangle, triangle, year, ton, seconds, kilogram, distance, miles, liter [dupl.]

New Vocabulary in this Range: right angle, circumference, minutes, decades, milligrams, gram, cubic feet, volume, liters, length, weight, kilometers, millimeters, mass [dupl.]

M: 191-200

M: 201-210

290.CONCEPTS AND LANGUAGE OF ALGEBRA






b. Write a number sentence using symbols (boxes or letters) to represent an unknown number.

Use boxes or other symbols to stand for any number in expressions or equations [dupl.]

A: 221-230

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

Use symbols of inequality, < and > to write and complete number sentences [dupl.]

A: 191-200

d. Explore inverse


(reversal) of operations with multiplication and division.

02. Evaluate algebraic expressions.

a. Explore and use the commutative properties of addition and multiplication.

Demonstrate the associative, commutative, and zero property of addition [dupl.]

Identify the associative, commutative, identity and zero property of multiplication [dupl.]

C: 191-200

C: 191-200

03. Solve algebraic equations and inequalities.

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

Use inverse operations to find missing equation

Identify missing elements in number sentences

Solve whole number equations with any operation

A: 181-190

A: 181-190

A: 191-200

291.CONCEPTS AND PRINCIPLES OF GEOMETRY





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

Describe and measure right angles

Identify right angles

Identify intersecting, parallel lines

G: 191-200

G: 191-200

G: 191-200


Identify the diagonal of a circle

Identify characteristics of plane figures (sides and corners) [dupl.]

Identify and name solid figures: cube, cylinder, cone, rectangular prism, and sphere [dupl.]

Identify points, lines, line segments, rays, planes, and angles figures [dupl.]

Identify the diameter of a circle figures [dupl.]

Identify intersecting, parallel, and perpendicular lines figures [dupl.]

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

Identify faces, edges, and corners (vertices) on solid figures [dupl.]

Identify polygons: triangle,

G: 191-200

G: 191-200

G: 191-200

G: 201-210

G: 201-210

G: 201-210

G: 201-210

G: 201-210

G: 201-210


quadrilateral, pentagon, and octagon [dupl.]

Identify quadrilaterals: square, rectangle, and parallelogram [dupl.]

G: 201-210

b. Explore congruence, similarity, and symmetry.

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

Identify figures with line symmetry and symmetrical parts [dupl.]

Identify congruent figures, angles and line segments figures [dupl.]

G: 181-190

G: 191-200

G: 201-210

c. Investigate perimeters in real-world situations.

Find the perimeter of polygons

Solve practical word problems involving perimeter and area of a square, rectangle or triangle [dupl.]

Find the perimeter of a square or rectangle using the formula [dupl.]

M: 191-200

M: 201-210

M: 201-210

d. Predict and describe the results of sliding, flipping, and turning two-dimensional shapes.

Recognize transformations of plane figures (slides, flips, and turns) [dupl.]

G: 181-190

e. Use appropriate New Vocabulary in G: 191-200


vocabulary. this Range: symmetrical, parallel, intersecting, diagonal, pair, angle, cylinder, outside, inside, sphere, faces, corresponding, point, intersect, outside, axis of symmetry, line segment, pentagon [dupl.]

New Vocabulary in this Range: intersection, quadrilaterals, octagon, parallelogram, pyramid, isosceles, right angle, diameter, right angle, geometric, perpendicular, plane [dupl.]

G: 200-201



292.DATA ANALYSIS, PROBABILITY, AND STATISTICS

Standard – The student

will:Content Knowledge and

Skills:Item Description: Item Source:


a. Interpret information found in tables, charts, and graphs.

Read and interpret dual bar graphs and dual broken-line graphs

Solve problems using information from a bar graph [dupl.]

S: 191-200

S: 191-200


Solve multi-step word problems with pictographs, bar graphs, or line graphs [dupl.]

S: 191-200

b. Explain and justify conclusions drawn from tables, charts, and graphs.



a. Collect, organize, and display data in tables, charts, or graphs in order to answer a question and/or test a hypothesis.

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

S: 191-200

S: 191-200

P: 191-200



Develop concept of chance and make predictions for events (ex. rolling a number dice) [dupl.]

Compute simple probability outcomes [dupl.]

Determine the probability of an outcome (multiple events) [dupl.]

S: 191-200

S: 201-210

S: 201-210


Use the counting principle to determine probability [dupl.]

S: 201-210


a. Make predictions or decisions based on probable results or past experiences.


New Vocabulary in this Range: average, bar graph, percentage [dupl.]

New Vocabulary in this Range: least often, how many ways, ordered pairs, coordinates, distance formula [dupl.]

S: 191-200

S: 201-210

293.FUNCTIONS AND MATHEMATICAL MODELS





a. Extend patterns and identify the rule (function) that creates the pattern.

Find and extend patterns, both increasing and decreasing [dupl.]

Use of a function “machine” to determine input and output [dupl.]

Find and extend patterns [dupl.]

A: 181-190

A: 191-200

C: 191-200

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


A: 191-200


pictorial representations.


New Vocabulary in this Range: if-then, product, sum [dupl.]

New Vocabulary in this Range: input, output, table, associative, equation [dupl.]

A: 191-200

A: 201-210








a. Read, write, order, and compare whole numbers to 1,000,000, commonly used fractions, and decimals through hundredths.

Compare and order decimals to the hundredths place

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

Write numerals in expanded form through the hundred thousands

Compare and order fractions and mixed numbers

Write a decimal for a shaded region (hundredths)

Order numbers from least to greatest and greatest to least

Use a number line to identify a fractional point

Write the word name for a decimal and vice versa

N: 181-190

N: 191-200

N: 191-200

N: 191-200

N: 201 – 210

N: 201 – 210

N: 201 – 210

N: 201 – 210

DMA4

N4

b. Demonstrate and apply Identify and N: 181-190


the knowledge of whole numbers, decimal place value, and patterns of periods (hundredths to millions).

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

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

N: 191-200

DMA4

N4

c. Determine by counting the value of a collection of bills and coins up to $100.00.

Compute and count change up to and including $100.00

M: 191-200

DMA4

d. Use concrete materials to recognize, represent, and compare commonly used fractions. N4

e. Understand decimals with money through hundredths.

DMA4

N4



New Vocabulary in this Range: counting number, portion, fractional part, lowest terms, reciprocal, order,

N: 201-210

N: 211-220


scientific notation, prime factorization, not prime, factor tree, common multiples, greatest common denominator, equivalent, nearest dollar [dupl.]


a. Consistently and accurately add and subtract whole numbers.

Add multi-digit numbers without using a calculator [dupl.]

Subtract multi-digit numbers without using a calculator [dupl.]

C: 181-190

C: 201-210

DMA4

N4

b. Multiply and divide whole numbers.

Understand the concept of division using pictorial representation [dupl.]

Divide a 2-digit number by a 2-digit number with a remainder [dupl.]

Multiply by multiples of 10 and 100 with an emphasis on mental math [dupl.]

Divide a 3-digit number by a multiple of 10 [dupl.]

Divide a 3-digit number by a 2-digit number (no zeros) [dupl.]

C: 201-210

C: 201-210

C: 201-210

C: 201-210

C: 201-210

DMA4


N4

c. Add and subtract fractions with like denominators (without requiring simplification).

Add fractions with like denominators

Subtract fractions with like denominators [dupl.]

Add mixed numbers with like denominators with regrouping

Subtract mixed numbers with like denominators with regrouping

Add fractions with like denominators, answer in lowest terms [dupl.]

C: 171-180

C: 191-200

C: 201-210

C: 201-210

C: 211-220

N4

d. Add and subtract decimals using money.

Add decimals to hundredths place using both horizontal and vertical format

Subtract decimals to hundredths place

Compute and count change greater than $20.00

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

Compute and count change up to and including $5.00

C: 201-210

C: 201-210

C: 201-210

M: 201-210P: 201-210

M: 201-210


(addition and subtraction only)

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

M: 211-220

DMA4

N4

e. Instantly recall multiplication facts through 10s.

f. Select and use an appropriate method of computation from mental math, paper and pencil, calculator, or a combination of the three. N4



New Vocabulary in this range: smallest, tenth [dupl.]

C: 201-210

C: 211-220



Round 4- and 5-digit numbers to the nearest hundred thousand, thousand, hundred or ten

Use front-end estimation strategy for multiplication and division [dupl.]

Round to the nearest millions and billions

Round decimals to

C: 191-200

C: 201-210

N: 201-210

C: 211-220


nearest whole number, tenth, or hundredth [dupl.]

DMA4

N4

b. Evaluate the reasonableness of an answer. N4








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 [dupl.]

P: 201-210P: 211-220

DMA4


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

P: 211-220

DMA4

N4

c. Make predictions and decisions based on information. DMA4

02. Use reasoning a. Use a variety of


skills to recognize problems and express them mathematically.

methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain mathematical reasoning and concepts. DMA4


a. Appropriately use a 4-function calculator to solve complex grade-level problems.

b. Select appropriate models to represent mathematical ideas.


a. Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to communicate mathematical information. DMA4


New Vocabulary in this Range: equation, product, increased, number line, information not needed, division, estimate, odd, prime, cube, pattern, geometric patterns, extra information [dupl.]

New Vocabulary in this Range: decimals, fractions, what shape, hour, minutes, gallons, average, probability, graph, squares [dupl.]

P: 201-210

P: 211-220

DMA4

c. Use appropriate


notation. DMA4






a. Select and use appropriate units and tools to make formal measurements in both systems (time, length, temperature, perimeter, area).

Solve word problems involving customary and metric measurement [dupl.]



P: 201-210

M: 201-210

M: 211-220

DMA4

N4


DMA4

N4

c. Apply understanding of relationships within the U.S. customary system.


Perform conversions between units of capacity in the

M: 191-200

M: 191-200


customary system; also as necessary in addition or subtraction problems [dupl.]

DMA4

N4

d. Apply understanding of relationships within the metric system.


M: 201-210

DMA4

N4

e. Tell time using both digital and analog clocks, to the nearest minute.

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

M: 181-190

DMA4

N4

f. Apply understanding of relationships to solve real-world problems related to time.

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

Compute basic operations with units of time (include basic concept of time zones) [dupl.]

M: 191-200

M: 201-210

DMA4

N4


New Vocabulary in this Range: right angle, circumference, minutes, decades, milligrams, gram, cubic feet, volume, liters, length, weight, kilometers, millimeters, mass

M: 201-210


[dupl.]

New Vocabulary in this Range: yards, measure of angle, degrees, protractor, centuries, below zero, Celsius, rectangular solid, rectangular prism, decades, ounces [dupl.]

M: 211-220


Standard - The student will:





b. Write a number sentence using symbols (boxes or letters) to represent an unknown number.

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


P: 191-200

A: 221-230

DMA4

N4



A: 191-200

DMA4

N4



a. Explore and use the commutative properties of addition and multiplication.

Demonstrate the associative, commutative, and zero property of addition [dupl.]

Identify the associative, commutative, identity and zero property of multiplication [dupl.]

Evaluate an expression involving more than one operation (order of operations) [dupl.]

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

Use the basic properties of addition to write an algebraic expression equivalent to a given algebraic expression [dupl.]

C: 191-200

C: 191-200

A: 201-210

A: 201-210

A: 201-210



Solve equations involving more than one operation [dupl.]

Solve decimal equations (one step,

A: 201-210

A: 211-220


addition and subtraction) [dupl.] N4







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

Identify faces, edges, and corners (vertices) on solid figures [dupl.]




Identify polygons: triangle, quadrilateral, pentagon, and octagon [dupl.]

Identify

G: 201-210

G: 201-210G: 211-220

G: 201-210

G: 201-210

G: 201-210

G: 201-210

G: 201-210


quadrilaterals: square, rectangle, and parallelogram [dupl.]

Contrast open and closed figures [dupl.]

Identify polygons: triangle, quadrilateral, pentagon, hexagon, and octagon [dupl.]

Identify quadrilaterals: square, rectangle, parallelogram, trapezoid, rhombus [dupl.]

Analyze solid figures: triangular pyramid and rectangular pyramid (faces, edges, and vertices) [dupl.]

Identify angles: right, obtuse, and acute [dupl.]

Identify when two intersecting lines are perpendicular [dupl.]

Identify points, lines, line segments, rays, and angles [dupl.]

G: 211-220

G: 211-220

G: 211-220

G: 211-220

G: 211-220

G: 211-220

G: 211-220

DMA4

N4

b. Explore relationships among and properties of shapes (congruence,

Identify congruent figures, angles and line segments

G: 201-210


similarity, symmetry). figures [dupl.]

Identify similar figures (same shape, may or may not be the same size) [dupl.]

Identify congruent polygons and their corresponding sides and angles [dupl.]

Identify properties of similar figures [dupl.]

G: 211-220

G: 211-220

G: 211-220

N4

c. Use concrete objects to determine perimeters of triangles, and areas and perimeters of rectangles/squares.



M: 201-210P: 211-220

M: 201-210

N4

d. Predict and describe the results of sliding, flipping, and turning two-dimensional shapes.

Identify types of transformations (rotation) [dupl.]

G: 211-220

N4



G: 201-210


New Vocabulary in this Range: symmetrical, perpendicular, ray, vertex, rotation, triangular prism, corresponding parts, supplementary, acute angle, transformation [dupl.]

G: 211-220




Standard – The student

will:Content Knowledge and

Skills:Item Description: Item Source:


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

Solve problems using information from a picture graph (symbol may represent more than one) [dupl.]

Interpret data given in percent form on a circle graph and broken line graph [dupl.]

S: 201-210

S: 201-210

N4


DMA4


c. Understand and use vocabulary.


a. Collect, order, and display data in appropriate notation in tables, charts, and graphs (bar graphs, tally charts, pictographs), in order to answer a question and/or test a hypothesis.

DMA4

N4

03. Apply simple statistical measurements.

a. Determine an average (mean) of a set of whole numbers.

Solve practical problems involving the mean (average) of a set of numbers [dupl.]

S: 201-210

N4



Compute simple probability outcomes [dupl.]

Use the counting principle to determine probability [dupl.]

Investigate experimental probability of an event using a coin or spinner [dupl.]

S: 201-210

S: 201-210

P: 211-220

N4


a. Make predictions based on simple experimental probabilities.

Determine the probability of an outcome (multiple events) [dupl.]

S: 201-210

N4




New Vocabulary in this Range: dice, arranged, highest mean [dupl.]

S: 201-210

S: 211-220






a. Extend patterns and identify a rule (function) that creates the pattern.

Use of a function “machine” to determine input and output [dupl.]

Use logic to solve a problem involving a function table [dupl.]

A: 201-210

A: 211-220

DMA4

N4

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

DMA4

N4


New Vocabulary in this Range: input, output, table, associative, equation [dupl.]

New Vocabulary in this Range: commutative, solve, square numbers, input, output,

A: 201-210

A: 211-220


number sequence [dupl.]








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

Match word names to numerals through billions

Compare and order numbers through the billions

Compare and order fractions with the same denominator and with different denominators [dupl.]

Order decimals to thousandths; identify the greater or lesser of two decimals to thousandths [dupl.]

Model and write numerical fractions [dupl.]

N: 191-200

N: 201-210

N: 211-220

N: 211-220

N: 211-220

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

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

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

Write numerals in

N: 201-210

N: 201-210P: 211-220

N: 231-240


expanded form through the billions

c. Explore the relationship between equivalent fractions.

Write the missing number in two equivalent ratios [dupl.]

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

Write improper fractions from picture presentations

Determine if a pair of ratios is equal or not equal using the equivalent fractions method [dupl.]

N: 201-210N: 221-230

N: 201-210N: 211-220

N: 211-220

N: 221-230

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

Write a terminating decimal as a fraction or mixed number [dupl.]

Write the decimal equivalent of a fraction and label as repeating or terminating [dupl.]

Write a decimal or mixed decimal for a fraction (2/3=0.66) [dupl.]

Relate fractions to decimals [dupl.]

N: 201-210C: 211-220

N: 211-220

N: 221-230

C: 221-230

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

Compare and order fractions with the same denominator and with different

N: 211-220


simple fractions. denominators [dupl.]

Order decimals to thousandths; identify the greater or lesser of two decimals to thousandths [dupl.]

N: 211-220

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

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

Apply rules of divisibility

Identify the greatest common factor of two whole numbers each of which is less than 100

Understand and use rules of divisibility [dupl.]

Identify the greatest common factor of two whole numbers: list the factors or prime factorization [dupl.]

Identify the greatest common factor and least common multiple of two whole numbers [dupl.]

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

P: 201-210

N: 201-210

N: 201-210

N: 211-220

N: 211-220

N: 211-220

N: 221-230


prime factorization [dupl.]


a. Multiply and divide whole numbers.

Understand the concept of division using pictorial representation [dupl.]

Divide a 2-digit number by a 2-digit number with a remainder [dupl.]

Multiply by multiples of 10 and 100 with an emphasis on mental math [dupl.]

Divide a 3-digit number by a multiple of 10 [dupl.]

Divide a 3-digit number by a 2-digit number (no zeros) [dupl.]

Use multiplication as a check for division [dupl.]

Divide a 3-digit or 4-digit number by a 1-digit number [dupl.]

Divide a 4-digit number by a 2-digit number [dupl.]

Develop computational fluency with division facts

C: 201-210

C: 201-210

C: 201-210C: 211-220

C: 201-210

C: 201-210

C: 211-220

C: 211-220

C: 211-220

C: 221-230


[dupl.]

Divide multi-digit numbers using a calculator [dupl.]

C: 221-230

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

Subtract fractions with like denominators [dupl.]

Add fractions with like denominators, answer in lowest terms [dupl.]

C: 191-200

C: 211 - 220

c. Add and subtract decimals through thousandths.

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

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

C: 191-200

C: 191-200

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

Develop computational fluency with division facts [dupl.]

C: 221-230

e. Evaluate numerical expressions that include parentheses.


Evaluate expressions using the order of operations (may

A: 201-210

A: 211-220


include parentheses or exponents) [dupl.]


Solve whole number equations with one variable (multiplication and division) [dupl.]

A: 221-230

A: 221-230

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



New Vocabulary in this Range: counting number, portion, fractional part, lowest terms, reciprocal, order, scientific notation, prime factorization, not prime, factor tree, common multiples, greatest

N: 201-210

N: 211-220


common denominator, equivalent, nearest dollar [dupl.]

New Vocabulary in this Range: always true, proportion, multiply, between, tens digit, standard numeral, ratio [dupl.]



New Vocabulary in this range: product, divide, most, if – then, compute, lowest terms [dupl.]

N: 221-230

C: 201-210

C: 211-220

C: 221-230



Round decimals to nearest whole number, tenth, or hundredth [dupl.]

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

C: 211-220

C: 211-220

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


Use estimation to

P: 201-210

P: 221-230


answer. determine if solutions to word problems are reasonable [dupl.]

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

d. Use appropriate vocabulary.






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


Use logic to solve problems

Solve word problems using proportional reasoning

Solve geometry problems by making a drawing or diagram

Use estimation to determine if solutions to word problems are reasonable [dupl.]

Choose and use an appropriate problem solving strategy: Draw a

P: 201-210

P: 201-210

P: 201-210

P: 201-210

P: 221-230

P: 201-210P: 211-220P: 221-230


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 [dupl.]

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


Predict outcomes using probability [dupl.]

P: 221-230



b. Apply solutions and strategies to new problem situations.

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


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

b. Use computer applications to display and manipulate data.


c. Select appropriate models to represent mathematical ideas.




New Vocabulary in this Range: equation, product, increased, number line, information not needed, division, estimate, odd, prime, cube, pattern, geometric patterns, extra information [dupl.]


New Vocabulary in this Range: mortality, odometer, magic square, deducted, less than twice, addends, less than sum, rectangle, diameter, radius, label (units), area, perimeter [dupl.]

P: 201-210

P: 211-220

P: 221-230

c. Use appropriate


notation.






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

Solve word problems involving customary and metric measurement [dupl.]



Select the appropriate unit of measure for length, area, and volume [dupl.]

Measure length with metric measures (centimeter) [dupl.]

Measure length with customary measures (inch) [dupl.]

P: 201-210

M: 201-210

M: 211-220

M: 221-230P: 221-230

M: 221-230

M: 221-230

b. Apply estimation of measurement to real-world and content


problems using actual measuring devices.

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

Understand the effects of changing dimensions on perimeter and area [dupl.]

M: 211-220

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



Calculate the area of a triangle [dupl.]

Calculate the surface area of a rectangular prism [dupl.]

Calculate the area of irregular shapes [dupl.]

M: 201-210P: 211-220

M: 201-210

M: 201-210

M: 201-210

M: 211-220

e. Convert unit of measurement within each system.


Perform conversions between units of

M: 191-200

M: 191-200


capacity in the customary system; also as necessary in addition or subtraction problems [dupl.]


M: 201-210


Compute basic operations with units of time (include basic concept of time zones) [dupl.]

M: 201-210


New Vocabulary in this Range: right angle, circumference, minutes, decades, milligrams, gram, cubic feet, volume, liters, length, weight, kilometers, millimeters, mass [dupl.]


M: 201-210

M: 211-220


New Vocabulary in this Range: reasonable, formula, segment BC, pi, radius squared, diameter, metric units, quarts, gallons, rectangular box, base, rate [dupl.]

M: 221-230

02. Apply dimensional analysis.

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






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

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

A: 191-200

A: 191-200

A: 191-200

b. Translate simple word statements and story problems into algebraic equations.

Write and solve an equation for a word problem [dupl.]

P: 221-230




A: 191-200


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

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

Use the basic properties of addition to write an algebraic expression equivalent to a given algebraic expression [dupl.]

A: 201-210

A: 201-210

b. Investigate the order of operations (parentheses only).


Evaluate expressions using the order of operations (may include parentheses or exponents) [dupl.]

A: 201-210

A: 211-220





Solve decimal equations (one step, addition and subtraction) [dupl.]

Solve for missing addends in an addition or subtraction sentence [dupl.]

A: 201-210

A: 211-220

C: 221-230








Identify polygons: triangle, quadrilateral, pentagon, and octagon [dupl.]

Identify quadrilaterals: square, rectangle, and parallelogram [dupl.]


Identify quadrilaterals:

G: 201-210

G: 201-210

G: 201-210

G: 211-220

G: 211-220


square, rectangle, parallelogram, trapezoid, rhombus [dupl.]


Identify the center, radius and diameter of a circle [dupl.]

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

Analyze circles: center, chord, diameter, radius, arc, semicircle, and circumference [dupl.]

G: 211-220

G: 221-230

G: 221-230

M: 221-230P: 221-230

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



Identify points, lines, line segments, rays, and

G: 201-210

G: 201-210

G: 211-220


angles [dupl.]



Find the missing angle measurement in a triangle when two angles are known [dupl.]

G: 211-220

G: 211-220

M: 221-230

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




Identify congruent triangles according to corresponding parts (SSS, SAS, ASA) [dupl.]

G: 211-220

G: 211-220

G: 211-220

G: 221-230

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


Find the perimeter of a square or

M: 201-210

M: 201-210


rectangle using the formula [dupl.]

e. Predict and describe the results of sliding, flipping, and turning two-dimensional shapes.


G: 211-220

f. Use appropriate vocabulary.



New Vocabulary in this Range: radius, polygon, circumference, trapezoid, rectangular box, equilateral, similar, obtuse angle, straight angle, slide [dupl.]

G: 201-210

G: 211-220

G: 221-230


a. Identify and plot points on a coordinate plane.

Graph ordered pairs in all four quadrants

S: 221-230


(coordinate geometry) [dupl.]


312. DATA ANALYSIS, PROBABILITY AND STATISTICS





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

Solve problems using information from a picture graph (symbol may represent more than one) [dupl.]

Interpret data given in percent form on a circle graph and broken line graph [dupl.]

Interpret data given in horizontal and vertical bar graphs to solve problems [dupl.]

S: 201-210

S: 201-210

S: 221-230




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


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


Know the concepts

P: 211-220

S: 221-230


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 [dupl.]

b. Determine the range of a set of data.

Calculate range, mode, median, and mean [dupl.]

S: 231-240




S: 221-230P: 211-220

b. Understand and use the language of probability.

Predict whether common events are certain, likely, unlikely, possible, impossible, fair or unfair

S: 181-190






New Vocabulary in this Range: even

S: 201-210

S: 211-220

S: 221-230


numbers, mean, median, integer, intersection, table, frequency, origin, quadrant [dupl.]






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


State a rule to explain a number pattern, including arithmetic progression [dupl.]

Complete a function table according to a rule [dupl.]

A: 211-220

A: 221-230

A: 221-230


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

Investigate geometric patterns and relationships and describe them algebraically [dupl.]

A: 221-230

A: 221-230

c. Use mathematical models to show change


in real context.

d. Understand and use appropriate vocabulary.

02. Apply functions to a variety of problems.

a. Use patterns to represent and solve simple problems.





Content and Knowledge Skills:



a. Read, write, order, and compare whole numbers, fractions, and decimals.

Write numerals in expanded form through the hundred billions

Order decimals and fractions to the hundred thousandths [dupl.]


Compare and order fractions and mixed numbers [dupl.]

Identify and order decimal and fractional coordinates on a number line [dupl.]


Match word names to numerals to the hundred thousands in decimals

Understand and identify place value and value of each

N: 201-210

N: 201-210

N: 211-220

C: 211-220

N: 221-230

N: 221-230

N: 221-230

N: 231-240


digit in numerals through the hundred billions

b. Understand the use of fractions and decimals and their interrelationship.




Solve proportions using the cross product method [dupl.]

Relate fractions to decimals [dupl.]

N: 211-220

N: 211-220

N: 221-230

N: 221-230

C: 221-230

c. Expand the use of decimals and fractions to explore the use of percents and ratios.

Calculate the cost of one item or the unit cost using a proportion [dupl.]

Determine the discount price and sale price [dupl.]

Express a fraction as a decimal and as a percent

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

P: 211-220

P: 211-220

N: 211-220

C: 221-230N: 221-230


[dupl.]

Find the percent one number is of another (20 is what % of 90) [dupl.]

Find a number from a percent (4 is 9% of what number) [dupl.]

Write the missing number in 2 equivalent ratios [dupl.]

Determine if a pair of ratios is equal or not equal using the equivalent fractions method [dupl.]


Understand the concept of ratio using concrete and pictorial models [dupl.]

C: 221-230

C: 221-230

N: 221-230

N: 221-230

N: 221-230

N: 221-230

d. Show a sense of magnitudes and relative magnitudes of real numbers (whole numbers, fractions, decimals).

Order decimals and fractions to the hundred thousandths [dupl.]


Compare and order

N: 201-210

N: 211-220

C: 211-220


fractions and mixed numbers [dupl.]


N: 221-230

e. Develop and apply number theory concepts [prime, composite, Greatest Common Factor (GCF), Lowest Common Multiple (LCM), prime factorization].




Identify the least common denominator for 3 or more fractions: list the multiples or prime factorization [dupl.]

N: 211-220

N: 211-220

N: 211-220

N: 221-230

f. Explore the use of integers in real-world situations.

Understand the meaning of integers

N: 221-230


a. Consistently and accurately multiply and divide whole numbers.

Use multiplication as a check for division [dupl.]

Divide a 3-digit or 4-digit number by a 1-digit number [dupl.]

C: 211-220

C: 211-220


Divide a 4-digit number by a 2-digit number [dupl.]


Divide multi-digit numbers using a calculator [dupl.]

C: 211-220

C: 221-230

C: 221-230

b. Add, subtract, multiply, and divide decimals.

Add decimals through hundred-thousandths with a calculator [dupl.]

Multiply a decimal by a decimal, factors to thousandths [dupl.]

Divide a decimal by a whole number and vice versa [dupl.]

Subtract decimals through hundred-thousandths with a calculator [dupl.]

Multiply a decimal by multiples of 10, 100, or 1000 [dupl.]

Subtract whole numbers and decimals to the hundredths place (same number of digits) [dupl.]

C: 211-220

C: 211-220

C: 211-220

C: 221-230

C: 221-230

C: 221-230


Divide a whole number (or decimal) by a decimal to thousandths [dupl.]

C: 221-230

c. Add and subtract fractions with unlike denominators and simplify as necessary.

Add mixed numbers with unlike denominators with regrouping

Subtract fractions having unlike denominators, answer in lowest terms [dupl.]

Add and subtract fractions with like denominators; change improper fractions to mixed numbers [dupl.]

Change a fractional numeral to its simplest form (lowest terms) [dupl.]

Add and subtract whole numbers, fractions and mixed numbers [dupl.]

C: 211-220

C: 221-230

C: 221-230

C: 221-230

C: 221-230

d. Instantly recall basic multiplication and division facts from a 12 x 12 Times Table.


C: 221-230

e. Evaluate numerical expressions using the order of operations.

Evaluate expressions using the order of operations (may include parentheses

A: 211-220


or exponents) [dupl.]



A: 221-230

A: 221-230

f. Explore the use of exponents.

Calculate the square of any number less than 100 [dupl.]

Order of “powers” [dupl.]

Write a whole number or a decimal in scientific notation [dupl.]

Write a number expressed in scientific notation in standard form [dupl.]

Identify and use powers of 10 [dupl.]

P: 211-220

N: 211-220

N: 211-220

N: 211-220

N: 221-230

g. Explore multiplication and division of fractions.

Multiply a whole number by a fraction [dupl.]

Divide a fraction by a fraction [dupl.]

Divide a mixed number by a whole

C: 211-220

C: 211-220

C: 211-220


number or a fraction [dupl.]

Divide a whole number, fraction or mixed number by a mixed number [dupl.]

C: 221-230

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

i. Use appropriate vocabulary.

New Vocabulary in this Range: 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 [dupl.]



New Vocabulary in this range: product,

N: 211-220

N: 221-230

C: 211-220

C: 221-230


divide, most, if – then, compute, lowest terms [dupl.]



Use estimation to solve problems involving mixed numbers [dupl.]

Introduce the math strategy of compatible numbers in estimating for all four operations [dupl.]

C: 221-230

C: 221-230

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


P: 221-230




Standards - The student will:




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


Choose and use an appropriate

P: 221-230

P: 211-220


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 [dupl.]

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

P: 221-230

C: 221-230

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



P: 221-230















P: 211-220

P: 221-230


c. Use appropriate notation.











Measure angles using a protractor [dupl.]

M: 211-220

M: 221-230P: 221-230

M: 221-230

M: 221-230

M: 211-220


c. Recognize the differences and relationships between perimeter and area in

Understand the effects of changing dimensions on perimeter and area

M: 211-220


both systems. [dupl.]

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


Calculate the surface area of a rectangular prism



Calculate the area of a parallelogram and rectangle [dupl.]


Calculate the circumference of a circle using the formula [dupl.]

Find the perimeter of polygons [dupl.]

P: 211-220

M: 201-220

M: 211-220

M: 231-240

M: 231-240

M: 231-240

M: 231-240

M: 231-240







M: 211-220

M: 221-230

02. Apply concepts of rates and other derived or indirect measurements.

a. Explore the use of rates to make indirect measurements.


Solve simple interest problems (amount x rate x time) [dupl.]

P: 211-220

P: 221-230

03. Apply the concepts of ratios and proportions.

a. Explore the use of proportions, ratios, and scales.









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


A: 221-230

b. Translate simple word statements and story problems into algebraic equations.


Write and solve an equation using ratios, given a word problem [dupl.]

P: 221-230

P: 221-230



A: 191-200


a. Explore and use the following properties in evaluating mathematical and algebraic expressions: commutative, associative, identity, zero, inverse, and distributive.

b. Explore the order of operations.


A: 211-220

03. Solve algebraic a. Solve one-step equations Solve decimal A: 211-220


equations and inequalities.

using inverse operations with whole numbers.

equations (one step, addition and subtraction) [dupl.]


C: 221-230






a. Precisely describe, classify, and understand relationships among types of one-, two-, and three-dimensional objects using their defining properties.





Analyze solid figures: rectangular prism, triangular prism, triangular pyramid, square, pyramid (faces,

G: 211-220

G: 211-220

G: 211-220

G: 221-230

G: 221-230


edges and vertices) [dupl.]

Classify polygons by sides and angles [dupl.]


G: 221-230

M: 221-230P: 221-230

b. Construct and measure various angles and shapes using appropriate tools.


M: 211 - 220 G: 221-230

c. Apply fundamental concepts, properties, and relationships among points, lines, angles, and shapes.




Classify angles: supplementary and complementary [dupl.]

Classify angles: adjacent, vertical, corresponding, and supplementary [dupl.]

Find the missing angle measurement in a triangle when

G: 211-220

G: 211-220

G: 211-220

G: 221-230

G: 221-230

M: 221-230


two angles are known [dupl.]

d. Recognize and apply congruence, similarities, and symmetry of shapes.





G: 211-220

G: 211-220

G: 211-220

G: 221-230

e. Develop and apply formulas for perimeter, circumference, and area to triangles, quadrilaterals, and circles.






P: 211-220

G: 221-230

M: 231-240

M: 231-240

M: 231-240




M: 231-240

M: 231-240

f. Explore the relationship between two- and three-dimensional objects.

g. Explore reflections, translations, and rotations on various shapes.

Identify mirror-images figures


G: 201-210

G: 211-220

h. Use appropriate vocabulary.



G: 211-220

G: 221-230



Graph ordered pairs in all four quadrants (coordinate

S: 221-230


geometry) [dupl.]






a. Read and interpret tables, charts, and graphs (line graphs, bar graphs, frequency lines or line plots, and circle graphs).


S: 221-230




a. Collect, organize, and display data with appropriate notation in tables, charts, and graphs (line graphs, bar graphs, frequency lines or line plots, and circle graphs).


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


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

P: 211-220

S: 221-230


[dupl.]

b. Determine the range of a set of data.


S: 231-240




P: 211-220 S: 221-230






New Vocabulary in this Range: even numbers, mean, median, integer, intersection, table, frequency, origin, quadrant [dupl.]

S: 211-220

S: 221-230







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




A: 211-220

A: 221-230

A: 221-230



Investigate geometric patterns and relationships and describe them algebraically [dupl.]

A: 221-230

A: 221-230

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

d. Understand and use appropriate vocabulary.


a. Use patterns and functions to represent and solve simple problems.








a. Read, write, order, and compare real numbers (integers, fractions, decimals) and absolute values.


Identify the greater or lesser of 2 integers

Order integers on a number line [dupl.]






C: 211-220

C: 211-220

S: 211-220

N: 211-220

N: 211-220

N: 211-220

N: 221-230N: 231-240

N: 221-230



Order a set of integers from least to greatest [dupl.]

Definition and application of absolute value [dupl.]

N: 221-230

N: 221-230

A: 221-230

b. Expand the use of percents and ratios to solve problems.


Determine the discount price and sale price [dupl.]

Write a ratio (fraction) as a percent and percent as a ratio (fraction: denominators are factors of 100) [dupl.]


Find a number from a percent (4 is 9% of what number) [dupl.]


P: 211-220

P: 211-220

C: 221-230N: 221-230

C: 221-230

C: 221-230

N: 221-230



Solve proportions using the cross product method [dupl.]

Define ratio [dupl.]

Write ratios in a variety of ways [dupl.]

Find the percent one number is of another (8 is what % of 20?) [dupl.]

Find a number from a percent (20 is 45% of what number?) [dupl.]

N: 221-230

N: 221-230

N: 231-240

N: 231-240

C: 231-240

C: 231-240

c. Show a sense of magnitudes and relative magnitudes of real numbers (integers, fractions, decimals).


Order integers on a number line [dupl.]



Identify and order decimal and

C: 211-220

S: 211-220

N: 211-220

N: 221-230

N: 221-230


fractional coordinates on a number line [dupl.]

d. Develop and apply number theory concepts.





N: 211-220

N: 211-220

N: 211-220

N: 221-230

e. Understand the position of rational numbers on a number line.


N: 221-230


a. Add, subtract, multiply, and divide fractions and decimals.

Add decimals through hundred-thousandths with a calculator [dupl.]

Multiply a decimal by a decimal, factors to thousandths [dupl.]

Divide a decimal by

C: 211-220

C: 211-220

C: 211-220


a whole number and vice versa [dupl.]





Add mixed numbers with unlike denominators with regrouping [dupl.]

Subtract fractions having unlike denominators, answer in lowest terms [dupl.]

Multiply a whole number by a fraction [dupl.]


Divide a mixed

C: 221-230

C: 221-230

C: 221-230

C: 221-230

C: 211-220

C: 221-230

C: 211-220

C: 211-220

C: 211-220


number by a whole number or a fraction [dupl.]

Divide a whole number, fraction or mixed number by a mixed number [dupl.]




Add whole numbers and decimals to the hundredths place (same number of digits) [dupl.]

Subtract decimals to the hundredths place (not the same number of digits) [dupl.]

Subtract decimals to thousandths, vertically and horizontally, with and without regrouping [dupl.]

C: 221-230

C: 221-230

C: 211-220C: 221-230

C: 221-230

C: 231-240

C: 231-240

C: 231-240


Subtract a decimal from a whole number [dupl.]

Multiply a decimal by a decimal, factors to thousandths place [dupl.]


Divide a whole number (or decimal) by a decimal to thousandths place [dupl.]

Add fractions having unlike denominators with answer reduced to lowest terms [dupl.]

Subtract fractions having unlike denominators with answer reduced to lowest terms [dupl.]

Add and subtract mixed numbers with like denominators with regrouping

Add and subtract mixed numbers with unlike denominators with

C: 231-240

C: 231-240

C: 231-240

C: 231-240

C: 231-240

C: 231-240

C: 231-240

C: 231-240


regrouping [dupl.]

Add and subtract whole numbers, fractions, and mixed numbers [dupl.]

Multiply a fraction by a fraction; answer in lowest terms [dupl.]

Multiply mixed numbers [dupl.]


Divide a mixed number by a whole number or a fraction [dupl.]

Multiply three factors using fractions, mixed numbers, and whole numbers in any combination, answer in lowest terms [dupl.]

Divide a whole number, fraction, or mixed number by a mixed number [dupl.]

Compute and count change greater than $20.00 [dupl.]

C: 231-240

C: 231-240

C: 231-240

C: 231-240

C: 231-240

C: 231-240

C: 231-240

M: 231-240

b. Evaluate numerical expressions using the order of operations.

Evaluate expressions using the order of operations (may

A: 211-220


include parentheses or exponents) [dupl.]



Use the correct order of operations to evaluate numeric and algebraic expressions [dupl.]

A: 221-230

A: 221-230

A: 231-240

c. Explore the use of exponents.

Calculate the square of any number less than 100 [dupl.]

Order of “powers” [dupl.]

Write a whole number or a decimal in scientific notation [dupl.]

Write a number expressed in scientific notation in standard form [dupl.]


Evaluate expressions using

P: 211-220

N: 211-220

N: 211-220

N: 211-220

N: 221-230

N: 231-240


the order of operations that include exponents [dupl.]

Find products by applying rules for exponents [dupl.]

Write a whole number or a decimal in scientific notation (negative exponents) [dupl.]

N: 231-240

N: 231-240

d. Explore basic operations with integers.

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

Add integers with like signs

Add integers with unlike signs [dupl.]

Add several integers [dupl.]

Multiply integers with unlike signs

Divide integers with unlike signs

Divide integers

P: 211-220

C: 211-220

C: 211-220C: 231-240

C: 211-220C: 231-240

C: 211-220

C: 211-220

C: 221-230


with like signs [dupl.] Multiply integers with like signs [dupl.]

Subtract Fahrenheit temperatures [dupl.]

C: 231-240

C: 231-240

M: 231-240

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


New Vocabulary in this Range: 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 [dupl.]



N: 211-220

N: 221-230

C: 211-220



New Vocabulary in this range: ‘Solve for n” [dupl.]

C: 221-230

C: 231-240





C: 221-230

C: 221-230



P: 221-230









a. Use a variety of strategies including common mathematical formulas to compute problems drawn from real-world situations.



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 [dupl.]

Work backwards to solve problems [dupl.]

Solve if-then logic problems [dupl.]

Solve complex word problems

C: 221-230

P: 221-230

P: 211-220P: 221-230

P: 231-240

P: 231-240

P: 231-240


involving ratio, percent, discount, sale price, rounding and estimation, averaging, length, volume, rate, calendars, probability, money, and time [dupl.]

Find simple interest earned [dupl.]

Formulate expressions and equations to model problem solving situation [dupl.]

Solve multi-step problems involving computation [dupl.]

Find correct mathematical expressions to represent word problems [dupl.]

Given the answer to a problem, determine the question [dupl.]

Find commission and total pay [dupl.]

P: 231-240

P: 231-240

P: 231-240

P: 231-240

P: 231-240

M: 231-240

b. Recognize pertinent information for problem solving.


Use logic to predict outcomes [dupl.]

P: 231-240

02. Use reasoning a. Use a variety of


skills to recognize problems and express them mathematically.

methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain mathematical reasoning and concepts.









Use a tree diagram to determine the number of possible outcomes of an event [dupl.]

S: 221-230



New Vocabulary in

P: 211-220

P: 221-230


this Range: mortality, odometer, magic square, deducted, less than twice, addends, less than sum, rectangle, diameter, radius, label (units), area, perimeter [dupl.]

New Vocabulary in this Range: regression equation [dupl.]

P: 231-240

c. Use appropriate notation.











M: 211-220

M: 211-220

M: 221-230P: 221-230

M: 221-230



M: 221-230


c. Recognize the differences and relationships among measures of perimeter, area, and volume (capacity) in both systems.

d. Solve problems involving length, perimeter, area, volume (capacity), weight, mass, and temperature.






Calculate the area

P: 211-220

M: 201-210

M: 211-220

M: 231-240

M: 231-240

M: 231-240


of a triangle [dupl.]

Find the volume of a pyramid [dupl.]


Convert from Celsius to Fahrenheit [dupl.]


M: 231-240

M: 231-240

M: 231-240

M: 231-240





New Vocabulary in this Range: rectangular house, height and base, algebraic

M: 211-220

M: 221-230

M: 231-240


expression, rows and columns, checking account, car purchase, commission, simple interest [dupl.]


a. Develop the use of rates to make indirect measurements.



P: 211-220

P: 221-230


a. Develop the use of proportions, ratios, and scales.

Use map scales to solve problems [dupl.]

P: 231-240








a. Develop the use of variables in simple expressions and equations.


Explore equivalent ratios involving missing variables [dupl.]

A: 221-230

A: 231-240


b. Translate simple word statements and story problems into algebraic expressions and equations.

Write an algebraic expression to model a situation [dupl]



A: 231-240

P: 221-230

P: 221-230

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


a. Develop an understanding of using the following properties in evaluating mathematical and algebraic expressions: commutative, associative, identity, zero, inverse, and substitution.

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

A: 221-230

b. Understand and use the order of operations in evaluating basic algebraic expressions.



Evaluate an algebraic expression for given values [dupl.]

A: 211-220

A: 231-240

A: 231-240



a. Solve one-step equations using inverse operations.



A: 221-230

C: 221-230

b. Explore solutions of simple one-step equations using negative numbers.

Solve integer equations (one step, all four operations)

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

A: 221-230

A: 221-230

c. Explore graphical representation to show simple linear equations.

Graph linear functions, noting that the vertical change (change in y-value) per unit of horizontal change (change in x-value) is constant [dupl.]Identify linear equation for a straight line [dupl.]

Identify linear equation for a straight line [dupl.]

A: 231-240

A: 231-240







a. Precisely describe, classify, and understand relationships among types of one-, two-, and three-dimensional objects using their defining properties.







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

G: 211-220

G: 211-220

G: 211-220

G: 221-230

G: 221-230

G: 221-230

M: 221-230P: 221-230


circumference [dupl.]

Classify triangles by sides (equilateral, isosceles, and scalene) and angles (acute, obtuse, and right) [dupl.]

Identify and discriminate between regular and irregular polygons [dupl.]

Identify the base angles of a triangle [dupl.]

Know the definition of the hypotenuse of a triangle [dupl.]

G: 231-240

G: 231-240

G: 231-240

G: 231-240



M: 211 - 220 G: 221-230

c. Apply fundamental concepts, properties, and relationships among points, lines, planes, angles, and shapes.




Classify angles: adjacent, vertical, corresponding, and

G: 211-220

G: 211-220

G: 211-220

G: 221-230


supplementary [dupl.]



G: 221-230G: 231-240

M: 221-230G: 231-240






Solve word problems involving similar polygons [dupl.]

G: 211-220

G: 211-220

G: 211-220

G: 221-230

G: 231-240

e. Apply formulas for perimeter, circumference, and area to triangles, quadrilaterals, and circles.


P: 211-220








G: 221-230

M: 231-240

M: 231-240

M: 231-240

M: 231-240

M: 231-240

f. Explore the concept of surface area and volume (capacity).



M: 201-210

M: 231-240

g. Explore and model the effects of reflections, translations, and rotations on various shapes.


Understand meaning and representation of a dilation [dupl.]

G: 211-220

G: 231-240


New Vocabulary in this Range: symmetrical, perpendicular, ray, vertex, rotation,

G: 211-220


triangular prism, corresponding parts, supplementary, acute angle, transformation [dupl.]


New Vocabulary in this Range: transformation, hypotenuse, edge, isosceles, scalene triangle, similar trapezoids, alternate interior angles, sum of angles in triangle [dupl.]

G: 221-230

G: 231-240

02. Apply the geometry of right triangles.

a. Explore right triangle geometry.


G: 231-240



Graph ordered pairs in all four quadrants (coordinate geometry) [dupl.]

Find location of coordinates on a number line

Locate the vertex on a coordinate grid [dupl.]

S: 221-230

S: 231-240

S: 231-240


Create a table of (x, y) values for the given linear equation and graph the function [dupl.]

S: 231-240






a. Read and interpret tables, charts, and graphs (scatter plots, line graphs, bar graphs, pie charts).


S: 221-230




a. Collect, organize, and display data with appropriate notation in tables, charts, and graphs (scatter plots, line graphs, bar graphs, pie charts).


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


Know the concepts of mode, median, and mean; compute and compare them in simple examples to demonstrate that

P: 211-220

S: 221-230


these measures of central tendency may differ for a given set of data [dupl.]


S: 231-240

b. Explore the significance of range, frequency, and informal distribution.




P: 211-220 S: 221-230


c. Recognize equally likely outcomes.


a. Make predictions based on simple experimental and theoretical probabilities.


P: 221-230




New Vocabulary in this Range: vertex, fractional part,

S: 211-220

S: 221-230

S: 231-240


amount of sales, translation, matrix, possibility, mean salary, coordinates of points [dupl.]






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




Using whole numbers, complete a function table based on a given rule [dupl.]

A: 211-220

A: 221-230

A: 221-230

A: 231-240

b. Use functional relationships to explain how a change in one quantity results in a change in another.


02. Represent equations, inequalities, and

a. Represent a simple set of data in a table, as a graph, and as a


functions in a variety of formats.

mathematical relationship.


a. Use patterns and functions to represent and solve problems.

Find missing numbers in a diagram by using patterns [dupl.]

P: 231-240








a. Read, write, order, and compare real numbers (integers, fractions, decimals, percents, ratios) and absolute values.






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


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

N: 221-230

N: 221-230

N: 221-230

N: 221-230

N: 221-230

N: 221-230 C: 221-230

C: 221-230

C: 221-230


what number) [dupl.]

Definition and application of absolute value [dupl.]

Write a decimal or mixed decimal for a fraction [dupl.]

Define ratio [dupl.]

Write ratios in a variety of ways [dupl.]



Understand the meaning of integers [dupl.]

A: 221-230

N: 231-240

N: 231-240

N: 231-240

C: 231-240

C: 231-240

C: 241-250

DMA8

N8

b. Understand and use real numbers, both rational and irrational.

Evaluate expressions using square roots [dupl.]

Identify perfect squares in a list of numbers and calculate the positive square root of a perfect square [dupl.]

N: 221-230N: 241-250

N: 231-240

N8

c. Show a sense of Order a set of N: 221-230


magnitudes and relative magnitudes of real numbers (integers, fractions, decimals) using scientific notation and exponential numbers.

integers from least to greatest [dupl.]

DMA8

N8

d. Develop and apply number theory concepts.


N: 221-230

N8

e. Understand the position of real numbers on a number line.


N: 221-230

DMA8

N8


a. Consistently and accurately add, subtract, multiply, and divide rational numbers.





Divide a whole number, fraction or mixed number by a mixed number

C: 221-230

C: 221-230

C: 221-230

C: 221-230

C: 221-230


[dupl.]




Add whole numbers and decimals to the hundredths place (same number of digits) [dupl.]

Subtract decimals to the hundredths place (not the same number of digits) [dupl.]

Subtract decimals to thousandths, vertically and horizontally, with and without regrouping [dupl.]

Subtract a decimal from a whole number [dupl.]

Multiply a decimal by a decimal, factors to thousandths place [dupl.]

C: 221-230

C: 221-230

C: 221-230

C: 231-240

C: 231-240

C: 231-240

C: 231-240

C: 231-240



Divide a whole number (or decimal) by a decimal to thousandths place [dupl.]

Add fractions having unlike denominators with answer reduced to lowest terms [dupl.]

Subtract fractions having unlike denominators with answer reduced to lowest terms [dupl.]

Add and subtract mixed numbers with like denominators with regrouping [dupl.]

Add and subtract mixed numbers with unlike denominators with regrouping [dupl.]

Add and subtract whole numbers, fractions, and mixed numbers [dupl.]

Multiply a fraction by a fraction; answer in lowest terms [dupl.]

Multiply mixed numbers [dupl.]

C: 231-240

C: 231-240

C: 231-240

C: 231-240

C: 231-240

C: 231-240

C: 231-240

C: 231-240

C: 231-240



Divide a mixed number by a whole number or a fraction [dupl.]

Multiply three factors using fractions, mixed numbers, and whole numbers in any combination, answer in lowest terms [dupl.]

Divide a whole number, fraction, or mixed number by a mixed number [dupl.]

Add integers with unlike signs [dupl.]

Add several integers [dupl.]

Divide integers with like signs [dupl.] Multiply integers with like signs [dupl.]

Compute and count change greater than $20.00 [dupl.]


Multiply a whole number by a fraction

C: 231-240

C: 231-240

C: 231-240

C: 231-240

C: 231-240

C: 231-240

C: 221-230 C: 231-240

C: 231-240

M: 231-240

M: 231-240

C: 241-250


Subtract integers, subtracting a negative

C: 241-250

DMA8

N8

b. Instantly recall common equivalent fractions, decimals, and percents. DMA8

c. Evaluate numerical expressions using the order of operations.




A: 221-230

A: 221-230

A: 231-240

DMA8

N8

d. Understand and use exponents.


Evaluate expressions using the order of operations that include exponents [dupl.]

Find products by applying rules for exponents [dupl.]


Understand and use

N: 221-230

N: 231-240

N: 231-240

N: 231-240

A: 241-250


the rules of exponents, including negative exponents [dupl.]

DMA8

N8

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




New Vocabulary in this range: ‘Solve for n” [dupl.]

New Vocabulary in this range: decimal fractions, opposite [dupl.]

N: 221-230

C: 221-230

C: 231-240

C: 241-250





C: 221-230

C: 221-230

DMA8

N8




P: 221-230

N8

c. Determine whether a given estimate is an overestimate or underestimate. N8







a. Use a variety of strategies, including common mathematical formulas to compute problems drawn from real-world situations.



Choose and use an appropriate problem solving strategy: Draw a picture, Make a model, Guess and

C: 221-230

P: 221-230

P: 221-230


test, Make a list, Make a table, Find a pattern, Work backwards, Solve a simpler problem, Draw a diagram, or Write an equation [dupl.]

Work backwards to solve problems [dupl.]


Solve complex word problems involving ratio, percent, discount, sale price, rounding and estimation, averaging, length, volume, rate, calendars, probability, money, and time [dupl.]





P: 231-240

P: 231-240

P: 231-240

P: 231-240

P: 231-240

P: 231-240

P: 231-240




Manipulate problems with time and a half and overtime wages [dupl.]

Solve complex word problems involving rate, ratio, percent, averages, and sale price [dupl.]

P: 231-240

M: 231-240

P: 241-250

P: 241-250

DMA8

b. Recognize pertinent information for problem solving.

DMA8


Use logic to predict outcomes [dupl.]

P: 231-240

DMA8


a. Use a variety of methods, such as words, numbers, symbols charts, graphs, tables, diagrams, and models, to explain mathematical reasoning and concepts. DMA8

b. Apply solutions and strategies to new problem situations. DMA8

c. Formulate conjectures and justify (short of formal proof) why they must be or seem to be


true.



DMA8


DMA8


DMA8



Use a tree diagram to determine the number of possible outcomes of an event [dupl.]

S: 221-230

DMA8



New Vocabulary in this Range: regression equation [dupl.]

New Vocabulary in this Range: matrix [dupl.]

P: 221-230

P: 231-240

P: 241-250

c. Use appropriate


notation.






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




Select appropriate unit of measure [dupl.]

M: 221-230P: 221-230

M: 221-230

M: 221-230

M: 241-250

DMA8

N8


DMA8

N8

c. Recognize the differences and relationships among measures of perimeter, area, and volume (capacity) in both systems. DMA8

d. Solve problems involving length,

Find the perimeter of a square or

M: 231-240


perimeter, area, volume (capacity), weight, mass, and temperature.

rectangle using the formula [dupl.]





Convert from Celsius to Fahrenheit [dupl.]


Calculate the area of a parallelogram and rectangle using algebra tiles [dupl.]

Calculate the surface area of a rectangular prism and cylinder [dupl.]

Compare volume of different dimensional containers [dupl.]

M: 231-240

M: 231-240

M: 231-240

M: 231-240

M: 231-240

M: 231-240

M: 241-250

M: 241-250

P: 241-250

N8

e. Convert unit of measurement within each system. N8


New Vocabulary in this Range: reasonable,

M: 221-230


formula, segment BC, pi, radius squared, diameter, metric units, quarts, gallons, rectangular box, base, rate [dupl.]

New Vocabulary in this Range: rectangular house, height and base, algebraic expression, rows and columns, checking account, car purchase, commission, simple interest [dupl.]

New Vocabulary in this Range: doubled and tripled, rectangular solid, cylindrical tank, algebra tiles, inscribed, time-and-a-half, sales tax, discount [dupl.]

M: 231-240

M: 241-250


a. Use rates to make indirect measurements.


P: 221-230

DMA8

N8


a. Understand and use proportions, ratios, and scales.


P: 231-240

DMA8

N8



DMA8







a. Understand and use variables in expressions, equations, and inequalities.


A: 231-240

DMA8

N8

b. Translate simple word statements and story problems into algebraic expressions and equations.

Write an algebraic expression to model a situation [dupl.]



A: 231-240

P: 221-230

P: 221-230

DMA8

N8

c. Use symbols (<, >, =, , , ) to express relationships. N8


a. Understand and use the following properties in evaluating algebraic expressions: commutative, associative, identity, zero, inverse, distributive, and substitution.

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

A: 221-230

DMA8


b. Understand and use the order of operations in evaluating basic algebraic expressions.


Evaluate an algebraic expression for given values [dupl.]

A: 231-240

A: 231-240

DMA8

N8

c. Simplify algebraic expressions.

Simplify and evaluate expressions that include positive and negative integral components [dupl.]

A: 231-240

DMA8

N8


a. Solve one- and two-step equations and inequalities using inverse operations.



Solve simple linear equations and inequalities over the rational numbers [dupl.]

C: 221-230

A: 221-230

A: 231-240

DMA8

N8

b. Explore graphical representation to show simple linear equations.

Graph linear functions, noting that the vertical change (change in y-value) per unit of horizontal change (change in x-value) is constant [dupl.]

Identify linear

A: 231-240

A: 231-240


equation for a straight line [dupl.] DMA8

N8






a. Precisely describe, classify, and understand, relationships among types of one-, two-, and three-dimensional objects using their defining properties.





Classify triangles by sides (equilateral, isosceles, and scalene) and angles (acute, obtuse, and right) [dupl.]

Identify and discriminate between regular

G: 221-230

G: 221-230

G: 221-230

M: 221-230P: 221-230

G: 231-240

G: 231-240


and irregular polygons [dupl.]

Identify the base angles of a triangle [dupl.]


G: 231-240

G: 231-240

DMA8

N8



Construct congruent segments and angles

Construct angle bisectors

G: 221-230

G: 241-250

G: 241-250

DMA8

c. Understand and apply fundamental concepts, properties, and relationships among points, lines, planes, angles, and shapes.


Classify angles: adjacent, vertical, corresponding, and supplementary [dupl.]


Identify properties of parallel lines

Identify angle bisectors

M: 221-230G: 231-240

G: 221-230

G: 221-230G: 231-240

G: 241-250

G: 241-250


Solve problems regarding relationships among chords of a circle

Determine endpoints and midpoint of a line on a coordinate graph [dupl.]

G: 241-250

S: 241-250

DMA8

N8



Solve word problems involving similar polygons [dupl.]

Identify symmetry of a sphere

Use of symmetry to determine grouping properties

G: 221-230

G: 231-240

G: 241-250

P: 241-250

DMA8

N8

e. Apply formulas for perimeter, circumference, and area to polygons and circles.




Calculate the area

G: 221-230

M: 231-240

M: 231-240

M: 231-240


of a triangle [dupl.]




M: 231-240

M: 231-240

M: 241-250

DMA8

N8

f. Understand the concept of surface area and volume (capacity).



Understand the effects of changing dimensions on perimeter, area, and volume [dupl.]

M: 231-240

M: 241-250

M: 241-250

DMA8

N8

g. Explore and model the effects of reflections, translations, and rotations on various shapes.

Understand meaning and representation of dilation [dupl.]

G: 231-240

N8



G: 221-230


New Vocabulary in this Range: transformation, hypotenuse, edge, isosceles, scalene triangle, similar trapezoids, alternate interior angles, sum of angles in triangle [dupl.]

New Vocabulary in this Range: symmetrical halves, diameter, radius, angle bisector, tangent, corresponding parts of congruent triangles, Pythagorean theorem, corresponding angles, complementary angles, construction [dupl.]

G: 231-240

G: 241-250


a. Investigate right triangle geometry using the Pythagorean Theorem.

Use the Pythagorean theorem to calculate the measure of one side of a right triangle when the other two sides are known [dupl.]

G: 241-250

DMA8

N8


a. Use the coordinate plane as it relates to real-world applications.

Graph ordered pairs in all four quadrants (coordinate geometry) [dupl.]

Locate the vertex on a coordinate grid [dupl.]

S: 221-230

S: 231-240


Create a table of (x, y) values for the given linear equation and graph the function [dupl.]

S: 231-240

DMA8

N8






a. Analyze and interpret tables, charts, and graphs (scatter plots, line graphs, bar graphs, pie charts).


S: 221-230

DMA8

N8




a. Collect, organize, and display data with appropriate notation in tables, charts, and graphs (scatter plots, line graphs, bar graphs, pie charts).

DMA8

N8


a. Choose and calculate the appropriate measure of central tendency – mean, median, and mode.

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 [dupl.]

S: 221-230



S: 231-240

DMA8

N8

b. Explore the significance of range, frequency, and informal distribution.

DMA8

N8


a. Model situations of probability using simulations.


S: 221-230

DMA8

N8


DMA8

c. Recognize equally likely outcomes.

DMA8


a. Make predictions based on experimental and theoretical probabilities.


Predict outcomes using a six-sided cube [dupl.]

P: 221-230

S: 241-250

DMA8

N8



New Vocabulary in this Range: vertex, fractional part, amount of sales,

S: 221-230

S: 231-240


translation, matrix, possibility, mean salary, coordinates of points [dupl.]

New Vocabulary in this Range: coordinate, Venn diagram, greatest decrease, endpoints, midpoint [dupl.]

S: 241-250

c. Conduct statistical experiments and interpret results using tables, charts, or graphs. N8






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




Using whole numbers, complete a function table

A: 221-230

A: 221-230

A: 221-230

A: 231-240

DMA8


based on a given rule [dupl.] N8

b. Use functional relationships to explain how a change in one quantity results in a change in another.

Use a function table to determine inverse variation [dupl.]

A: 241-250

DMA8


02. Represent equations, inequalities, and functions in a variety of formats.

a. Represent a set of data in a table, as a graph, and as a mathematical relationship.

Students analyze a given set of data for the existence of a pattern and represent the pattern algebraically and graphically [dupl.]

A: 241-250


a. Use patterns and functions to represent and solve problems.

Find missing numbers in a diagram by using patterns [dupl.]

P: 231-240

N8


346. MATHEMATICS STANDARDS – GRADES 9 and 10 (GRADE 9 AVERAGE SCORE: 233-249, GRADE 10 AVERAGE SCORE: 238-251)






a. Understand and use positive and negative numbers, fractions, decimals, percentages, and scientific notation.


Write a decimal or mixed decimal for a fraction [dupl.]



Understand the meaning of integers [dupl.]

N: 231-240

N: 231-240

C: 231-240

C: 231-240

C: 241-250

b. Understand properties of the real number system.

Use the additive inverse property to solve problems

Identify and use the arithmetic properties of subsets of integers and rational, irrational, and real numbers

C: 251-260

A: 251-260

c. Understand properties of roots, exponents, and

Identify perfect squares in a list of

N: 231-240


logarithms. numbers and calculate the positive square root of a perfect square [dupl.]

Evaluate expressions using square roots [dupl.]

Evaluate powers with a negative exponent

Understand and use the rules of exponents, including negative exponents [dupl.]

N: 241-250

N: 251-260

A: 241-250

d. Use number theory concepts (divisibility rules, factors, multiples, primes) to solve problems.


a. Use the proper order of operations. Perform operations with real numbers.


Use order of operations rules

A: 231-240

C: 251-260

b. Use graphs, matrices, and sequences to represent and solve problems.

Use a matrix to identify given figure on a graph

Multiplcation of matrices

P: 241-250

P: 251-260


a. Apply number sense to every day situations.



a. Use a variety of methods, including common mathematical formulas, to solve problems drawn from daily life.



Solve complex word problems involving ratio, percent, discount, sale price, rounding and estimation, averaging, length, volume, rate, calendars, probability, money, and time [dupl.]






Manipulate problems with time and a half and overtime wages

M: 231-240

P: 231-240

P: 231-240

P: 231-240

P: 231-240

P: 231-240

P: 231-240

P: 231-240

P: 241-250


[dupl.]

Solve complex word problems involving rate, ratio, percent, averages, and sale price [dupl.]

Solve complex word problems with surface area, area, circumscribed figures, Pythagorean Theorem, consecutive integers

Use clues given in word problems to decode correct answer

Determine correct formula needed to solve problem

P: 241-250

P: 251-260

P: 251-260

P: 251-260


a. Use inductive and deductive reasoning to set up a problem.

b. Use logic to make mathematical proofs.

c. Make and evaluate logical arguments.


a. Understand the purpose and capabilities of appropriate technology.

b. Understand the nature and use of mathematical models.



a. Select the appropriate means to communicate mathematical information.






a. Determine length, area, capacity, weight, time, and temperature, with appropriate units.






Select appropriate unit of measure [dupl.]


Compare volume of different dimensional

M: 231-240

M: 231-240

M: 231-240

M: 231-240

M: 241-250

M: 241-250

M: 241-250

M: 241-250


containers [dupl.]

Find volume of cones and rectangular prisms and cylinders

Find area of inscribed figure by using midpoints and endpoints

P: 241-250

M: 251-260

M: 251-26002. Apply concepts of

rates and other derived or indirect measurements.

a. Understand equivalent units, comparable units, and conversions.


a. Understand and use proportions, ratios, and scaling.


Solve problems involving ratio of a side of a figure to its area, perimeter, or volume

Determine proportional parts of a number

Use proportional relationships to determine lengths of sides of a figure that are represented by algebraic relationships

P: 231-240

P: 251-260

P: 251-260

P: 251-260


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

05. Perform error analysis.

a. Understand tolerance, precision, and their applications.

Actual versus precise measurements

P: 241-250


b. Understand that error accumulates in a computation when there is rounding at intermediate steps.






a. Understand and use variables, expressions, equations and inequalities.


A: 231-240


a. Understand and use procedures for operating on algebraic expressions.

Add, subtract, multiply, and divide rational expressions and functions

Simplify an expression containing imaginary roots

Find the difference of two squares

Simplify embedded expressions before solving linear equations and inequalities in one variable

Solve problems that use variables in expressions describing geometric quantities by solving for one variable

A: 241-250

A: 241-250

A: 241-250

A: 251-260

A: 251-260


Simplify expressions containing cube roots

Solve expressions containing factorials

A: 251-260

A: 251-260


a. Understand and use appropriate procedures to solve linear equations and inequalities such as

3x - 4 = 2or

3x - 4 > 2.

Solve simple linear equations and inequalities over the rational numbers [dupl.]

Identify linear equation for a straight line [dupl.]

Students solve equations and inequalities involving absolute values [dupl.]

Derive linear equations by using the point-slope function

Cube a binomial

Derive linear equations by using the point-slope formula [dupl.]

A: 231-240

A: 231-240

A: 241-250

A: 251-260

A: 251-260

S: 251-260

b. Use appropriate procedures to simplify and solve polynomial equations and inequalities such as

x2 + 3x = 7or

x2 + 3x 7.

Apply basic factoring techniques to second- and simple third-degree polynomials, including finding a common factor for all terms in a polynomial,

A: 231-240

A: 231-240


recognizing the difference of two squares, and recognizing perfect squares of binomials

Solve equations with variables as exponents

Simplify monomials containing integer powers and roots

Find the solution set for inequalities that include absolute values [dupl.]

Solve a quadratic equation by factoring or completing the square

Know the quadratic formula and demonstrates its proof by completing the square

Identify discriminant and roots

Use the quadratic formula to find the roots of a second-degree polynomial and solve quadratic equations

Solve problems

A: 241-250

A: 241-250

A: 241-250

A: 251-260

A: 251-260

A: 251-260

A: 251-260


involving regression equations

A: 251-260

A: 251-260

A: 251-260

S: 251-26004. Solve simple linear

systems of equations or inequalities.

a. Understand and use appropriate procedures to solve simple linear systems of equations and inequalities such as

x + y = 72x + 3y = 21

orx + y < 7

2x + 3y 21.

Solve a system of two linear equations in two variables algebraically and interpret the answer graphically

Solve a system of two linear inequalities in two variables and identify the solution set

Find the number of possible solutions for a system of equations

A: 241-250

A: 241-250

A: 251-260







a. Understand congruence and similarity as they apply to reflection, rotation, and translation.

Solve problems involving rotations (turns) and reflections (flips)

Know the effect of rigid motions on figures in the coordinate plane and space, including rotations, translations, and reflections

G: 251-260

S: 251-260

b. Understand scaling as it relates to size variations in one, two, and three-dimensional objects, while shape is maintained.

Understand meaning and representation of dilation [dupl.]

G: 231-240


a. Understand the basic concepts of right triangle trigonometry (basic trigonometry ratios such as sine, cosine, and tangent).

Find sin and cosine of a given angle

A: 251-260

b. Use trigonometric ratio methods to solve problems.

c. Know and apply the Pythagorean Theorem to solve real world problems.

Use the Pythagorean theorem to calculate the measure of one side of a right triangle when the other two sides are known [dupl.]

G: 241-250



a. Understand concepts of the Cartesian Coordinate System.

Determine endpoints and midpoint of a line on a coordinate graph [dupl.]

Understand the concepts of parallel lines and perpendicular lines and how those slopes are related

Derive linear equations by using the point-slope formula [dupl.]

Derive and solve problems involving use of ordered pairs to determine area of a figure

Determine the axis of symmetry of a linear graph

Find the slope given two points on the line of a given graph

Write the equation of a line when given the graph of the line, two points on the line, or the slope of the line and a point on the line

Identify the equation of a parabola

S: 241-250

A: 241-250

S: 251-260

S: 251-260

S: 251-260

A: 251-260

A: 251-260

A: 251-260


Identify properties and slope of lines

Identify plane

Identify midpoint and endpoint

Identify perpendicular bisector

G: 251-260

G: 251-260

G: 251-260

G: 251-260

b. Understand the characteristics and uses of vectors.






a. Read and interpret tables, charts, and graphs (scatter plots, line graphs, three-dimensional graphs, and pie charts).


a. Collect and organize data, and display the data in tables, charts, and graphs (scatter diagrams, frequency tables, bar graphs, or pie charts).


a. Understand basic statistical concepts including mean (average), median, mode, range, and standard deviation.


S: 231-240


a. Understand experimental and theoretical probability.

Predict outcomes using a six-sided cube [dupl.]

S: 241-250


Calculate basic probability theoretically and use results to make predictions

S: 251-260

b. Distinguish between independent and dependent events.

c. Know that probability ranges from 0% to 100%. Understand randomness and chance.


a. Use appropriate technology to employ simulation techniques, curve fitting, correlation, and graphical models to make predictions or decisions based on data.

b. Design, conduct, and interpret results of statistical experiments.

c. Analyze the effect of biased data on statistical predictions.







a. Solve problems that involve varying quantities with variables, expressions, equations, inequalities, and absolute values.

Determine whether a relation is defined by a graph, a set of ordered pairs, or a symbolic expression is a function and justify the conclusion

Students solve equations and inequalities involving absolute values [dupl.]

Find the solution set for inequalities that include absolute values [dupl.]

Solve logarithmic functions

A: 241-250

A: 241-250

A: 251-260

A: 251-260

02. Represent equations, inequalities and functions in a variety of formats.

a. Represent a set of data in a table, a graph, and as a mathematical relationship.

Students analyze a given set of data for the existence of a pattern and represent the pattern algebraically and graphically [dupl.]

Graph a linear function in two variables using the slope-intercept method and identify intercepts

Graph quadratic

A: 241-250

A: 241-250

A: 241-250


functions and know that their roots are the x-intercepts

A: 251-26003. Apply functions to

a variety of problems.

a. Model real-world phenomena using polynomial, rational, and basic exponential functions, noting restricted domains.

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