Mathematics Support Guide · 2018-11-14 · Mathematics Support Guide ... Key Concept: Reasoning with Equations and Inequalities ... Ready Standards. The prioritized standards provide

Mathematics

Support Guide

Published: April 26, 2018

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TABLE OF CONTENTS

Mathematics Support Guide ...................................................................................................................... 1

Number Sense and Base Ten ...................................................................................................................... 2

The Number System ................................................................................................................................... 2

Arithmetic with Polynomials and Rational Expressions ......................................................................... 2

Creating Equations/Structure and Expressions ....................................................................................... 2

Reasoning with Equations and Inequalities .............................................................................................. 2

Key Concept: Number Sense and Base Ten ............................................................................................. 3



Key Concept: The Number System ........................................................................................................ 10



Key Concept: Arithmetic with Polynomials and Rational Expressions .................................................. 19

Key Concept: Creating Equations........................................................................................................... 20

Key Concept: Structure and Expressions ................................................................................................ 21

Key Concept: Reasoning with Equations and Inequalities ..................................................................... 22

Number Sense – Fractions ........................................................................................................................ 24

Number Sense and Operations – Fractions ............................................................................................ 24

Ratios and Proportional Relationships ................................................................................................... 24

Key Concept: Number Sense – Fractions ............................................................................................... 25

Key Concept: Number Sense and Operations – Fractions ...................................................................... 27

Key Concept: Number Sense and Operations – Fractions ...................................................................... 30

Key Concept: Ratios and Proportional Relationships ............................................................................. 32

Key Concept: Ratios and Proportional Relationships ............................................................................. 33

Algebraic Thinking and Operations ........................................................................................................ 35

Expressions, Equations, and Inequalities ............................................................................................... 35

Key Concept: Algebraic Thinking and Operations ................................................................................. 36



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Key Concept: Expressions, Equations, and Inequalities ......................................................................... 43



Geometry ................................................................................................................................................... 49

Geometry and Measurement.................................................................................................................... 49

Key Concept: Geometry ......................................................................................................................... 52

Key Concept: Geometry ......................................................................................................................... 54

Key Concept: Geometry and Measurement ............................................................................................ 56



Measurement and Data Analysis ............................................................................................................. 60

Key Concept: Measurement and Data Analysis...................................................................................... 61



Data Analysis and Statistics ..................................................................................................................... 68

Data Analysis, Statistics, and Probability ............................................................................................... 68

Functions .................................................................................................................................................... 68

Interpreting Functions .............................................................................................................................. 68

Interpreting Data ...................................................................................................................................... 68

Quantities ................................................................................................................................................... 68

Real Number System ................................................................................................................................ 68

Key Concept: Data Analysis and Statistics............................................................................................. 69

Key Concept: Data Analysis, Statistics, and Probability ........................................................................ 70

Key Concept: Functions .......................................................................................................................... 72

Key Concept: Interpreting Functions ...................................................................................................... 75

Key Concept: Data Analysis, Statistics, and Probability ........................................................................ 77

Key Concept: Interpreting Data .............................................................................................................. 79

Key Concept: Quantities ......................................................................................................................... 81

Key Concept: Real Number System ....................................................................................................... 83

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Introduction

The South Carolina Alternate Assessments (SC-Alt): Mathematics Assessment and Instructional Support Guide document was developed to

provide guidance to teachers for including students with significant cognitive disabilities in challenging academic instruction. The South Carolina

College- and Career-Ready Standards for Mathematics have been prioritized for students participating in the alternate assessment. This prioritized

content preserves the essence of the grade-level expectations while narrowing the depth and breadth of content that students with significant

cognitive disabilities are exposed to during instruction and assessment. This support guide identifies prioritized content by grade level, core

concept, and standard.

What Are Prioritized Standards?

Prioritized standards are a subset of the South Carolina College- and Career-Ready Standards that are considered essential for all students to attain.

This subset includes the standards that are assessed in the South Carolina Alternate Assessments for Mathematics. The prioritized standards are

intended to help teachers focus instruction on the most critical of the knowledge and skills included in the South Carolina College- and Career-

Ready Standards. The prioritized standards provide suggestions that are intended to help teachers make content accessible to students with a

varying range of abilities within the classroom. The activities and adaptations included here serve as a model for how students participating in the

South Carolina Alternate Assessments for Mathematics assessment may receive academic instruction in math.

What’s Included?

This guide includes the following sections:

• A list of the South Carolina College- and Career-Ready Standards has been prioritized for students with significant cognitive disabilities.

The Prioritized Standards are presented in a matrix to show the continuum of the concepts across complexity levels. The matrix shows

the range of access points to the prioritized standards. This matrix should not be perceived as a linear progression; students may be

stronger in one skill than another, so the matrix should be used as appropriate.

• A section called It Is Essential for Students to Know provides a “big picture” description of the content.

• Vocabulary and Skills sections describe the mathematical processes that students need to meet proficiency.

• Sections describing Daily Activities and Functional Activities provide suggestions for tying academic instruction to functional skills.

• A Resources section lists materials that may be helpful in instruction.

This document was developed to provide a foundation that supports and enhances the day-to-day activities which will lead to positive outcomes

for students with significant cognitive disabilities as they access the SCCCR Standards.

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Number Sense and Base Ten

The Number System

Arithmetic with Polynomials and Rational Expressions

Creating Equations/Structure and Expressions

Reasoning with Equations and Inequalities

3rd Grade 4th Grade 5th Grade 6th Grade 7th Grade 8th Grade 11th Grade 11th Grade 11th Grade

3.NSBT 4.NSBT 5.NSBT 6.NS 7.NS 8.NS 11.AAPR 11.ACE

11.ASE

11.AREI

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3rd Grade

Key Concept: Number Sense and Base Ten

SCCCR Standards: Use place value understanding to round whole numbers to the nearest 10 or 100 (3.NSBT.1). Add and subtract whole

numbers fluently to 1,000 using knowledge of place value and properties of operations (3.NSBT.2). Multiply one-digit whole numbers by

multiples of 10 in the range 10–90, using knowledge of place value and properties of operations (3.NSBT.3). Read and write numbers through

999,999 in standard form and equations in expanded form (3.NSBT.4). Compare and order numbers up to 999,999 and represent the comparison

using the symbols >, =, or < (3.NSBT.5).

Prioritized Standard Level 4: Exceeds Standard Level 3: Meets Standard Level 2: Emerging Level 1: Foundational

3.NSBT.1: Round whole

numbers up to 100 to the

nearest 10.


numbers from 0–100 to the

nearest 10.



nearest 10.

3.NSBT.1: Understand the

point when a number should

be rounded up (limited to

numbers from 1–10).

3.NSBT.1: Recognize a unit

in the place value system

(limited to ones and tens

place values).

3.NSBT.2: Add and subtract

single-digit numbers.

3.NSBT.2: Determine the

unknown in an addition or

subtraction equation.

3.NSBT.2: Demonstrate the

concept of addition and

subtraction (limited to

single-digit numbers from 1–

10).

3.NSBT.2: Identify the

functions of addition,

subtraction, and equal signs

(limited to numbers 1–5).

3.NSBT.2: Recognize the

addition, subtraction, and

equal signs.

3.NSBT.3: Multiply one-

digit whole numbers by 10.

3.NSBT.3: Count by tens

starting at a multiple of 10

(using a set of 10 objects,

numbers, etc., e.g., count

with dimes).


concept of counting by 10 by

counting the sets of 10 and

adding a zero to the end of

number of sets (limited to

numbers 1–50).

3.NSBT.3: Identify sets of

numbers in tens using

numbers 1–30.

3.NSBT.3: Recognize the

numbers 1–10 as a set for the

tens place.

3.NSBT.4: Read numbers up

to 999.

3.NSBT.4: Read numbers up

to 999.

3.NSBT.4: Identify numbers

in word form (numbers

ranging from 1–100).


in word form (numbers

ranging from 1–50).


in word form (limit to

numbers 1–50).

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3.NSBT.5: Compare and

order numbers up to 999

using the symbols >, =, or <.

3.NSBT.5: Compare two

numbers up to 100 using

symbols (=, <, >).


numbers up to 50 using

symbols (=, <, >).

3.NSBT.5: Arrange a set of

numbers from least to

greatest.

3.NSBT.5: Recognize the <,

>, and = signs.

It Is Essential for Students to Know: Students need to recognize place value up to hundreds place and recognize mathematical symbols in order

to round whole numbers, compare numbers, add and subtract numbers, and multiply one-digit whole numbers by 10.

Applications to Daily Tasks, Activities, Routines, or Life Experiences

• Using a hundred chart or ones place value chart, demonstrate place value concepts by showing students that a collection of 10 pennies is

the same value as one dime.

• Demonstrate addition and subtraction of single-digit numbers using student-preferred items such as crackers, stickers, coins, counting

bears, etc. This can be done as a group activity or individually with students.

• Using items two students have in their desks or pencil boxes, demonstrate comparing numbers by counting the number of items each

student has and comparing who has the most or least amount.

Standard Vocabulary Skills Daily Activities Functional Activities

3.NSBT Round

Addition/

Subtraction

Multiply

Compare

Greater than

Less than

Order

Equal

Place Value

Ones

Tens

Count by ones and tens

Add with numbers to 10

Subtract with numbers to

10

Recognize numbers

Read number words

Order numbers

Compare numbers

Recognize symbols (+, –,

=, <, >)

Round numbers from 0–

30 to nearest 10

Play bingo (digit, number words, sets)

Use various number cubes (6-sided, 20-sided, etc.)

Count with pennies, dimes, and dollar bills

Play games that include number cubes, but use numbered

cubes that have digits or words on sides or use spinners

Practice place value using a weekly pill case with

numbered cubes

Scavenger hunt in newspaper, magazine, cupboards to find

numbers, number words

Color by number – in spaces include words, digits,

equations

Play dominos

Match words to numbers

Making a grocery list

Cooking

Learning room numbers (such as by

collecting items from classrooms)

Comparing scores to determine game

winners

Finding seats at events using seat numbers

Reading numbers on buses or cars

Reading addresses and telephone numbers

Counting objects

Identifying page numbers

Identifying dates on calendars

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4th Grade


SCCCR Standards: Recognize math periods and number patterns within each period to read and write in standard form large numbers through

999,999,999 (4.NSBT.2). Use rounding as one form of estimation and round whole numbers to any given place value (4.NSBT.3). Fluently add

and subtract multi-digit whole numbers using strategies to include a standard algorithm (4.NSBT.4). Multiply up to a four-digit number by a one-

digit number and multiply a two-digit number by a two-digit number using strategies based on place value and the properties of operations.

Illustrate and explain the calculation by using rectangular arrays, area models and/or equations (4.NSBT.5). Divide up to a four-digit dividend by a

one-digit divisor using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division

(4.NSBT.6).


4.NSBT.2: Recognize mathematical

periods through 999,999.

4.NSBT.2: Recognize word

form for numbers through

999,999.

4.NSBT.2: Recognize word

form for numbers through

999.

4.NSBT.2: Recognize

word form for numbers

through 99.

4.NSBT.2: Recognize

word form for numbers

through 9.

4.NSBT.3: Round whole numbers up

to 1,000 to the nearest 10 or 100.


numbers 0–100 to the

nearest 10 or nearest 100.



nearest 10.

4.NSBT.3: Identify when

a number can be rounded

up to the nearest unit.

4.NSBT.3: Recognize a

place value unit.

4.NSBT.4: Add and subtract two-digit

whole numbers.

4.NSBT.4: Solve addition

and subtraction word

problems with numbers up

to 100.

4.NSBT.4: Add and

subtract numbers up to 100

with a two-digit number

and a multiple of 10.

4.NSBT.4: Add and

subtract two-digit whole

numbers up to 20.

4.NSBT.4: Recognize

the addition or

subtraction symbols.

4.NSBT.5: Demonstrate basic

multiplication facts of products

through 100.

4.NSBT.5: Multiply two

whole numbers using 0–10.

4.NSBT.5: Multiply two

single-digit whole numbers

using 0–5.

4.NSBT.5: Demonstrate

the concept of

multiplication.

4.NSBT.5: Recognize

multiplication factors

and products.

4.NSBT.6: Divide up to a two-digit

dividend by a one-digit divisor without

remainders using strategies based on

place value, the properties of

operations, and/or the relationship

4.NSBT.6: Solve a division

word problem using a two-

digit dividend by a one-digit

divisor.


concept of division using

manipulatives to divide into

equal groups.


components of a division

problem (i.e., What is the

dividend? What is the

4.NSBT.6: Recognize

the division sign.

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between multiplication and division

(excluding long division).

divisor? What is the

quotient?).

It Is Essential for Students to Know: Students need to recognize place value up to the thousands place and recognize the written form of

numbers. Students need to be able to add and subtract two-digit whole numbers and recognize multiplication facts.


• Read and recognize the word form of numbers through bingo game activities.

• Demonstrate solving addition, subtraction, multiplication, and division problems using preferred objects.

• Demonstrate multiplication and division facts with preferred objects displayed in arrays.


4.NSBT Round

Place value

Addition/Subtraction

Symbol

Multiply

Division/Quotient

Periods

Single-digit/two-digit

Dividend

Divisor

Divide into equal groups

Add and subtract with

numbers to 100

Multiply with whole

numbers to 5

Recognize division symbol

Build shapes with building blocks

Cut a sheet of stickers

Teach arrays with preferred objects

(egg cartons, ice cube trays, pill boxes,

paint palette, cookie trays, muffin tins,

boxes with dividers, teacher mailboxes)

Practice play-dough math

Practice menu math

Sharing – do you have enough for everyone?

Planning a party – do you have enough seating and

food for everyone?

Planning a pizza party – counting toppings

(addition/multiplication), cutting/sharing

(subtraction/division)

Breaking apart a chocolate bar

Cutting wood

Sorting supplies for activities

Asking “Do I have enough money?” for a purchase

Doubling or dividing a recipe

Purchasing tickets – if three tickets cost $5, how

much money do you need to buy three tickets?

Calculating hourly wages/piece pay

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5th Grade


SCCCR Standards: Use whole number exponents to explain: a. patterns in the number of zeroes of the product when multiplying a number by

powers of 10; b. patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10 (5.NSBT.2). Read and

write decimals in standard and expanded form. Compare two decimal numbers to the thousandths using the symbols >, =, or < (5.NSBT.3). Round

decimals to any given place value within thousandths (5.NSBT.4). Fluently multiply multi-digit whole numbers using strategies to include a

standard algorithm (5.NSBT.5). Divide up to a four-digit dividend by a two-digit divisor, using strategies based on place value, the properties of

operations, and the relationship between multiplication and division (5.NSBT.6). Add, subtract, multiply, and divide decimal numbers to

hundredths using concrete area models and drawings (5.NSBT.7).


5.NSBT.2: Use whole number exponents to

explain patterns in the number of zeroes of the

product when multiplying a number by

powers of 10.

5.NSBT.2: Identify the power

of 10, given the product.


product, given the

number 10, with an

exponent.

5.NSBT.2:

Multiply a product

of 10 by 10.

5.NSBT.2: Identify or

continue a pattern.

5.NSBT.3: Read and write decimals in

standard form. Compare two decimal numbers

to the hundredths using the symbols >, =, or

<.


decimals to the hundredths

(=, <, >). Read and write

monetary values.


decimals to the

hundredths (=, <, >).

5.NSBT.3: Identify

and define a

decimal.

5.NSBT.3: Recognize

larger, smaller, and

equal.

5.NSBT.4: Round decimals to the nearest

whole number.

5.NSBT.4: Round a decimal

to the nearest whole number.

5.NSBT.4: Round a

decimal to the nearest

whole number (limit to

decimals over 0.50).

5.NSBT.4: Identify

a decimal.

5.NSBT.4: Identify a

unit.

5.NSBT.5: Multiply a multi-digit whole

number by a one-digit whole number using

strategies to include a standard algorithm.

5.NSBT.5: Multiply by 1, 2,

3, 4, and/or 5.

5.NSBT.5: Demonstrate

the concept of

multiplication related to

repeated addition.

5.NSBT.5: Solve

repeated addition

problems.

5.NSBT.5: Identify and

represent repeated

addition with an

equation.

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5.NSBT.6: Divide up to a four-digit dividend

by a one-digit divisor, using strategies based

on place value, the properties of operations,

and the relationship between multiplication

and division.

5.NSBT.6: Divide by 1, 2, 3,

4, and/or 5.

5.NSBT.6: Apply the

relationship between

multiplication and

division.

5.NSBT.6:

Understand that

equal groups can be

represented by

division.

5.NSBT.6: Identify

equal groups.

5.NSBT.7: Add and subtract decimal

numbers to hundredths using concrete area

models and drawings.

5.NSBT.7: Add and subtract

multi-digit decimal numbers

without regrouping. Add and

subtract monetary amounts

including dollars and cents.

Students may use a model or

drawing.

5.NSBT.7: Add and

subtract monetary

amounts, including in

whole numbers (with the

$.00 included). Students

may use a model or

drawing.

5.NSBT.7: Identify

a whole number

when presented in

monetary form.

Identify a decimal

when presented in

monetary form.

5.NSBT.7: Identify

whole and part.

It Is Essential for Students to Know: Students need to be able to continue a pattern and identify equal groups. Students need to be able to

recognize multiplication facts up to 100. Students also need to be able to define decimals, compare decimals up to hundredths place, and recognize

decimals when written as money.


• Use advertisements, printed website pages, or sales flyers to demonstrate adding, subtracting, and comparing decimals.

• Use student-preferred objects to demonstrate that repeated addition is the same as a multiplication array and multiplication expression.

• Use student-preferred objects to demonstrate similarities between multiplication facts and division.


5.NSBT Decimal

Standard form

Tenths

Hundredths

Expanded form

Comparing decimals

Rounding decimals

Multiply by 10

Adding and subtracting

monetary amounts

Practice menu math


Use seed trays

Make arrays with preferred objects

Add money (coins)

Reading sale ads

Calculating prices while using coupons

Comparing prices

Sharing – do you have enough for everyone?

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Algorithm

Exponent

Unit

Equivalent

+, -, =, x, ÷

<, >

Pattern

Larger

Smaller

Equal

Whole

Part

Repeated addition

Using models

Sort money and make change using a

money tray

Play card games

Planning a party – do you have enough seating

and food for everyone?

Planning a pizza party – counting toppings

(addition/multiplication), cutting/sharing

(subtraction/division)

Breaking apart a chocolate bar

Cutting wood

Sorting supplies for activities

Asking “Do I have enough money?”

Forming relay teams

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6th Grade

Key Concept: The Number System

SCCCR Standards: Fluently divide multi-digit whole numbers using a standard algorithmic approach (6.NS.2). Fluently add, subtract, multiply

and divide multi-digit decimal numbers using a standard algorithmic approach (6.NS.3). Find common factors and multiples using two whole

numbers. a. Compute the greatest common factor (GCF) of two numbers both less than or equal to 100. b. Compute the least common multiple

(LCM) of two numbers both less than or equal to 12. c. Express sums of two whole numbers, each less than or equal to 100, using the distributive

property to factor out a common factor of the original addends (6.NS.4). Understand that the positive and negative representations of a number are

opposites in direction and value. Use integers to represent quantities in real-world situations and explain the meaning of zero in each situation

(6.NS.5). Extend the understanding of the number line to include all rational numbers and apply this concept to the coordinate plane. a. Understand

the concept of opposite numbers, including zero, and their relative locations on the number line. b. Understand that the signs of the coordinates in

ordered pairs indicate their location on an axis or in a quadrant on the coordinate plane. c. Recognize when ordered pairs are reflections of each

other on the coordinate plane across one axis, both axes, or the origin. d. Plot rational numbers on number lines and ordered pairs on coordinate

planes (6.NS.6). Understand and apply the concepts of comparing, ordering, and finding absolute value to rational numbers. a. Interpret statements

using equal to (=) and not equal to (≠) (6.NS.7a). b. Interpret statements using less than (<), greater than (>), and equal to (=) as relative locations

on the number line (6.NS.7b). c. Use concepts of equality and inequality to write and to explain real-world and mathematical situations (6.NS.7c).

d. Understand that absolute value represents a number’s distance from zero on the number line and use the absolute value of a rational number to

represent real-world situations (6.NS.7d). Investigate and translate among multiple representations of rational numbers (fractions, decimal

numbers, percentages). Fractions should be limited to those with denominators of 2, 3, 4, 5, 8, 10, and 100 (6.NS.9).


6.NS.2: Fluently divide multi-digit

whole numbers limited to four-digit

dividends and two-digit divisors

using a standard algorithmic

approach.

6.NS.2: Divide by numbers up

to and including 10.

6.NS.2: Divide by 1, 2, 3,

4, and 5.

6.NS.2: Apply the

relationship between

multiplication and

division.

6.NS.2: Demonstrate

the concept of division.

6.NS.3: Fluently add and subtract

multi-digit decimal numbers to the

hundredths place using a standard

algorithmic approach.

6.NS.3: Add and subtract

multi-digit decimal numbers

without regrouping. Add and

subtract monetary amounts

including dollars and cents;

students may use a model or

drawing.

6.NS.3: Add and subtract

monetary amounts

including in whole

numbers (with the $.00

included); students may

use a model or drawing.

6.NS.3: Identify a whole

number when presented in

monetary form. Identify a

decimal when presented in

monetary form.

6.NS.3: Identify whole

and part.

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6.NS.4: Find common factors and

multiples using two whole numbers

up to 50 for factors, and less than or

equal to 10 for multiples.

6.NS.4: Find common factors

for whole numbers up to 50

and less than or equal to 10 for

multiples.

6.NS.4: Given the factors

of two numbers, identify

the common factors (for

two whole numbers up to

50 and multiples of 5 or

10).

6.NS.4: Find the factors of

a number (limit to fact

families under 50).

6.NS.4: Identify fact

families of a number

using multiplication.

6.NS.5: Understand that the positive

and negative representations of a

number are opposites in direction

and value. Use integers to represent

quantities in real-world situations.

6.NS.5: Given a real-world

context, identify the value of

the situation which may

include negative numbers.

6.NS.5: Given a real-

world context, identify

whether the value in the

situation is positive,

negative, or zero.


world context, identify the

value of the situation

(limit to positive numbers

under 100).


world context, identify

the value of the

situation (limit to

positive numbers under

15).

6.NS.6: Plot integers on number

lines and ordered pairs on the

coordinate plane.

6.NS.6: Plot an ordered pair

on a coordinate plane.

6.NS.6: Identify an

ordered pair on a

coordinate plane.

6.NS.6: Plot a number on

a vertical or horizontal

number line.

6.NS.6: Identify a

number on a vertical or

horizontal number line.

6.NS.7a: Interpret statements using

equal to (=) and not equal to (≠).

6.NS.7a: Identify the absolute

value of a number as the

distance from zero on a

number line.

6.NS.7a: Given a real-

world or mathematical

situation, identify a

statement of equality or

inequality that describes it.

6.NS.7a: Given two points

on a number line, identify

a statement using less than

(<), greater than (>), and

equal to (=) to describe

their locations on the

number line.

6.NS.7a: Identify if two

statements are equal (=)

or not equal (≠).

6.NS.7b: Interpret statements using

less than (<), greater than (>), and

equal to (=) as relative locations on

the number line.

6.NS.7b: Identify the absolute



number line.

6.NS.7b: Given a real-





6.NS.7b: Given two points






number line.

6.NS.7b: Identify if

two statements are

equal (=) or not equal

(≠).

-12-


6.NS.7c: Use concepts of equality

and inequality to write and to explain

real-world and mathematical

situations.

6.NS.7c: Identify the absolute



number line.

6.NS.7c: Given a real-





6.NS.7c: Given two points






number line.

6.NS.7c: Identify if two

statements are equal (=)

or not equal (≠).

6.NS.7d: Understand that absolute

value represents a number’s distance

from zero on the number line and

use the absolute value of an integer

number to represent real-world

situations.

6.NS.7d: Identify the absolute



number line.

6.NS.7d: Given a real-





6.NS.7d: Given two points






number line.

6.NS.7d: Identify if

two statements are

equal (=) or not equal

(≠).

6.NS.9: Explore and translate among

multiple representations of rational

numbers (fractions, decimal

numbers, percentages). Fractions

should be limited to those with

denominators of 2, 3, 4, 5, 8, 10, and

100.

6.NS.9: Translate multiple

representations of rational


numbers, and percentages).

Fractions should be limited to

those with denominators of 2,

3, 4, 5, 8, 10, and 100.

6.NS.9: Identify multiple

representations of a

rational number.

6.NS.9: Identify the

definition of a rational

number.

6.NS.9: Identify a

whole number.

It Is Essential for Students to Know: Students need to be able to add and subtract decimals to the hundredths place. Students need to know

multiplication and division fact families. Students need to be able to recognize and compare points on a number line. Students also need to

recognize points on the first quadrant of a coordinate plane.


• Identify equality statements when given a real-world situation. For example, Mary is 12 years old, and Chris is 11 years old. Which

statement correctly compares Mary and Chris’s ages?

• Create a number line using painter’s tape on the ground and measure steps from zero in both directions to demonstrate the concept of

absolute value.

-13-

• Add and subtract monetary amounts including dollars and cents. For example, Craig has $20.45. He spends $2.65 to buy a notebook and

$1.50 on an eraser from the school store. How much money does Craig have left?

• Calculate the final price when things are on sale. For example, calculate 25% off a pair of jeans that are $25.50.


6.NS Positive

Negative

Zero

Coordinate Plane

Equality

Inequality

Rational number

LCM

GCF

Factors

Integers

Vertical

Horizontal

Not equal to

Plot

Order pair

Whole/part

Add

Subtract

Fact families

Factor

Divide by 1, 2, 3, 4

Use arrays or models for division and

multiplying and factors

Buy items in the school stores

Play “Battleship” on a coordinate plane

Use maps during a scavenger hunt

Use a thermometer to find the temperature

Use an elevator or stairs to understand positive,

negative, zero

Throw objects and compare distance

Practice number line activities (placing number

words, digits, sets on points)

Use spreadsheets.

Using maps of amusement parks, zoos, etc.

to find places

Reading thermometers to decide what

clothes to wear

Practicing banking (making deposits,

withdrawals)

Weighing grocery items

Comparing food labels

Determining price of produce based on

weight

Locating objects on shelves (coordinate

plane)

Using a balance to compare amounts

-14-

7th Grade


SCCCR Standards: Extend prior knowledge of operations with positive rational numbers to add and to subtract all rational numbers and

represent the sum or difference on a number line. a. Understand that the additive inverse of a number is its opposite and their sum is equal to zero.

b. Understand that the sum of two rational numbers (𝑝 + 𝑞) represents a distance from p on the number line equal to |q| where the direction is

indicated by the sign of q. c. Translate between the subtraction of rational numbers and addition using the additive inverse, 𝑝 – 𝑞 = 𝑝 + (−𝑞). d.

Demonstrate that the distance between two rational numbers on the number line is the absolute value of their difference. e. Apply mathematical

properties (e.g., commutative, associative, distributive, or the properties of identity and inverse elements) to add and subtract rational numbers

(7.NS.1). Extend prior knowledge of operations with positive rational numbers to multiply and to divide all rational numbers. a. Understand that

the multiplicative inverse of a number is its reciprocal and their product is equal to one. b. Understand sign rules for multiplying rational numbers.

c. Understand sign rules for dividing rational numbers and that a quotient of integers (with a non-zero divisor) is a rational number. d. Apply

mathematical properties (e.g., commutative, associative, distributive, or the properties of identity and inverse elements) to multiply and divide

rational numbers. e. Understand that some rational numbers can be written as integers and all rational numbers can be written as fractions or

decimal numbers that terminate or repeat (7.NS.2). Apply the concepts of all four operations with rational numbers to solve real-world and

mathematical problems (7.NS.3). Understand and apply the concepts of comparing and ordering to rational numbers. a. Interpret statements using

less than (<), greater than (>), less than or equal to (≤), greater than or equal to (≥), and equal to (=) as relative locations on the number line. b. Use

concepts of equality and inequality to write and explain real-world and mathematical situations (7.NS.4). Extend prior knowledge to translate

among multiple representations of rational numbers (fractions, decimal numbers, percentages). Exclude the conversion of repeating decimal

numbers to fractions (7.NS.5).


7.NS.1: Extend prior knowledge

of operations with positive

rational numbers to add and to

subtract all rational numbers and

represent the sum or difference on

a number line.

7.NS.1: Extend prior

knowledge of operations with

positive rational numbers to add

and subtract all rational

numbers and represent the sum

or difference on a number line.


knowledge of operations

with positive rational

numbers to add and subtract

all rational numbers.

7.NS.1: Convert a whole

number into a fraction.


number or a fraction.


of operations with positive

rational numbers to multiply and

divide all rational numbers.


knowledge of operations with

positive rational numbers to

multiply and divide all rational

numbers and represent the

result on a number line.


knowledge of operations

with positive rational

numbers to multiply and

divide all rational numbers.

7.NS.2: Convert a whole

number into a fraction.


number or a fraction.

-15-


7.NS.3: Apply the concepts of all

four operations with positive

rational numbers to solve one-

step, real-world and mathematical

problems.

7.NS.3: Apply the concepts of

all four operations with positive

rational numbers to solve two-

step, real-world and

mathematical problems.

7.NS.3: Apply the concepts

of all four operations with

positive rational numbers to

solve one-step, real-world

and mathematical problems.

7.NS.3: Apply the

concepts of the operations

of multiplication and

division with positive

rational numbers to solve

one-step, real-world and


7.NS.3: Apply the

concepts of the

operations of addition

and subtraction with

positive rational

numbers to solve one-

step, real-world and


7.NS.4: Understand and apply the

concepts of comparing and

ordering rational numbers on a

number line. Interpret statements

using less than (<), greater than

(>), less than or equal to (≤),

greater than or equal to (≥), and

equal to (=) as relative locations

on the number line.

7.NS.4: Understand and apply

the concepts of comparing and

ordering rational numbers on a

number line. Interpret

statements using less than (<),

greater than (>), less than or

equal to (≤), greater than or

equal to (≥), and equal to (=) as

relative locations on the number

line.

7.NS.4: Understand and

apply the concepts of

comparing and ordering

rational numbers on a


statements using less than


equal to (=) as relative

locations on the number line.




whole numbers on a


statements using less than


equal to (=) as relative

locations on the number

line.




whole numbers on the

number line.


to translate among multiple



numbers). Exclude the conversion

of repeating decimal numbers to

fractions.


knowledge to translate among

multiple representations of

rational numbers (fractions,

decimal numbers). Exclude the

conversion of repeating decimal

numbers to fractions.


knowledge to translate

among fractions and decimal

numbers up to 100. Exclude

the conversion of repeating

decimal numbers to

fractions.

7.NS.5: Identify

equivalent fractions and

decimal numbers up to

100. Exclude the

conversion of repeating

decimal numbers to

fractions.

7.NS.5: Identify same

and different fractions or

decimal numbers from

pictorial representations.

It Is Essential for Students to Know: Students need to be able to differentiate between a whole number, a fraction, and a decimal. Students need

to be able to order whole numbers, fractions, and decimals on a number line. Students need to be able to convert a fraction (with single-digit

numerators and a denominator of 10) to the equivalent decimal. Students also need to be able to apply all four operations to solve problems with

decimals in the tenths place.

-16-


• Using a scale and some fruits and vegetables, create a store scenario and have the students calculate the total cost of the fruits and

vegetables per pound by weighing the fruits and vegetables and then multiplying by the price per pound.

• Have students calculate the price of an item that is discounted to practice solving real-world problems involving all rational numbers.


7.NS Order of operations

Repeating decimals

Signs (<, >, +, =, -)

Solve

Number line

Fraction

Decimal

Add and subtract

Multiply and divide

Convert whole numbers

into fractions

Convert decimals into

fractions up to 100

Add and subtract with models

Multiply and divide with models

Shopping, budgeting

Cooking or baking using recipes

Taking inventory to determine what you have and

what you need

Feeding pet, watering plant using measuring cups

(combinations of cups)

-17-

8th Grade


SCCCR Standards: Explore the real number system and its appropriate usage in real-world situations. a. Recognize the differences between

rational and irrational numbers. b. Understand that all real numbers have a decimal expansion. c. Model the hierarchy of the real number system,

including natural, whole, integer, rational, and irrational numbers (8.NS.1). Estimate and compare the value of irrational numbers by plotting them

on a number line (8.NS.2). Extend prior knowledge to translate among multiple representations of rational numbers (fractions, decimal numbers,

percentages). Include the conversion of repeating decimal numbers to fractions (8.NS.3).


8.NS.1: Recognize the

differences between rational and

irrational numbers. Understand

that all real numbers have a

decimal expansion.


differences between rational and

irrational numbers. Understand

that all real numbers have a

decimal expansion.


differences between

rational and irrational

numbers.

8.NS.1: Identify rational

numbers.

8.NS.1: Identify whole

numbers and fractions.

8.NS.2: Estimate the value of

irrational and rational numbers

by plotting them on a number

line.

8.NS.2: Estimate the value of

irrational and rational numbers

by plotting them on a number

line.

8.NS.2: Plot irrational and

rational numbers on a

number line.

8.NS.2: Plot rational

numbers on a number line.

8.NS.2: Plot whole

numbers and fractions

on a number line.


to translate among multiple



numbers, percentages). Exclude

the conversion of repeating

decimal numbers to fractions.

8.NS.3: Translate among


rational numbers (fractions,

decimal numbers, percentages).

Exclude the conversion of

repeating decimal numbers to

fractions.

8.NS.3: Translate among


rational numbers (fractions

and decimal numbers).

Exclude the conversion of

repeating decimal numbers

to fractions.

8.NS.3: Translate fractions

with the denominators 2, 4,

6, 8, and 10 into decimals.

8.NS.3: Identify

fractions.

It Is Essential for Students to Know: Students need to be able to identify rational numbers and plot fractions on a number line. Students need to

be able to convert fractions with denominators of 2, 4, 6, and 8 to equivalent decimals.


• Students can practice translating among multiple representations of rational numbers by doing everyday things like making a monthly

lunch budget and calculating a percentage of their monthly allowance that they want to save.

-18-


8.NS Percentage

Rational

Irrational

Recognize difference between

rational and irrational numbers

Plot rational and irrational

numbers

Use painter’s tape on the floor or wall to

practice number line activities such as

whole numbers and fractions

Use a hundred chart to illustrate percentage

Creating pie chart of data collected in class (eye color,

hair color, etc.)

Practicing money activities (quarters, parts of dollar)

Comparing calories of various foods

Calculating fractions of time

-19-

11th Grade

Key Concept: Arithmetic with Polynomials and Rational Expressions

SCCCR Standards: Add, subtract, and multiply polynomials and understand that polynomials are closed under these operations (A1.AAPR.1).


A1.AAPR.1: Add and

subtract polynomials (limit

to linear).

A1.AAPR.1: Add and

subtract like terms with

simple expressions.

A1.AAPR.1: Add and

subtract like terms that may

include a variable.

A1.AAPR.1: Add and

subtract like terms (limited

to constants).

A1.AAPR.1: Add two like

terms (limited to constants).

It Is Essential for Students to Know: Students need to be able to add and subtract like terms.


• The students can practice adding and subtracting polynomials by determining which objects should be grouped together. For example,

comedy movies should be grouped with other comedy movies, action movies with other action movies, and drama movies with other

drama movies.


11.AAPR Variable

Term

Like terms

Add and subtract

like terms

Use manipulatives to group and

add/subtract

Sorting laundry – if two people add their amounts together, how many

shirts and pants do they have together?

Creating job-related materials

Using any preferred objects to add and subtract like terms

Calculating amounts using money

-20-

11th Grade

Key Concept: Creating Equations

SCCCR Standards: Create and solve equations and inequalities in one variable that model real-world problems involving linear, quadratic,

simple rational, and exponential relationships. Interpret the solutions and determine whether they are reasonable (A1.ACE.1).


A1.ACE.1: Solve linear

equations with one variable.

A1.ACE.1: Solve a linear

equation with one variable.

A1.ACE.1: Solve a linear

equation with one variable

with one step (addition,

subtraction).

A1.ACE.1: Solve an

equation written with the

variable isolated on the left

side.

A1.ACE.1: Given a linear

equation, identify parts of

the equation (variable,

constant, and coefficient).

It Is Essential for Students to Know: Students need to be able to identify a variable, coefficient, and constant in a linear equation. Students need

to be able to solve one-step equations with the variable isolated to one side (i.e., x = 2 * 4; x = 8 + 9).


• Solve simple linear equations with one variable. For example, if John earns $10 per hour, how many hours should he work to earn $100?


11.ACE

Constant

Variable

Coefficient

Term

Expression

Solve equation with one

variable with one step

Identify parts of equation

Model real-life situations

Example: Give a student $5 for the week and then give a

quarter for every day of attendance. If the student comes to

school for three days, how much money would he have?

Calculating amounts using savings

accounts

Calculating amounts using piggy banks

(with a starting amount as constant)

-21-

11th Grade

Key Concept: Structure and Expressions

SCCCR Standards: Interpret the meanings of coefficients, factors, terms, and expressions based on their real-world contexts. Interpret

complicated expressions as being composed of simpler expressions. (A1.ASE.1).


A1.ASE.1: Determine the

meanings of coefficients,

variables, terms, and

expressions based on their

real-world contexts.

A1.ASE.1: Determine the

meanings of coefficients,

variables, terms, and

expressions based on their

real-world contexts.

A1.ASE.1: Given a real-

world context and a variable,

determine what the variable

represents.

A1.ASE.1: Identify the

meaning of the unknown in a

real-world context.

A1.ASE.1: Given an

expression, identify a part

(variable, term).

It Is Essential for Students to Know: Students need to be able to differentiate between an equation and an expression. Students need to be able to

identify the unknown.


• Create a real-world context and expression, and determine the meaning of each part of the expression. For example, Jim is using the

expression 5x + 20 to calculate his savings based on his weekly allowance. What does each part of the expression represent? The slope,

which represents Jim’s weekly allowance, is $5. The variable represents the number of weeks, and the y-intercept represents the amount of

money that Jim has already saved.


11.ASE Constant

Variable

Coefficient

Term

Expression

Solve equation with one

variable with one step

Identify parts of

equations

Model real-life situations

Example: Give a student $5 for the week and then give a

quarter for every day of attendance. If the student comes to

school for three days, how much money would he have?

Calculating amounts using savings

accounts

Calculating amounts using piggy banks

(with a starting amount as constant)

-22-

11th Grade

Key Concept: Reasoning with Equations and Inequalities

SCCCR Standards: Understand and justify that the steps taken when solving simple equations in one variable create new equations that have the

same solution as the original (A1.AREI.1). Solve systems of linear equations algebraically and graphically focusing on pairs of linear equations in

two variables. (Note: AREI.6a and 6b are not Graduation Standards.) a. Solve systems of linear equations using the substitution method. b. Solve

systems of linear equations using linear combination (A1.AREI.6). Explain that the graph of an equation in two variables is the set of all its

solutions plotted in the coordinate plane (A1.AREI.10). Graph the solutions to a linear inequality in two variables (A1.AREI.12).


A1.AREI.1: Understand

that the steps taken when

solving simple equations

in one variable create new

equations that have the

same solution as the

original.

A1.AREI.1: Understand that

the steps taken when solving

simple equations in one

variable create new equations

that have the same solution as

the original.

A1.AREI.1: Identify the

possible next step in solving an

equation.


possible first step in solving

an equation.

A1.AREI.1: Determine if

two expressions are equal

(2 x 3, 3 x 2,

commutative property,

associative property).

A1.AREI.6: Solve

systems of linear equations

graphically focusing on

pairs of linear equations in

two variables.

A1.AREI.6: Solve systems of

linear equations, graphically

focusing on pairs of linear

equations in two variables.

A1.AREI.6: Given the graph of

one equation and a simple

equation, identify the graph that

models the solution.


point at which a given set of

lines intersect.

A1.AREI.6: Identify a

set of lines that intersect.

A1.AREI.10: Understand

that the graph of an

equation in two variables

is the set of all its

solutions plotted in the

coordinate plane.

A1.AREI.10: Understand that

the graph of an equation in two

variables is the set of all its


coordinate plane.

A1.AREI.10: Identify the graph

of an equation in two variables

that models the set of all its


coordinate plane (limit to the

first quadrant).

A1.AREI.10: Identify an

equation in the first

quadrant.


point in the first quadrant.

-23-


A1.AREI.12: Graph the

solutions to a simple

inequality with one

variable on a number line.

A1.AREI.12: Identify a simple

inequality with one variable on

the number line (include

greater than or equal to).


inequality on the number line

(where the solution is a positive

number but the number line may

include negative numbers).


inequality on the number

line (limit to greater than and

less than, limit to positive

number line starting at zero).


point on the number line.

It Is Essential for Students to Know: Students need to be able to differentiate between an equation and an inequality. Students need to be able to

identify an inequality on a number line (i.e., x > 4). Students also need to be able to recognize the first step to solve an equation.


• To solve real-world inequality problems, students must determine if they have enough money to make a certain purchase. For example,

Jim gets $5 per week for his allowance. He already has $20 saved. How many more weeks will Jim need to save his allowance to have

$60? 60 = 5x + 20, solve for x, which is the number of weeks, x = 8. Jim needs to save his allowance for 8 more weeks to reach his goal.


11.AREI Graph

Equation

Quadrant

Intersect

Commutative

Associative

Compare expressions

Determine that

expressions are equal

Intersecting lines

Identify point of

intersection

Compare similar groups of objects that are in containers

Compare arrays of pictures (e.g., 2x3 is the same as 3x2 – same

amount of objects)

Compare steps taken (e.g., one student takes 6 steps and then 4;

the other student takes 4 steps and then 6)

Have students dip the wheels of toy cars in paint and “drive”

them on chart paper to illustrate intersecting lines

Place sticky notes or ink with a dot stamper on chart paper with

X and Y axes, and then plot the points

Cooking recipes to compare amounts

Using directions to and from places to

illustrate the commutative property

Using maps to understand intersections

Comparing amounts using objects on

shelves

Using shoe storage containers to

compare groups of objects

-24-

Number Sense – Fractions

Number Sense and Operations –

Fractions

Ratios and Proportional Relationships

3rd Grade 4th Grade 5th Grade 6th Grade 7th Grade

3.NSF 4.NSF 5.NSF 6.RP 7.RP

-25-

3rd Grade

Key Concept: Number Sense – Fractions

SCCCR Standards: Develop an understanding of fractions (i.e., denominators 2, 3, 4, 6, 8, 10) as numbers. a. A fraction 1

𝑏 (called a unit

fraction) is the quantity formed by one part when a whole is partitioned into 𝑏 equal parts; b. A fraction 𝑎

𝑏 is the quantity formed by 𝑎 parts of

size 1

𝑏; c. A fraction is a number that can be represented on a number line based on counts of a unit fraction; d. A fraction can be represented

using set, area, and linear models (3.NSF.1) Explain fraction equivalence (i.e., denominators 2, 3, 4, 6, 8, 10) by demonstrating an

understanding that: a. two fractions are equal if they are the same size, based on the same whole, or at the same point on a number line; b.

fraction equivalence can be represented using set, area, and linear models; c. whole numbers can be written as fractions (e.g., 4 = 4/1 and 1=

4/4); d. fractions with the same numerator or same denominator can be compared by reasoning about their size based on the same whole

(3.NSF.2).


3.NSF.1: Develop an

understanding of fractions (i.e.,

denominators 2, 3, 4, 6, 8, 10) as

numbers.

3.NSF.1: Match fractions to

their models (i.e.,

denominators to 2, 3, 4, 6, 8,

10).

3.NSF.1: Identity a part of a

whole using fraction models.

3.NSF.1: Identify

parts of a fraction

(denominator and

numerator).

3.NSF.1: Identify a fraction

from a list of numbers (i.e.,

3 choices, 2 whole

numbers, and 1 fraction).

3.NSF.2: Explain fraction

equivalence (i.e., denominators 2,

3, 4, 6, 8, 10) by demonstrating an

understanding that two fractions

are equal if they are the same size,

based on the same whole, or at the

same point on a number line.

3.NSF.2: Identify equal

fractions that are the same

size but have different

fraction sizes using models

and numbers to show

fractions using the

denominators 2, 3, 4, 6, 8, 10.

3.NSF.2: Recognize that two

fractions are equal if they are

the same using different

numbers in the denominators

(using pictures limiting the

denominators to 2, 3, and 4).

3.NSF.2: Identify

fraction models that

are divided into the

same number of parts.

3.NSF.2: Identify shapes

divided into equal parts.

It Is Essential for Students to Know: Students need to identify parts of a fraction and recognize when a fraction model is divided into equal

parts. Students can share a bar of chocolate equally between two people to practice being able to recognize equal parts.


• Use pizza or square crackers to practice fractions. Demonstrate breaking or cutting the item into equal parts such as halves or fourths.

-26-

• Demonstrate the denominator and numerator; the total number of parts of the cracker or slices of pizza (denominator) and the number of

parts remaining, eaten, or shared (numerator).


3NSF Numerator

Denominator

Fraction

Distinguish between fractions

and whole numbers

Identify parts of a fraction

Compare equal fractions

Color or cut paper plates into fractions

Practice menu math


Use seed trays

Use arrays with preferred objects

Add and subtract money (coins)

Use a money tray to sort money and make change

Play card games

Hosting a fraction picnic

Comparing groups of boys or girls to the

whole group (at recess, at lunch)

Sorting parts/whole for everyday objects

Folding towels into ½, ¼, etc.

-27-

4th Grade

Key Concept: Number Sense and Operations – Fractions

SCCCR Standards: Explain why a fraction (i.e., denominators 2, 3, 4, 5, 6, 8, 10, 12, 25, 100), 𝑎

𝑏 , is equivalent to a fraction,

𝑛 × 𝑎

𝑛 × 𝑏, by using visual

fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this

principle to recognize and generate equivalent fractions (4.NSF.1). Compare two given fractions (i.e., denominators 2, 3, 4, 5, 6, 8, 10, 12, 25,

100) by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1

2 and represent the comparison using the

symbols >, =, or < (4.NSF.2). Develop an understanding of addition and subtraction of fractions (i.e., denominators 2, 3, 4, 5, 6, 8, 10, 12, 25, 100)

based on unit fractions. a. Compose and decompose a fraction in more than one way, recording each composition and decomposition as an

addition or subtraction equation; b. Add and subtract mixed numbers with like denominators; c. Solve real-world problems involving addition and

subtraction of fractions referring to the same whole and having like denominators (4.NSF.3). Express a fraction with a denominator of 10 as an

equivalent fraction with a denominator of 100 and use this technique to add two fractions with respective denominators of 10 and 100 (4.NSF.5).

Compare and order decimal numbers to hundredths, and justify using concrete and visual models (4.NSF.7).


4.NSF.1: Using visual

fraction models, recognize

equivalent fractions (i.e.,

denominators 2, 3, 4, 5, 6, 8,

10, 12, 25, 100).

4.NSF.1: Use same-size

models that have been

divided differently to solve

equivalent fraction problems

(i.e., denominators 2, 3, 4, 5,

6, 8, 10, 12, 25, 100).

4.NSF.1: Use same-size models

that have been divided

differently to solve equivalent

fraction problems (i.e.,

denominators 2, 3, 4, 5, 6, 8, 10,

12, and 25).

4.NSF.1: Identify models that

have been divided in half or

equal parts (i.e., denominators

limited to 2–10).

4.NSF.1: Identify a

fraction from a whole

number.

4.NSF.2: Compare two given

fractions (i.e., denominators

2, 3, 4, 5, 6, 8, 10, 12, 25,

100) with common

denominators using the

symbols >, =, or <.

4.NSF.2: Compare two

fractions with like

denominators (=, <, >).

4.NSF.2: Compare two fractions

with like denominators using a

pictorial model (=, <, >).

4.NSF.2: Demonstrate the

concepts of greater than and

less than using models/groups

of manipulatives to choose

which ones have more, less,

or equal amounts (<, >, =).

4.NSF.2: Recognize

greater than and less

than signs.

-28-


4.NSF.3: Develop an

understanding of addition and

subtraction of fractions with a

common denominator (i.e.,

denominators 2, 3, 4, 5, 6, 8,

10, 12, 25, 100) based on unit

fractions. a. Develop an

understanding of mixed

numbers.

4.NSF.3: Add and subtract

fractions with common

denominators (denominators

limited to 2, 3, 4, 5, 6, 8, 10,

12, 25, 100). Develop an

understanding of mixed

numbers.

4.NSF.3: Using simple fractions

with common denominators

(limited between the numbers 2–

9), add or subtract the

numerators in the fraction.

4.NSF.3: Identify numerators

and denominators in

fractions.

4.NSF.3: Identify

common denominators

in fractions.

4.NSF.5: Express a fraction

with a denominator of 10 as

an equivalent fraction with a

denominator of 100 and use

this technique to add two

fractions with respective

denominators of 10 and 100.

4.NSF.5: Identify fractions

with the denominators of 10

and 100 when comparing

two fractions.

4.NSF.5: Identify when two

fractions are equivalent with the

denominators of 10 and 100.

4.NSF.5: Given a model,

recognize tenths/hundredths

using a model.

4.NSF.5: Recognize

part of a whole using

models.

4.NSF.6: Write a fraction

with a denominator of 10 or

100 using decimal notation.

4.NSF.6: Write a fraction

with denominator of 10 or

100 as a decimal.

4.NSF.6: Write a fraction from a

decimal notation with the

denominator of 10.


function of a decimal point as

it represents a fraction using a

place value chart.

4.NSF.6: Identify

where a decimal point

is on the place value

chart. Identify the

tenths and hundredths

place on the value

chart.

4.NSF.7: Compare decimal

numbers to hundredths using

visual models.

4.NSF.7: Compare decimal

numbers to hundredths

place.

4.NSF.7: Using visual models,

compare decimals to hundredths

place.


function of a decimal point as

it represents a fraction using a

place value chart.

4.NSF.7: Recognize

greater than, less than,

and equal signs.

It Is Essential for Students to Know: Students need to be able to identify a fraction of a whole and compare fractions using models. Students

also need to recognize decimals, understand the place value of decimals using models, and compare decimals using symbols.

-29-


• Demonstrate adding and subtracting fractions by sharing objects that can be divided, such as a piece of paper or large crackers.

• Demonstrate decimals using a hundred chart with pennies and dimes. Connect the decimals shown with the coins to the written decimal

number.

• Compare decimals using a hundred chart and two sets of pennies and dimes (e.g., 2 dimes and 1 penny is greater than 4 pennies).


4NSF Mixed number

Tenths

Hundredths

Comparing fractions –

greater than, less than,

and equal to

Fold or cut objects (construction paper, newspaper)

into equal parts

Tabulate voting results to find votes of groups

compared to total of votes

Compare attributes, clothing of students, etc. to

understand fractions represented and compare groups

Use tangrams to make a whole

Using shirts, socks, etc. with fractions

written on them to compare and order

fractions

Using pizza toppings representing fractions

to compare amounts to the whole

Practicing measurement using cups and

spoons

-30-

5th Grade

Key Concept: Number Sense and Operations – Fractions

SCCCR Standards: Add and subtract fractions with unlike denominators (including mixed numbers) using a variety of models, including an area

model and number line (5.NSF.1). Extend the concept of multiplication to multiply a fraction or whole number by a fraction. a. Recognize the

relationship between multiplying fractions and finding the areas of rectangles with fractional side lengths; b. Interpret multiplication of a fraction

by a whole number and a whole number by a fraction and compute the product; c. Interpret multiplication in which both factors are fractions less

than one and compute the product (5.NSF.4).


5.NSF.1: Add and subtract

fractions with unlike

denominators using a variety

of models, including an area

model and number line.

5.NSF.1: Add or subtract

fractions with unlike

denominators (limit to

halves, thirds, fourths, sixths,

and use visual models).

5.NSF.1: Add or subtract

fractions with like

denominators using models

(limit to halves, thirds,

fourths, sixths, and eighths).

5.NSF.1: Create a model of

a fraction (partition and

shade).

5.NSF.1: Partition any shape

into equal parts.

5.NSF.4: Multiply a whole

number by a fraction.


number by a fraction.


number by a fraction (limit

to compatible numbers that

result in a whole number

product).

5.NSF.4: Understand the

relationship between adding

and multiplying the fraction.

5.NSF.4: Add two of the

same fraction (limit to

halves, thirds, fourths).

It Is Essential for Students to Know: Students need to be able to divide a whole into equal parts. Students need to be able to add, subtract, and

multiply fractions using models.


• Have students add and subtract fractions with like denominators by using a large measuring cup and an individual measuring spoon.

-31-


5NSF Add

Subtract

Fractions

Partition

Denominator

Numerator

Halves

Thirds

Fourths

Sixths

Eights

Shade

Compatible

Adding fractions

Subtracting fractions

Multiplying fractions with

whole numbers

Practice with fractions using concrete models;

example: 5 x ½ – give students five halves of an

apple and have them put the halves together to

determine how many total apples there are (2 ½)

Doubling or halving a recipe

-32-

6th Grade

Key Concept: Ratios and Proportional Relationships

SCCCR Standards: Interpret the concept of a ratio as the relationship between two quantities, including part-to-part and part-to-whole (6.RP.1).


6.RP.1: Understand the

concept of a ratio as the

relationship between two

quantities, including part-to-

part and part-to-whole.




quantities, including part-to-

part and part-to-whole.




quantities (limit to part-to-

whole).

6.RP.1: Identify a ratio that

matches a context.

6.RP.1: Identify a ratio.

It Is Essential for Students to Know: Students need to be able to recognize ratios.


• Determine solutions to real-world problems. For example, the recipe for 12 muffins uses 2 eggs. How many eggs are needed to make 36

muffins?


6RP Ratio

Context

Part

Whole

Identify ratio

Understand part-to-whole

relationships

Color or cut paper plates into fractions

Practice menu math


Use seed trays

Use arrays with preferred objects

Add and subtract money (coins)

Use a money tray to sort money and make change

Hosting a fraction picnic

Comparing groups of boys or girls to the

whole group (at recess, at lunch)

Sorting parts/whole for everyday objects

Folding towels into ½, ¼, etc.

-33-

7th Grade

Key Concept: Ratios and Proportional Relationships

SCCCR Standards: Identify and model proportional relationships given multiple representations, including tables, graphs, equations, diagrams,

verbal descriptions, and real-world situations (7.RP.2). Determine when two quantities are in a proportional relationship (7.RP.2a). Investigate the

graph of a proportional relationship and explain the meaning of specific points (e.g., origin, unit rate) in the context of the situation (7.RP.2e).

Solve real-world and mathematical problems involving ratios and percentages using proportional reasoning (e.g., multi-step dimensional analysis,

percent increase/decrease, tax) (7.RP.3).


7.RP.2: Identify proportional

relationships given multiple

representations, including

tables, graphs, and real-world

situations. a. Determine when

two quantities are in a

proportional relationship.

e. Identify the graph of a

proportional relationship in a

real-world situation.



representations, including tables,

graphs, and real-world



proportional relationship. e.

Identify the graph of a

proportional relationship in a

real-world situation.



representations, including

tables, graphs, and real-world



proportional relationship.

7.RP.2: Identify

proportional relationships

in real-world situations.

7.RP.2: Identify

equivalent relationships

in real-world situations.

7.RP.3: Solve real-world and

mathematical problems

involving ratios and

percentages.

7.RP.3: Solve real-world and

mathematical problems

involving ratios and percentages.

7.RP.3: Solve real-world

problems involving ratios and

percentages.

7.RP.3: Solve real-world

problems involving

percentages.

7.RP.3: Understand part

and whole relationships.

It Is Essential for Students to Know: Students need to be able to recognize part-to-whole relationships. Students need to be able to recognize

ratios in real-world settings, such as what proportion of the class is made up of boys or what proportion is made up of girls.


• The students can collect data on how many boys and girls are in the classroom and discuss the proportion of boys to the whole class and

the proportion of girls to the whole class. This can be extended to collecting data and identifying proportions with other objects and

resources in the classroom.

-34-


7RP Proportional

Ratio

Percentages

Unit rate

Solve problems

with ratio

percentages

(equivalent

fractions)

Fold or cut objects (construction paper, newspaper) into equal parts

Tabulate voting results to find groups compared to whole)

Compare attributes, clothing of students, etc. to understand

fractions represented and compare groups

Use tangrams to make a whole

Calculating mileage and miles/hour

Calculating distances in inches and feet

Taking a medication a specified

number of times per day

Calculating an hourly rate of pay

-35-

Algebraic Thinking and Operations

Expressions, Equations, and Inequalities

3rd Grade 4th Grade 5th Grade 6th Grade 7th Grade 8th Grade

3.ATO 4.ATO 5.ATO 6.EE 7.EE 8.EE

-36-

3rd Grade

Key Concept: Algebraic Thinking and Operations

SCCCR Standards: Use concrete objects, drawings and symbols to represent multiplication facts of two single-digit whole numbers and

explain the relationship between the factors (i.e., 0–10) and the product (3.ATO.1). Solve real-world problems involving equal groups,

area/array, and number line models using basic multiplication and related division facts. Represent the problem situation using an equation

with a symbol for the unknown (3.ATO.3). Determine the unknown whole number in a multiplication or division equation relating three

whole numbers when the unknown is a missing factor, product, dividend, divisor, or quotient (3.ATO.4). Apply properties of operations

(i.e., Commutative Property of Multiplication, Associative Property of Multiplication, Distributive Property) as strategies to multiply and

divide and explain the reasoning (3.ATO.5). Demonstrate fluency with basic multiplication and related division facts of products and

dividends through 100 (3.ATO.7). Solve two-step real-world problems using addition, subtraction, multiplication, and division of whole

numbers and having whole number answers. Represent these problems using equations with a letter for the unknown quantity (3.ATO.8).

Identify a rule for an arithmetic pattern (e.g., patterns in the addition table or multiplication table) (3.ATO.9).


3.ATO.1: Use concrete objects,

drawings, and symbols to represent

multiplication facts of two single-

digit whole numbers (i.e., 0–5).

3.ATO.1: Multiply two

single-digit whole numbers

using 0–5.

3.ATO.1: Demonstrate the

concept of multiplication

using the multiplication sign

and numbers (limited to

numbers 0–3).



by using the repeated

addition strategy (limited

to numbers 0–2).

3.ATO.1: Identify the

multiplication symbol.

3.ATO.3: Solve real-world problems

involving equal groups, area/array,

and number line models using basic

multiplication (i.e., 0–5).

3.ATO.3: Solve a real-world

problem using basic

multiplication with equal

groups, arrays, and/or the

number line.

3.ATO.3: Apply the concept

of multiplying using equal

groups by solving a simple

word problem (limited to

numbers 0–5).

3.ATO.3: Match a basic

multiplication expression

with its model.

3.ATO.3: Recognize a

group, an array, and a

number line using

models or pictures.

-37-


3.ATO.4: Determine the unknown

whole number in a multiplication

equation relating three whole

numbers when the unknown is a

missing factor or product.

3.ATO.4: Determine the

unknown whole number in a

multiplication equation by

selecting the missing factor

and product from a set of

whole numbers (limited to

numbers 0–5).


unknown whole number in a

multiplication equation by

selecting the missing factor

from a set of whole numbers

(one missing factor between

the numbers 0 and 5).


unknown whole number in

a multiplication equation

by selecting the missing

product from a set of

whole numbers (limited to

numbers 0–5).


key terms,

factor/product, in a

multiplication equation.

3.ATO.5: Apply the Commutative

Property of Multiplication.

3.ATO.5: Demonstrate

understanding of the concept

by filling in the missing

factors in a commutative

property equation (filling in

one missing factor from both

sides).

3.ATO.5: Match equivalent

multiplication expressions

using models.

3.ATO.5: Match a basic

multiplication expression

with its model.

3.ATO.5: Identify

multiplication

problems.

3.ATO.7: Demonstrate basic

multiplication facts of products

through 25.

3.ATO.7: Demonstrate basic

multiplication facts of

products through 25.


concept of multiplication by

matching pictures of

multiplication to the correct

multiplication equation

(limited to factors between 0

and 5).



by using pictures of group

members being distributed

as a set number of items.

3.ATO.7: Recognize

basic multiplication sets

(limited to the multiples

of 0, 1, and 2).

3.ATO.8: Solve one-step, real-world

problems using addition and

subtraction of whole numbers and

having whole number answers.

3.ATO.8: Solve addition or

subtraction word problems

(limited to products up to

10).


unknown in an addition or

subtraction equation.

3.ATO.8: Demonstrate

addition or subtraction

problems using

manipulatives.

3.ATO.8: Recognize

one-step equations.

3.ATO.9: Identify a rule for an

arithmetic pattern limited to

multiples of 1, 2, 5, 10, and 25, up to

100.

3.ATO.9: Identify a rule for

an arithmetic pattern limited

to multiples of 1, 2, 5, 10,

and 25, up to 100.

3.ATO.9: Identify a rule for

an arithmetic pattern limited

to multiples of 1, 2, 5, and

10.

3.ATO.9: Count by 10. 3.ATO.9: Count by 1,

2, and 5.

-38-

It Is Essential for Students to Know: Students need to be able to count by multiples and recognize number patterns. Students need to also

recognize visual models of expressions (e.g., 2 rows of 3 apples is the same as 2 x 3).


• The teacher can use real objects to show 3 groups of 2, which demonstrates the multiplication expression “3 x 2.” The students can match

or name the multiplication expression that is being demonstrated and find the solution. For example, there are 3 baskets and there are 2

apples in each basket. This shows 3 x 2, so how many apples are there in all?

• Using a hundred chart and preferred objects, the teacher can demonstrate counting multiples of 2, 5, and 10.


3ATO Multiplication

Equal

Array

Factors

Expressions

Word problems

Number line

Patterns

Multiply whole numbers

Determine unknowns

Identify the multiplication sign

Count by 1, 2, 5, and 10

Solve addition/subtraction story

problems with missing addend

Practice skip counting

Using preferred objects, create addition and

subtraction stories

Use a hundred chart to color in patterns

Assign class jobs to students (water plants

every 5th day)

Create concrete models of arrays using muffin

tins, beads on pipe cleaners, blocks on wall,

etc. and match to written expression

Lacing – counting by multiples (2, 5, 10)

Ordering combo meals at restaurants – 2

combo meals equal how many of each

item in each combo meal?

Comparing prices (e.g., 2 for $2,

3 for $5; which is the better price?)

-39-

4th Grade


SCCCR Standards: Solve real-world problems using multiplication (product unknown) and division (group size unknown, number of groups

unknown) (4.ATO.2). Recognize that a whole number is a multiple of each of its factors. Find all factors for a whole number in the range 1–100

and determine whether the whole number is prime or composite (4.ATO.4). Generate a number or shape pattern that follows a given rule and

determine a term that appears later in the sequence (4.ATO.5).


4.ATO.2: Solve one-step,

real-world problems using

basic multiplication (0–10)

or division (with no

remainders).

4.ATO.2: Solve one-step

multiplication or division

word problems.


unknown in a multiplication

or division equation.


concepts of multiplication

and division.


components of a

multiplication problem.

4.ATO.4: Find all factor

pairs for whole numbers 1–

24.

4.ATO.4: Identify factors

for whole numbers 1–24.





4.ATO.4: Recognize what a

factor pair is for a whole

number.

4.ATO.5: Given the rule for

a pattern, determine the next

term in the sequence/pattern.

4.ATO.5: Given the rule,

determine the next term in a

number pattern or sequence.

4.ATO.5: Given the rule,

determine the next term in a

picture pattern or sequence.

4.ATO.5: Identify symbolic,

repeating, and pictorial

patterns.

4.ATO.5: Recognize

patterns.

It Is Essential for Students to Know: Students need to be able to recognize symbol and picture patterns. Students need to also recognize

multiplication facts for numbers 1–10 to solve multiplication and division problems.

-40-


• Use a rug with a pattern or another familiar object with a pattern, and have the student identify the pattern shown on the object.

• Use student-preferred objects and create real-life word problems demonstrating multiplication facts for numbers 1–10.

• Show the student a multiplication fact they know using objects and the written fact (e.g., 2 x 3 = 6). Connect how the multiplication fact

helps solve the related division problem (6 / 2 = 3 or 6 / 3 = 2).


4ATO Multiplication

Equal

Array

Factors

Expressions

Word problems

Number line

Patterns

Division

Sequence

Multiply whole numbers

Determine unknowns

Identify multiplication sign

Count by 1, 2, 5, and 10

Solve addition/subtraction

story problems with

missing addend

Find next number in a

sequence or picture pattern

Practice skip counting

Use preferred objects to create addition and subtraction

stories

Use a hundred chart to fill in or color patterns

Assign class jobs to students (water plants every 5th day)

Use concrete models of arrays such as muffin tins,

beads on pipe cleaners, blocks on wall, etc. and match

to written expression

Use pattern blocks or containers

Use tally marks to count by 5

Making jewelry to create

patterns (use beads or cereal)

Making fruit or vegetable

kabobs to create patterns

-41-

5th Grade


SCCCR Standards: Evaluate numerical expressions involving grouping symbols (i.e., parentheses, brackets, braces) (5.ATO.1). Translate verbal

phrases into numerical expressions and interpret numerical expressions as verbal phrases (5.ATO.2).


5.ATO.1: Evaluate two-step

numerical expressions involving

grouping symbols (i.e.,

parentheses, brackets, braces).

5.ATO.1: Evaluate two-step

numerical expressions involving

grouping symbols (i.e.,

parentheses, brackets, braces;

limit to addition and subtraction).

5.ATO.1: Evaluate a two-step

numerical expression

involving grouping symbols

(limit to addition and

subtraction).

5.ATO.1: Evaluate a

one-step expression

that contains grouping

symbols.

5.ATO.1: Identify

grouping symbols in an

expression (parentheses,

brackets, braces).

5.ATO.2: Translate verbal

phrases into simple numerical

expressions.



expressions.



expressions (limit to one-step

addition or subtraction).

5.ATO.2: Given a

verbal phrase, identify

the operation.


symbol that correlates

with sum, product, take

away, divide.

It Is Essential for Students to Know: Students need to be able to recognize computation terms (e.g., how many are left, altogether). Students

need to be able to create and solve one-step addition and subtraction equations.


• Demonstrate solving one-step addition and subtraction problems using student-preferred objects. For example, have students count how

many items they have in their pencil box. Then, have students give away or add more items to the box. Create addition or subtraction

expressions demonstrating how the amount of supplies changed.


5ATO Expression

Parenthesis

Brackets

Braces

Using grouping symbols

Identify operation needed

Write expressions into

numerical form

Use hula hoops, jump ropes, wiki sticks to

illustrate grouping symbols

Play games with cards (grouping)

Use real life examples with preferred objects to

explain operational vocabulary

Sponsoring a canned food drive to

compare class totals and practice

addition, subtraction, multiplication,

and division

-42-


Take away

Sum

Product

Use building blocks

-43-

6th Grade

Key Concept: Expressions, Equations, and Inequalities

SCCCR Standards: Write and evaluate numerical expressions involving whole-number exponents and positive rational number bases using the

Order of Operations (6.EEI.1). Extend the concepts of numerical expressions to algebraic expressions involving positive rational numbers.

a. Translate between algebraic expressions and verbal phrases that include variables. b. Investigate and identify parts of algebraic expressions

using mathematical terminology, including term, coefficient, constant, and factor. c. Evaluate real-world and algebraic expressions for specific

values using the Order of Operations. Grouping symbols should be limited to parentheses, braces, and brackets. Exponents should be limited to

whole numbers (6.EEI.2). Write and solve one-step linear equations in one variable involving nonnegative rational numbers for real-world and

mathematical situations (6.EEI.7).


6.EEI.1: Write numerical

expressions involving whole

numbers using the Order of

Operations.

6.EEI.1: Write numerical

expressions involving whole

numbers using the Order of

Operations.

6.EEI.1: Given an equation,

identify the Order of

Operations.


identify the first step for

Order of Operations.


identify the symbols for the

four functions (+, –, x, ÷).

6.EEI.2: Identify parts of

algebraic expressions using

mathematical terminology,

including term, coefficient,

constant, and variable.

6.EEI.2: Identify parts of

algebraic expressions using

mathematical terminology,

including term, coefficient,

constant, and variable.

6.EEI.2: Identify the parts of

an expression using

mathematical terminology

(limit to term and variable).

6.EEI.2: Identify an

algebraic expression.

6.EEI.2: Distinguish

between a number and a

letter.

6.EEI.7: Identify linear

equations for real-world

situations.

6.EEI.7: Identify linear

equations related to wages,

finances, time, and distance.

6.EEI.7: Identify a situation

where the variables create an

increasing linear equation

(e.g., the more hours you

work, the higher your

paycheck; the farther your

destination, the longer the

bus ride).

6.EEI.7: Identify the


variables.

6.EEI.7: Recognize that an

unknown value can be

represented by a variable.

It Is Essential for Students to Know: Students need to be able to differentiate between a variable and a number, and to recognize expressions and

equations. Students also need to know the Order of Operations.

-44-


• Read articles with graphs and interpret the graphs.

• Identify linear equations that represent real-life situations. For example, Peter is paid $5 for walking 1 dog, $10 for walking 2 dogs, and

$15 for walking 3 dogs. Which line shows how much Peter gets paid for walking dogs?


6EE Variables

Term

Symbols

Increasing

Linear

Use Order of Operations

Understand money and

measurement

Distinguish between

numbers/letters

Play the Twenty-four game

Sort magnetic numbers and letters

Use an outside activity such as running to

determine distance ran in a time or time to

run a distance, and then graph results

Play hopscotch to practice using the Order

of Operations

Use hula hoops, jump ropes, wiki sticks to

illustrate grouping symbols

Use visual schedule for Order of Operations

“Hiring” students for jobs and determining “pay”

Using a map of familiar places (school or town)

determine distance

Running a school store

Growing plants and measuring growth

Using a thermometer to understand temperature

Calculating electricity usage

Using a toaster and adjusting time for darkness of bread

Using a dryer to understand that a longer drying time

creates drier clothes

-45-

7th Grade


SCCCR Standards: Apply mathematical properties (e.g., commutative, associative, distributive) to simplify and to factor linear algebraic

expressions with rational coefficients (7.EEI.1). Extend previous understanding of Order of Operations to solve multi-step real-world and

mathematical problems involving rational numbers. Include fraction bars as a grouping symbol (7.EEI.3).


7.EEI.1: Apply mathematical

properties (e.g., commutative,

associative) to simplify linear

algebraic expressions with

whole number coefficients.


properties (e.g., commutative,

associative) to simplify linear

algebraic expressions with whole

number coefficients.


commutative property to simplify

linear algebraic expressions with

whole number coefficients.

7.EEI.1: Apply

mathematical

commutative

property of addition

and multiplication.

7.EEI.1: Apply

mathematical

commutative property

of addition.

7.EEI.3: Extend previous

understanding of Order of

Operations to solve multi-step


problems involving whole

numbers. Exclude exponents

and fraction bars as a grouping

symbol.


understanding of Order of

Operations to solve multi-step


problems involving whole

numbers. Exclude exponents and

fraction bars as a grouping

symbol.


understanding of the Order of

Operations to solve two-step real-

world problems involving whole

numbers. Exclude exponents and

fraction bars as a grouping symbol.

7.EEI.3: Know the

Order of Operations

in a mathematical

expression.

7.EEI.3: Identify a

mathematical operation

by its symbol.

It Is Essential for Students to Know: Students need to be able apply the Order of Operations and commutative property of addition and

multiplication.


• Use simple directions to show the real-world use of the commutative property. For example, here are directions to the principal’s office:

take a right out of the classroom door, walk 10 feet, then take a left, walk 5 feet, and the office is in front of you. When going back to

class, walk 5 feet from the principal’s office and then take a right, walk 10 feet, and the class will be on your left.

-46-


7EE Commutative

Coefficient

Linear

Add and subtract with

commutative property

Use Order of

Operations

Two-step equations

Compare steps taken (one student takes 6 steps then 4;

the other takes 4 steps and then 6)

Use sentence strips to take word problems apart and

put back together; put in correct order to match model

Use a calculator to get to correct answer (give answer

first and they determine order to get answer)

Using directions to and from places to

understand the commutative property (tasks

where order does not matter)

Completing activities where order does matter

(task analysis) such as making a sandwich,

getting dressed, or building something

-47-

8th Grade


SCCCR Standards: Understand and apply the laws of exponents (i.e., product rule, quotient rule, power to a power, product to a power, quotient

to a power, zero power property, negative exponents) to simplify numerical expressions that include integer exponents (8.EEI.1). Investigate

concepts of square and cube roots. a. Find the exact and approximate solutions to equations of the form 𝑥2 = 𝑝 and 𝑥3 = 𝑝 where 𝑝 is a positive

rational number. b. Evaluate square roots of perfect squares. c. Evaluate cube roots of perfect cubes. d. Recognize that square roots of non-perfect

squares are irrational (8.EEI.2). Apply concepts of proportional relationships to real-world and mathematical situations. a. Graph proportional

relationships. b. Interpret unit rate as the slope of the graph. c. Compare two different proportional relationships given multiple representations,

including tables, graphs, equations, diagrams, and verbal descriptions (8.EEI.5).


8.EEI.1: Understand

exponents to simplify

numerical expressions that

include integer exponents.

8.EEI.1: Understand exponents to

simplify numerical expressions that

include integer exponents.

8.EEI.1: Understand

exponents to simplify

numerical expressions.

8.EEI.1: Expand

exponents into repeated

multiplication.

8.EEI.1: Identify

repeated multiplication

(4 x 4 x 4) as the

exponent notation (43).

8.EEI.2: Investigate

concepts of square roots.

8.EEI.2: Understand that the square

root is the inverse of squaring a number.

8.EEI.2: Understand how

to square a number.

8.EEI.2: Understand

multiplication facts of

whole numbers with

products up to 100.

8.EEI.2: Understand

multiplication as

repeated addition.

8.EEI.5: Compare two

different proportional

relationships using tables

and graphs.

8.EEI.5: Compare two different

proportional relationships given

multiple representations, including

tables, graphs, equations, diagrams, and

verbal descriptions.


different proportional


and graphs.



and graphs.

8.EEI.5: Identify a table

or graph.

It Is Essential for Students to Know: Students need to be able to recognize the relationship between repeated addition and multiplication.

Students need to be able to convert repeated multiplication into exponents (i.e., 2 x 2 x 2 = 23). Students also need to be able recognize a

proportional relationship when displayed in a table or graph.

-48-


• Show repeated multiplication using objects.


8EE Square of a number

Exponent

Table

Graph

Proportion

Simplify

Product

Repeated addition

Repeated multiplication

Read tables and graphs

Use bingo dotters to illustrate repeated

multiplication

Use muffin tins to understand repeated

multiplication; put the same number of

objects in each space and then group

together to calculate answer

Grouping similar items or cans in a pantry or

grocery store and counting the totals

Stocking vending machines or items in the

school store

Filling class orders (such as using health

supplies, paper towels, Band-Aids, gloves, etc.)

-49-

Geometry

Geometry and Measurement

3rd Grade 4th Grade 5th Grade 6th Grade 7th Grade 8th Grade

3.G 4.G 5.G 6.GM 7.GM 8.GM

-50-

3rd Grade

Key Concept: Geometry

SCCCR Standards: Understand that shapes in different categories (e.g., rhombus, rectangle, square, and other 4-sided shapes) may share

attributes (e.g., 4-sided figures) and the shared attributes can define a larger category (e.g., quadrilateral). Recognize rhombuses, rectangles,

and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories (3.G.1). Partition two-dimensional shapes into 2, 3, 4, 6, or 8 parts with equal areas and express the area of each part using the same unit fraction.

Recognize that equal parts of identical wholes need not have the same shape (3.G.2).


3.G.1: Recognize

rhombuses, rectangles, and

squares as quadrilaterals.

3.G.1: Identify all attributes

of quadrilaterals (i.e., 4

sides, 4 angles).

3.G.1: Recognize

rhombuses, rectangles, and

squares as quadrilaterals.

3.G.1: Identify

quadrilaterals.

3.G.1: Identify sides or

angles of a quadrilateral.

3.G.2: Partition two-

dimensional shapes into two

parts with equal areas.

3.G.2: Recognize when a

shape is not equal to one

half.

3.G.2: Recognize one half

on an area model.

3.G.2: Recognize the equal

parts of a two-dimensional

shape.

3.G.2: Identify two-

dimensional shapes.

It Is Essential for Students to Know: Students need to be able to recognize quadrilaterals and their attributes, such as having 4 sides and 4

angles.


• Identify quadrilaterals in everyday objects; for example, unfold a box of cereal to see that it is made up of three differently sized

rectangles.


3G Rectangle

Rhombus

Square

Quadrilateral

Half

Recognize 2D shapes

Divide shapes in half

Sort shapes

Find shapes in environment

Take pictures with students and create a book of shapes

Build a “house”

Sweeping into shape

Recognizing street signs

Recognizing sports fields/courts

Sorting or stocking items in a pantry

-51-


Build shapes with toothpicks, cotton swabs, pipe cleaners,

geoboards, wiki sticks

Create a shape person (robot)

Play “Four Corners”

-52-

4th Grade


SCCCR Standards: Draw points, lines, line segments, rays, angles (i.e., right, acute, obtuse), and parallel and perpendicular lines. Identify these

in two-dimensional figures (4.G.1). Classify quadrilaterals based on the presence or absence of parallel or perpendicular lines (4.G.2).


4.G.1: Identify points, line

segments, and angles in two-

dimensional figures.

4.G.1: Recognize angles,

points, or line segments in a

two-dimensional figure.

4.G.1: Recognize different

types of angles (acute, right,

obtuse, and straight).

4.G.1: Identify a line or line

segment.

4.G.1: Recognize a point.

4.G.2: Identify parallel and

perpendicular lines.


perpendicular lines in

shapes.


perpendicular lines.

4.G.2: Identify shapes with

parallel lines.

4.G.2: Identify lines.

It Is Essential for Students to Know: Students need to be able to recognize points, lines, and line segments. Students need to be able to recognize

parallel and perpendicular lines.


• Place marking spots on the classroom floor and engage students to “act” or show points, lines, and line segments by moving to the

different marking spots in the classroom.

• Use objects in the classroom to demonstrate parallel and perpendicular lines.

-53-

• Use objects in the classroom or pictures of familiar places to demonstrate parallel and perpendicular lines.


4G Acute

Obtuse

Right angle

Straight

Parallel

Perpendicular

Recognize points

Identify lines

Identify shapes with parallel

and perpendicular lines

Recognize angles

Host a scavenger hunt that relies on lines

In gymnasium, find angles and lines

Use toothpicks/marshmallows to create angles

Find points in environment (pencil point, top of bottle)

Find angles in environment (clock, hallways, etc.)

Play shape bingo

Drawing hallways/maps

Looking at crosswalks to

understand parallel lines

Writing names on point or line

Creating parallel lines by pushing

strollers or wheelchairs outside

-54-

5th Grade


SCCCR Standards: Define a coordinate system (5.G.1). The x- and y-axes are perpendicular number lines that intersect at 0 (the origin) (5.G.1a).

Any point on the coordinate plane can be represented by its coordinates (5.G.1b). The first number in an ordered pair is the x-coordinate and

represents the horizontal distance from the origin (5.G.1c). The second number in an ordered pair is the y-coordinate and represents the vertical

distance from the origin (5.G.1d). Plot and interpret points in the first quadrant of the coordinate plane to represent real-world and mathematical

situations (5.G.2).


5.G.1: Define a coordinate system. 5.G.1: Identify an ordered

pair on a coordinate plane.

5.G.1: Plot a number on a

vertical or horizontal

number line.

5.G.1: Identify a number

on a vertical or horizontal

number line.

5.G.1: Recognize a point

on a number line (limit to

numbers greater than 0).

5.G.1a: The x- and y-axes are

perpendicular number lines that

intersect at 0 (the origin).

5.G.1a: Identify an ordered


5.G.1a: Plot a number on


number line.

5.G.1a: Identify a



5.G.1a: Recognize a point



5.G.1b: Any point on the coordinate

plane can be represented by its

coordinates.

5.G.1b: Identify an ordered


5.G.1b: Plot a number on


number line.

5.G.1b: Identify a



5.G.1b: Recognize a point



5.G.1c: The first number in an

ordered pair is the x-coordinate and

represents the horizontal distance

from the origin.

5.G.1c: Identify an ordered


5.G.1c: Plot a number on


number line.

5.G.1c: Identify a number

on a vertical or horizontal

number line.

5.G.1c: Recognize a point



5.G.1d: The second number in an

ordered pair is the y-coordinate and

represents the vertical distance from

the origin.

5.G.1d: Identify an ordered


5.G.1d: Plot a number on


number line.

5.G.1d: Identify a



5.G.1d: Recognize a point



5.G.2: Plot points in the first

quadrant.

5.G.2: Plot a point on a map

given the x and y variables.

5.G.2: Recognize

perpendicular lines and

line segments.

5.G.2: Recognize

intersecting lines and line

segments.

5.G.2: Recognize a point.

-55-

It Is Essential for Students to Know: Students need to be able to identify various points on a number line. Students need to be able to recognize

line segments and intersecting lines.


• Have students roll a die and place a marker on a number line corresponding to the number rolled on the die.

• Using pictures of real life locations and objects, demonstrate the difference between line segments and intersecting lines.


5G Vertical

Horizontal

Point

Plot

Line segment

Perpendicular

Intersecting

Plot a number on a line Use painter’s tape on the floor or wall to practice

number line activities

Place sticky notes or ink with a dot stamper on chart

paper with X and Y axes illustrated, and plot the points

Practicing reading temperature

from thermometers

-56-

6th Grade

Key Concept: Geometry and Measurement

SCCCR Standards: Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or

decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems (6.GM.1).


6.GM.1: Find the area of

right triangles and

rectangles.

6.GM.1: Find the area of

right triangles and rectangles

when given side lengths.

6.GM.1: Find the area of a

rectangle given the side

lengths and tiles.

6.GM.1: Identify a triangle

that has a right angle.

6.GM.1: Identify a triangle.

It Is Essential for Students to Know: Students need to be able to identify triangles and right angles.


• Students can practice finding the area by measuring the length and width of a window to determine what size curtains are needed, or they

can measure the length and width of the classroom and their desks to determine approximately how many desks would fit in the

classroom.

• Have students identify triangles inside everyday objects, such as pictures on flags, road signs, or the entrance of a tent.


6GM Triangle

Area

Rectangle

Find area

Identify right triangles

Identify triangles

Area formula

Use painter’s tape on the floor or count tiles to find area

Use square foods such as crackers to create rectangles and

triangles, and then find the area

Measure objects in class, such as tables, windows, etc.

Use pool table rack to illustrate the area of a triangle and

calculate how many of same object can fit inside

Use coat hangers to illustrate the area of a triangle and

calculate how many of same object can fit inside

Play area games, such as rolling number cubes, coloring in

the area of a shape on graph paper, and illustrating

percentage using 10x10 grid paper

Measuring area by making curtains,

bandanas, or pennants for sports teams

Making a simple floor plan

Cutting fabric and calculating area

Using pizza slices to understand how

many toppings fill slice

-57-

7th Grade


SCCCR Standards: Apply the concepts of two- and three-dimensional figures to real-world and mathematical situations. a. Understand that the

concept of area is applied to two-dimensional figures such as triangles, quadrilaterals, and polygons. b. Understand that the concepts of volume

and surface area are applied to three-dimensional figures such as cubes, right rectangular prisms, and right triangular prisms. c. Decompose cubes,

right rectangular prisms, and right triangular prisms into rectangles and triangles to derive the formulas for volume and surface area. d. Use the

formulas for area, volume, and surface area appropriately (7.GM.6).


7.GM.6: Understand that the

concept of area applies to

two-dimensional figures.

Understand that the concept

of volume applies to three-








Understand which formula to

use to calculate either area or

volume.







7.GM.6: Understand the

concept of area. Understand

the concept of volume.

7.GM.6: Understand the

difference between two-

dimensional and three-


It Is Essential for Students to Know: Students need to be able to differentiate between two- and three-dimensional objects. Students also need to

be able to determine when to find the area or volume of an object, such as how one finds the area of a window or the volume of a cereal box.


• Explore the concept of area by measuring the length and width of papers, then use unit squares to determine if your calculation methods

were correct.

• Explore the concept of volume by estimating the number of dried beans that can fill a three-dimensional object. First, count the number of

beans that cover the bottom of the shape. Then count the number of beans needed to make the height of the object and multiply the

numbers. Verify your findings by counting the number of beans in the container.

-58-


7GM Volume (3D)

Area (2D)

Link volume

to 3D figures

Link area to

2D figures

Fill bottles with objects (how many objects fill bottle?)

Use blocks/beans to fill 2D shapes and 3D objects

Use a flat square or open cube to illustrate volume;

“pour” contents to show which one will hold

Packing boxes for class picnics – how many boxes

are needed?

Packing book boxes for classes

Cooking

-59-

8th Grade


SCCCR Standards: Investigate the properties of rigid transformations (rotations, reflections, translations) using a variety of tools (e.g.,

grid paper, reflective devices, graphing paper, technology). a. Verify that lines are mapped to lines, including parallel lines. b. Verify that

corresponding angles are congruent. c. Verify that corresponding line segments are congruent (8.GM.1).


8.GM.1: Investigate the properties

of rigid transformations (rotations,

reflections, translations) using a

variety of tools to recognize

congruence.

8.GM.1: Investigate the properties

of rigid transformations (rotations,

reflections, translations) using a

variety of tools to recognize

congruence.

8.GM.1: Investigate the

properties of rigid

transformations (rotations,

reflections, translations).

8.GM.1: Recognize

congruent figures.

8.GM.1: Recognize

when two-dimensional

shapes are the same.

It Is Essential for Students to Know: Students need to be able to recognize that two shapes are congruent when displayed in different

orientations.


• Explore properties of rigid transformations by moving a small rug around the room or a desk. Describe how the orientation of the rug or

desk changes based on the transformation.


8GM 2D

Reflection

Translation

Rotation

Congruent

Recognize shapes

Understand reflection,

translation, and rotation

Sort objects by shape or size

Host a scavenger hunt to find congruent shapes

Create a color mandala by coloring congruent shapes the same color

Use a mirror to illustrate congruence

Create shapes using Tangrams

Use straws to create congruent shapes

Use grid paper to illustrate congruence

Sorting clothing or dishes

by shape/size

-60-

Measurement and Data Analysis

3rd Grade 4th Grade 5th Grade

3.MDA 4.MDA 5.MDA

-61-

3rd Grade

Key Concept: Measurement and Data Analysis

SCCCR Standards: Use analog and digital clocks to determine and record time to the nearest minute, using a.m. and p.m.; measure time

intervals in minutes; and solve problems involving addition and subtraction of time intervals within 60 minutes (3.MDA.1). Estimate and

measure liquid volumes (capacity) in customary units (i.e., c., pt., qt., gal.) and metric units (i.e., mL, L) to the nearest whole unit

(3.MDA.2). Collect, organize, classify, and interpret data with multiple categories and draw a scaled picture graph and a scaled bar

graph to represent the data (3.MDA.3). Generate data by measuring length to the nearest inch, half-inch and quarter-inch and organize the

data in a line plot using a horizontal scale marked off in appropriate units (3.MDA.4).


3.MDA.1: Use analog and

digital clocks to record time to

the nearest hour and half-hour,

using a.m. and p.m.

3.MDA.1: Demonstrate the

concept of telling time to the

hour and half-hour on both

types of clocks.

3.MDA.1: Use analog and digital

clocks to record time to the nearest

hour and half-hour, using a.m.

and p.m.

3.MDA.1: Match

the time to an

activity from a list.

3.MDA.1: Identify a

clock as a tool to

measure time.

3.MDA.2: Measure liquid

volumes (capacity) in

customary units (i.e., c., pt., qt.,

gal.) and metric units (i.e., mL,

L) to the nearest whole unit.

3.MDA.2: Demonstrate the

concept by choosing the

appropriate volume unit for

various given substances to be

measured.

3.MDA.2: Demonstrate the concept

by choosing the appropriate volume

unit for a given substance to be

measured (e.g., what is the best unit

to measure for a box of cereal?)

3.MDA.2: Identify

shapes that can have

volume.

3.MDA.2: Identify

three-dimensional

shapes.

3.MDA.3: Interpret data from a

picture graph and a bar graph.

3.MDA.3: Interpret data from

a picture graph and a bar

graph.

3.MDA.3: Identify information from

a picture graph.

3.MDA.3: Identify

information from a

bar graph.

3.MDA.3: Identify a

bar graph.

3.MDA.4: Measure length to

the nearest inch.

3.MDA.4: Measure length to

the nearest inch.

3.MDA.4: Recognize inches as a

measure of length.

3.MDA.4: Identify

an inch on a ruler.

3.MDA.4: Identify a

ruler.

It Is Essential for Students to Know: Students need to be able to identify tools of measurement. Students need to be able to read time (e.g., 2:30),

length with a ruler, and bar graphs. Students need to also identify objects that have volume (e.g., a cup can contain water).

-62-


• The students can practice reading a digital and/or analog clock or watch by incorporating activities throughout the day that require the

students to read the clock and compare the time to a class schedule that shows what is happening at different times in the day.

• Students can measure liquids using measuring cups or weigh objects using a scale to help with understanding of volume and units of

measure.

• Use bar graphs in newspapers and magazine articles to demonstrate how to interpret the graph data.

• Students can measure objects using an inch ruler; for example, the students can measure the length and width of a picture to see if it can fit

in a certain frame size.


3MDA Analog

Digital

AM

PM

Hour

Half Hour

Inches

Graph

Ruler

Volume

Tell time to hour

and half hour

Recognize numbers

Count by 5s

Read rulers

Rote count

Use hula hoops or paper plates to create clocks

Draw a large circle on the floor and let students become the

hands on the clock

Use timers to show the passage of time

Play clock bingo

Measure objects in classroom

Measure preferred food items

Create an art project using sand art to measure depth of different

colors of sand

Measure shoes, feet

Creating a daily schedule with clocks

Hosting a Classroom Olympics –

measure distances ran, objects

thrown, distances jumped

-63-

4th Grade


SCCCR Standards: Convert measurements within a single system of measurement, customary (i.e., in., ft., yd., oz., lb., sec., min., hr.) or metric

(i.e., cm, m, km, g, kg, mL, L) from a larger to a smaller unit (4.MDA.1). Apply the area and perimeter formulas for rectangles (4.MDA.3).

Determine the value of a collection of coins and bills greater than $1.00 (4.MDA.8).


4.MDA.1: Distinguish

measurements within a single

system of measurement—

customary (i.e., in., ft., yd., min.,

hr.) or metric (i.e., cm, m, km, g,

kg, mL, L)—as larger or smaller.

4.MDA.1: Compare the size of

measurements within one system

measure—customary (i.e., in.,

ft., yd., min., hr.) or metric (i.e.,

cm, m, km, g, kg, mL, L).

4.MDA.1: Determine if

measurements within one

system are larger or

smaller (i.e., in., ft., min.,

hr., mL, L).

4.MDA.1: Distinguish

between systems of

measurement.

4.MDA.1: Compare

two pieces of data with

the same unit of

measurement.

4.MDA.3: Find the area and

perimeter for rectangles when given

the side lengths.

4.MDA.3: Find the area and

perimeter for rectangles when

given the side lengths.

4.MDA.3: Find the area

and perimeter by counting

squares.

4.MDA.3: Recognize a

rectangle.

4.MDA.3: Recognize

side lengths.

4.MDA.8: Determine the value of a

collection of coins and bills greater

than $1.

4.MDA.8: Determine the value

of a collection of coins and bills

greater than $1.

4.MDA.8: Identify the

value of a penny, a nickel,

a dime, and a quarter.

4.MDA.8: Identify a

penny, a nickel, a dime,

and a quarter.

4.MDA.8: Recognize

money.

It Is Essential for Students to Know: Students need to be able to identify length and width of a shape. Students need to be able to distinguish

between and compare types of measurement (e.g., inches, minutes, feet). Students also need to be able to recognize coins.


• Show advertisements and sales flyers and have students select the appropriate coins needed to purchase certain items.

• Use classroom objects to measure side lengths.

• Use classroom objects and using counting squares to determine perimeter and area.

-64-


4MDA Inches

Feet

Minutes

Hours

Perimeter

Liters

Milliliters

Area

Coins

Compare

measurements with

same unit of

measurement

Count objects

Find area

Identify coins and

value of coins

Create a garden; plan size and shape, and then measure heights of plants

Weigh produce and compare weights

Measure distances using popcorn; without using the lid of the popper,

make popcorn and then measure the distance popcorn travels from

popper (extend into geometry – draw connecting lines and determine

area)

Make and launch paper helicopters activity

Measure heights of students and compare heights

Measuring and comparing

distances at school

Predicting sizes and shapes;

do we have room for 4 trays at

this table?

Counting money, making

purchases, and making change

-65-

5th Grade


SCCCR Standards: Convert measurements within a single system of measurement: customary (i.e., in., ft., yd., oz., lb., sec., min., hr.) or metric

(i.e., mm, cm, m, km, g, kg, mL, L) from a larger to a smaller unit and a smaller to a larger unit (5.MDA.1). Differentiate among perimeter, area,

and volume and identify which application is appropriate for a given situation (5.MDA.4).


5.MDA.1: Convert

measurements within a

single system of

measurement—customary

(i.e., in., ft., yd., min., hr.) or

metric (i.e., cm, m, km, mL,

L)—from a larger to a

smaller unit.

5.MDA.1: Convert

measurements within a

single system of

measurement.

5.MDA.1: Use an

appropriate tool for

measuring length using

inches; use an appropriate

tool for measuring length

using feet; use an appropriate

tool for measuring mass in

pounds; use an appropriate

tool for measuring mass in

ounces.

5.MDA.1: Make direct

comparison of two lengths.

Make direct comparison of

two masses.

5.MDA.1: Recognize

measurable attributes.

5.MDA.4: Differentiate

among perimeter, area, and

volume and identify which

application is appropriate for

a given situation.

5.MDA.4: Solve word

problems by using perimeter,

area, or volume.

5.MDA.4: Solve word

problems involving the

perimeter of polygons.

5.MDA.4: Calculate the

perimeter by adding all the

side lengths. Calculate the

area by counting the square

units.

5.MDA.4: Recognize

measurable attributes.

It Is Essential for Students to Know: Students need to be able to determine and compare the length of two objects or the mass of two objects.

Students need to be able to determine the perimeter and area of a shape.

-66-


• The students can practice the difference among perimeter, area, and volume by identifying which is needed for certain real-life activity.

For example:

The amount of water in the beaker requires calculating volume.

Determining where the rug can fit requires calculating area.

-67-

Determining the amount of fencing needed for the vegetable garden requires calculating perimeter.


5MDA Attributes

Tool (measurement)

Mass

Perimeter

Length

Polygon

Calculate

Use measuring tools

Compare lengths and

masses

Calculate perimeter

Use a see-saw to compare weights

Find perimeter throughout classroom,

school, etc. and compare

Using a kitchen scale, cups, and measurements

during cooking

Building or planning a project

Planning and creating a school garden; measure

perimeter, height of plants, etc.

-68-

Data Analysis and Statistics

Data Analysis, Statistics, and Probability

Functions

Interpreting Functions

Interpreting Data

Quantities

Real Number System

6th Grade 7th Grade 8th Grade 11th Grade 8th Grade 11th Grade 11th Grade 11th Grade

6.DS 7.DSP 8.F 11.FIF 8.DSP 11.SPID 11.NQ 11.NRNS

-69-

6th Grade

Key Concept: Data Analysis and Statistics

SCCCR Standards: Differentiate between statistical and non-statistical questions (6.DS.1).


6.DS.1: Find the mean,

median, mode, and range.

6.DS.1: Identify the median

and/or range of a data set.

6.DS.1: Determine the middle

point of a collection of objects.

6.DS.1: Put a data set in

order from least to greatest.

6.DS.1: Find the largest or

smallest number in a data set.

It Is Essential for Students to Know: Students need to be able to order numbers from least to greatest. Students need to be able to identify the

smallest and largest number within a data set.


• The students can collect data within the classroom such as shoes sizes. For example, the students can collect information on each person’s

shoe size and plot the information on a large number line on the board or interactive whiteboard. Discuss with students what the range,

median, and mode of the shoe sizes are in the classroom. This can be expanded to collecting data across people or classrooms in the school

building.


6DS Mean

Median

Mode

Range

Determine

smallest and

largest

Order (by

attribute)

Order common objects by attribute (size)

With popcorn activity (from 4th MDA), order

distance data to find mean, median, mode

Using bags of colored candy, have students sort

candy by color, collect data, and find mean,

median, mode

Make a rock collection and weigh rocks to find

mean, median, mode

Locating the middle step of a list of steps

Planning a schedule and managing time

Using a calendar to find the middle day of week or middle

day of the month

Using a pay schedule to calculate dates of pay during the

month

Calculating a median salary using a list

Practicing comparison shopping by putting prices in order

-70-

7th Grade

Key Concept: Data Analysis, Statistics, and Probability

SCCCR Standards: Investigate concepts of random sampling. a. Understand that a sample is a subset of a population and both possess the same

characteristics. b. Differentiate between random and non-random sampling. c. Understand that generalizations from a sample are valid only if the

sample is representative of the population. d. Understand that random sampling is used to gather a representative sample and supports valid

inferences about the population (7.DSP.1). Draw inferences about a population by collecting multiple random samples of the same size to

investigate variability in estimates of the characteristic of interest (7.DSP.2). Compare the numerical measures of center (mean, median, mode)

and variability (range, interquartile range, mean absolute deviation) from two random samples to draw inferences about the populations (7.DSP.4).

Investigate the concept of probability of chance events. a. Determine probabilities of simple events. b. Understand that probability measures

likelihood of a chance event occurring. c. Understand that the probability of a chance event is a number between 0 and 1. d. Understand that a

probability closer to 1 indicates a likely chance event. e. Understand that a probability close to 12 indicates that a chance event is neither likely nor

unlikely. f. Understand that a probability closer to 0 indicates an unlikely chance event (7.DSP.5).


7.DSP.1: Understand that a

sample is a subset of a

population. Distinguish between

populations and samples.

Distinguish between random and

nonrandom samples.



population. Distinguish between

populations and samples.

Distinguish between random and

nonrandom samples.



population. Identify populations

and samples. Identify random

and nonrandom samples.

7.DSP.1: Distinguish

between a population

or a sample.

7.DSP.1: Distinguish

between a whole and a

part.

7.DS.2: Draw inferences about a

population by collecting random

samples.


population by collecting random

samples.


population when given random

samples.

7.DS.2: Identify a

statement about a

given random

sample.

7.DS.2: Determine if a

sample is random.

7.DSP.4: Use the numerical

measures of center (mean,

median, mode, and range).


measures of center (mean,

median, mode, and range).


measures of center (mean and

median).

7.DSP.4: Identify the

median of a data set.

7.DSP.4: Determine the

middle point of a

collection of objects.

7.DSP.5: Understand that

probability measures likelihood

of a chance event occurring.

7.DSP.5: Determine the

probability of simple events.

7.DSP.5: Understand that

probability measures likelihood

of a chance event occurring.

7.DSP.5: Identify if

an event is possible

or impossible.

7.DSP.5: Recognize the

outcome of an event.

-71-

It Is Essential for Students to Know: Students need to be able to determine if an event is possible or likely. Students need to be able to

differentiate between a population and a sample. Students need to be able to make statements about a data set (e.g., lunch choices). Students also

need to be able to determine the median of a data set.


• Collect data in the classroom by asking everyone on the basketball team their shoe size, then find the mode of the data to help the coach

determine how many different sized shoes should be ordered for the team.


7DSP Sample

Subset

Population

Random

Nonrandom

Median

Center

Mean

Probability

(univariate)

Find middle

Identify population

Determine probability

Practice using probability; put items in a bag and calculate

chances of pulling specific item out

Determine probability by flipping a coin

Determine future predictions by shooting basketball and

collecting and analyzing data

Make predictions and understand probability by reviewing

classroom attendance data

Analyze school menu to make predictions

Determining probability by

analyzing the weather

Maintaining stock for school store;

determining buying trends to

predict future buying trends

Sampling students at random on

transportation mode to school

-72-

8th Grade

Key Concept: Functions

SCCCR Standards: Explore the concept of functions. a. Understand that a function assigns to each input exactly one output. b. Relate inputs

(𝑥-values or domain) and outputs (𝑦-values or range) to independent and dependent variables. c. Translate among the multiple representations of a

function, including mappings, tables, graphs, equations, and verbal descriptions. d. Determine if a relation is a function using multiple

representations, including mappings, tables, graphs, equations, and verbal descriptions. e. Graph a function from a table of values. Understand that

the graph and table both represent a set of ordered pairs of that function (8.F.1). Compare multiple representations of two functions, including

mappings, tables, graphs, equations, and verbal descriptions, in order to draw conclusions (8.F.2). Apply the concepts of linear functions to real-

world and mathematical situations. a. Understand that the slope is the constant rate of change and the 𝑦-intercept is the point where 𝑥 = 0.

b. Determine the slope and the 𝑦-intercept of a linear function given multiple representations, including two points, tables, graphs, equations, and

verbal descriptions. c. Construct a function in slope-intercept form that models a linear relationship between two quantities. d. Interpret the

meaning of the slope and the 𝑦-intercept of a linear function in the context of the situation. e. Explore the relationship between linear functions and

arithmetic sequences (8.F.4).


8.F.1: Understand that a function

assigns to each input exactly one

output. Determine if a relation is a

function using multiple representations,

including tables, graphs, and equations.

Graph a function from a table of x and y

values. Extend the knowledge of the

coordinate plane to use the set of

ordered pairs of that function.

8.F.1: Generate ordered pairs

from two distinct numerical

patterns. Extend a symbolic

pattern by applying the rule.

8.F.1: Graph a function

from a table of x and y

values.

8.F.1: Graph a point

when given an

ordered pair of

numbers.

8.F.1: Identify a point.

8.F.2: Compare two functions,

including tables, graphs, and equations,

in order to draw conclusions.

8.F.2: Compare two functions,

including tables, graphs, and

equations, to draw conclusions.

8.F.2: Compare the slopes

of two functions given in

equation form (slope-

intercept form).

8.F.2: Identify the

slope and intercepts

of a function given

in equation form.

8.F.2: Identify the

slope or intercepts of a

function in graph form.

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8.F.4: Understand that the slope is the

constant rate of change and the y-

intercept is the point where x = 0.

Interpret the meaning of the slope and

the y-intercept of a linear function in the

context of the situation.

8.F.4: Understand that the slope

is the constant rate of change,

and the y-intercept is the point

where x = 0. Interpret the

meaning of the slope and the y-

intercept of a linear function in

the context of the situation.

8.F.4: Understand that the

slope is the constant rate of

change, and the y-intercept

is the point where x = 0.

8.F.4: Understand

that slope is related

to the direction of

the line.

8.F.4: Identify a line on

a graph.

It Is Essential for Students to Know: Students need to be able to graph ordered pairs on a coordinate plane. Students need to be able to identify

the rise and run of a line on a graph. Students also need to be able to identify if a line has a positive or negative slope.


• Using a wooden plank and a toy car, explore the concept of steepness.

• Graph real-life situations and explore the meaning of slope and y-intercept within a real-world context. For example, the students can

analyze the following graph that shows the number of hours Mike works and the amount of cash he has. The y-intercept of the graph

shows that before he started working he had already saved $10, and the slope shows that as he works more his cash is increasing, which is

why the slope of the line is positive.

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8F Function

x value

y value

Slope

Intercept

Point

Line

Identify a point

Graph point

Identify slope

Compare slopes

Identify line

Understand slope

Practice using concept of slope using skiing, cars on different

ramps, etc.

Make sundials and measure shadows at different times of day

Plotting data from plant growth over time

-75-

11th Grade

Key Concept: Interpreting Functions

SCCCR Standards: Extend previous knowledge of a function to apply to general behavior and features of a function. a. Understand that a

function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range.

b. Represent a function using function notation and explain that f (𝑥) denotes the output of function 𝑓 that corresponds to the input 𝑥. c.

Understand that the graph of a function labeled as 𝑓 is the set of all ordered pairs (𝑥, y) that satisfy the equation 𝑦 = f (𝑥) (A1.FIF.1). Interpret key

features of a function that models the relationship between two quantities when given in graphical or tabular form. Sketch the graph of a function

from a verbal description showing key features. Key features include intercepts; intervals where the function is increasing, decreasing, constant,

positive, or negative; relative maximums and minimums; symmetries; end behavior and periodicity (A1.FIF.4). Graph functions from their

symbolic representations. Indicate key features including intercepts; intervals where the function is increasing, decreasing, positive, or negative;

relative maximums and minimums; symmetries; end behavior and periodicity. Graph simple cases by hand and use technology for complicated

cases. (Note: FIF.7a–d are not Graduation Standards.) a. Graph rational functions, identifying zeros and asymptotes when suitable factorizations

are available, and showing end behavior. b. Graph radical functions over their domain show end behavior. c. Graph exponential and logarithmic

functions, showing intercepts and end behavior. d. Graph trigonometric functions, showing period, midline, and amplitude (A1.FIF.7).


A1.FIF.1: Understand that a function

from one set (called the domain) to

another set (called the range) assigns

to each element of the domain exactly

one element of the range.

A1.FIF.1: Identify the

domain and range of a given

function.

A1.FIF.1: Identify if a

relation given in table form

is a function.

A1.FIF.1: Given a table

of values, identify a

possible missing x value

(so that an x value does

not repeat).

A1.FIF.1: Given a set

of table values, identify

the set of x values.

A1.FIF.4: Recognize features of a

linear function in graphical form (e.g.,

slope, intercepts; if the function is

increasing, decreasing, constant,

positive, or negative).

A1.FIF.4: Given the slope

and intercept of a function,

identify its graph.

A1.FIF.4: Given a

description of a function,

identify the graph (positive

slope, negative slope,

constant, given y-intercept;

limit to first quadrant).

A1.FIF.4: Given an

intercept of the graph,

identify the graph.

A1.FIF.4: Given a key

feature (increasing,

decreasing, or

constant), identify the

graph.

-76-


A1.FIF.7: Graph linear functions

using their key features.

A1.FIF.7: Given a graph of a

linear function, identify the

slope and intercepts.

A1.FIF.7: Given a graph of

a linear function in the first

quadrant, identify features

of the graph (positive slope,

negative slope, constant,

intercepts).

A1.FIF.7: Given a graph

of a linear function,

identify the x-intercept.

A1.FIF.7: Identify

whether a given graph

is increasing,

decreasing, or constant.

It Is Essential for Students to Know: Students need to be able to identify if a graph is increasing, decreasing, or constant. Students need to be

able to identify the domain and the range of a function.


• Identify the domain and range of a function in a real-world context. For example, the following function is used to find the temperature, F,

in degrees Fahrenheit for any given temperature C, given in Celsius. The domain of the function is the temperature given in Celsius and

the range is the temperature given in Fahrenheit.

• Another example would be the function y = 10x + 40, where y represents the total money Erika needs for a school trip. She is saving $10

per week and has already saved $40. She has 5 weeks to save the money. What are possible domains for the function? In this case, because

she has only 5 weeks to save the money, the only domains for this function would be {1, 2, 3, 4, 5}.


11FIF Increasing

Decreasing

Constant

Identify positive, negative

or constant slopes

Identify x-intercept

Use stairs to identify slopes and compare increasing

or decreasing quantities (1 step = 5 inches,

2 steps = 10 inches, etc.)

Calculate the total cost of items in the school store

(1 pencil, 2 pencils, 3 pencils)

Using a recipe – If 3 cakes need x eggs, how

many eggs are needed to make 2 cakes?

Estimating the materials needed for projects

– make 1 item; make 2 items; make 3 items

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8th Grade

Key Concept: Data Analysis, Statistics, and Probability

SCCCR Standards: Investigate bivariate data. a. Collect bivariate data. b. Graph the bivariate data on a scatter plot. c. Describe patterns observed

on a scatter plot, including clustering, outliers, and association (positive, negative, no correlation, linear, nonlinear) (8.DSP.1).


8.DSP.1: Recognize patterns

observed on a scatter plot,

including clustering, outliers,

and association (positive,

negative, or no correlation).



including clustering, outliers,

and association (positive,

negative, or no correlation).



including clustering and outliers.

8.DSP.1: Graph points

when given an ordered

pair of numbers.

8.DSP.1: Identify

a point.

It Is Essential for Students to Know: Students need to be able to identify a point on a scatterplot.


• Analyze patterns on scatter plots from articles and magazines. This article is looking at which states have the happiest people in the

United States.

-78-


8DSP Scatter plot

Pattern

Clustering and outliers

Ordered pair

(bivariate)

Identify a point

Graph point given an ordered pair

Recognize patterns

Find outliers

Put multicolored objects in bag and chart the

number of objects of each color

Create art using splatter paint, place a grid

over the paint, and identify ordered pairs

Charting the number of times that

certain foods are served in cafeteria

Gathering temperatures over time

and plotting the weather (i.e., dates

vs. temperatures)

-79-

11th Grade

Key Concept: Interpreting Data

SCCCR Standards: Using technology, create scatterplots and analyze those plots to compare the fit of linear, quadratic, or exponential models to

a given data set. Select the appropriate model, fit a function to the data set, and use the function to solve problems in the context of the data

(A1.SPID.6).


A1.SPID.6: Identify the

general form of a given data

set as linear or non-linear.

A1.SPID.6: Identify the

general form of a given data

set as linear or non-linear.

A1.SPID.6: Identify a data

set that is linear.

A1.SPID.6: Identify a data

set that can be modeled as a

straight line.

A1.SPID.6: Identify a graph

that is a straight line.

It Is Essential for Students to Know: Students need to be able to recognize a pattern in scatterplots, such as positive association, negative

association, and no association.

-80-


• Analyze data from articles, and determine if the data is linear or non-linear.


11SPID Graph

Linear

Straight line

Non-linear

Data set

Identify graphs that are

linear (straight line)

Measure anything that grows

Measure the depth of trash in a

trash can throughout the day

Calculating used and remaining cell phone minutes

Measuring the amount of water in glass set in the window over time

(evaporation)

Counting the laundry washed over time

Recording the amount of formula that a student is tube-fed over time

-81-

11th Grade

Key Concept: Quantities

SCCCR Standards: Use units of measurement to guide the solution of multi-step tasks. Choose and interpret appropriate labels, units, and scales

when constructing graphs and other data displays (A1.NQ.1).


A1.NQ.1: Choose the

appropriate labels, units, and

scales when constructing

graphs.

A1.NQ.1: Given a data set,

identify an appropriate scale

for a graph of the data.

A1.NQ.1: Given a data set,

identify the appropriate units

for a graph of the data.

A1.NQ.1: Given context,

identify a graph with correct

labels.

A1.NQ.1: Given data and a

context, identify an

appropriate title for a graph

of the data.

It Is Essential for Students to Know: Students need to be able to identify the different parts of the graph (such as the title and axis labels).


• Explore scale of graphs using Excel, where you can create graphs using data. Play around with the scale to show how you can manipulate

data to prove a point. For example, the graph below shows the average house prices for 1998 and 1999 in a certain city. See how the scale

of the vertical axes can make it look like the average price of the houses increased dramatically or barely.

-82-


11NQ Data set

Unit

Title

Graph

Identify unit

Identify graph

Identify title of the graph

Conduct school polls and graph the results,

such as how many students recycle, prefer a

sports team, wear an article of clothing, etc.

Locating graphs in newspapers or magazines and then

discussing the information presented in the graphs

-83-

11th Grade

Key Concept: Real Number System

SCCCR Standards: Rewrite expressions involving simple radicals and rational exponents in different forms (A1.NRNS.1).


A1.NRNS.1: Evaluate

square roots of perfect

squares.

A1.NRNS.1: Evaluate

square roots of perfect

squares.

A1.NRNS.1: Understand

that the square root is the

inverse of squaring a

number.


how to square a number.


multiplication facts of whole

numbers with products up to

100.

It Is Essential for Students to Know: Students need to be able to recognize perfect squares.


• Evaluating square roots is used when using the Pythagorean theorem. For example, “Simon leans a 10 ft. ladder against the wall. The

distance from the bottom of the ladder to the wall is 8 ft. How far up on the wall is the ladder placed?”

-84-


11NRNS Square root

Inverse

Squaring

Square numbers

(multiply)

Determine square

root

Use cubes or tiles to form squares and count the number

of cubes or tiles

Use a checker board to illustrate the concept of “square”

Baking a cake in a square pan and cutting into

equal parts to demonstrate the concept of

“square”

Planting a garden in square shape

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