General Information
Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.
Test Item Specifications
- starting temperature + change in temperature = final temperature
- final temperature – change in temperature = starting temperature
- final temperature – starting temperature = change in temperature
- starting temperature + change in temperature = final temperature
- final temperature – change in temperature = starting temperature
- final temperature – starting temperature = change in temperature
N/A
Neutral
Allowable
Sample Test Items (7)
Test Item # | Question | Difficulty | Type |
Sample Item 1 | A number line is shown. Use the Add Point tool to plot a point that is 14.5 units from 8 on the given number line.
|
N/A | GRID: Graphic Response Item Display |
Sample Item 2 | An expression is shown. What is the value of the expression? |
N/A | EE: Equation Editor |
Sample Item 3 | A number line is shown.
Jack knows that a + b = 0.
Which statement is true?
|
N/A | MC: Multiple Choice |
Sample Item 4 | An expression is shown. Kendrick is using number lines to find the value of the expression. His first two steps are shown. A. Use the Add Arrow tool to show the last two steps. B. Select the value of the expression. |
N/A | GRID: Graphic Response Item Display |
Sample Item 5 | An expression is shown. What is the value of the expression? |
N/A | EE: Equation Editor |
Sample Item 6 | The sum of a and b is c. The number line shows a and b.
Which statements about c are true?
|
N/A | MS: Multiselect |
Sample Item 7 | An expression is shown, where a < 0 and c > 0. a + b = c Drag the two points to the number line to show possible locations of a and b. |
N/A | GRID: Graphic Response Item Display |
Related Courses
Course Number1111 | Course Title222 |
1205020: | M/J Accelerated Mathematics Grade 6 (Specifically in versions: 2014 - 2015, 2015 - 2020, 2020 - 2022, 2022 - 2024, 2024 and beyond (current)) |
1205040: | M/J Grade 7 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 - 2024, 2024 and beyond (current)) |
1204000: | M/J Foundational Skills in Mathematics 6-8 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 - 2024, 2024 and beyond (current)) |
1200410: | Mathematics for College Success (Specifically in versions: 2014 - 2015, 2015 - 2022 (course terminated)) |
1200700: | Mathematics for College Algebra (Specifically in versions: 2014 - 2015, 2015 - 2022 (course terminated)) |
7812020: | Access M/J Grade 7 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2019, 2019 - 2022, 2022 and beyond (current)) |
7912115: | Fundamental Explorations in Mathematics 2 (Specifically in versions: 2013 - 2015, 2015 - 2017 (course terminated)) |
Related Resources
Educational Games
Name | Description |
Pinata Fever: A Visual Integer Sums Number Line Game | Practice adding and subtracting positive and negative numbers to intercept the descending piñatas and then whack them for candy. Come on, keep the party going! |
Integers Jeopardy Game | This interactive game has 4 categories: adding integers, subtracting integers, multiplying integers, and dividing integers. Students can play individually or in teams. |
Formative Assessments
Name | Description |
Using Positive and Negative Numbers in Context | This lesson unit is intended to help you assess how well students are able to understand and use directed numbers in context. It is intended to help identify and aid students who have difficulties in ordering, comparing, adding, and subtracting positive and negative integers. Particular attention is paid to the use of negative numbers on number lines to explore the structures:
|
Adding Integers | Students are asked to add integers using a number line. |
Rational Water Management | Students are asked to combine rational numbers, including fractions and decimals, and use the properties of operations to simplify calculations. |
Finding the Difference | Students are asked to find the difference between two integers using a number line. |
Rational Addition and Subtraction | Students are asked to rewrite a subtraction problem as an equivalent addition problem and explain the equivalence using a number line. |
Exploring Additive Inverse | Students are asked to describe an example of additive inverse and demonstrate the concept on a number line. |
Lesson Plans
Name | Description |
Run For Your Life! | Based on a student-focused scenario encouraging healthier lifestyles, students will perform a close and careful reading of an article encouraging active and healthy lifestyles. During the lesson, students will analyze data from Consumer Reports comparing and contrasting treadmills and elliptical exercisers. Using information gathered, students will compile data and persuade administrators to buy equipment that will align with the provided budget and fit in the given space. Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom. |
Using Positive and Negative Numbers in Context | This lesson unit is intended to help you assess how well students are able to understand and use directed numbers in context. It is intended to help identify and aid students who have difficulties in ordering, comparing, adding, and subtracting positive and negative integers. Particular attention is paid to the use of negative numbers on number lines to explore the following structures:
|
Discovering How to Subtract Rational Numbers Using the Additive Inverse | In this lesson, students will develop an understanding that opposite quantities combine to make zero-sum pairs and will learn how to subtract rational numbers using a horizontal number line and the additive inverse |
Add It Up with T-Charts | In this lesson, students will use T-charts as a strategy to add and subtract positive and negative numbers. |
Discovering Our Rules for Addition of Integers | In this lesson, students will develop an understanding of the rules for adding integers by using the absolute value of integers and number lines. |
Original Student Tutorial
Name | Description |
Amazing Adventures | Learn how to explain the meaning of additive inverse, identify the additive inverse of a given rational number, and justify your answer on a number line in this original tutorial. |
Problem-Solving Tasks
Name | Description |
Distances on the Number Line 2 | The purpose of this task is meant to reinforce students' understanding of rational numbers as points on the number line and to provide them with a visual way of understanding that the sum of a number and its additive inverse (usually called its "opposite") is zero. |
Comparing Freezing Points | In this task, students answer a question about the difference between two temperatures that are negative numbers. |
Operations on the Number Line | The purpose of this task is to help solidify students' understanding of signed numbers as points on a number line and to understand the geometric interpretation of adding and subtracting signed numbers. There is a subtle distinction between a fraction and a rational number. Fractions are always positive, and when thinking of the symbol ab as a fraction, it is possible to interpret it as a equal-sized pieces where b pieces make one whole. |
Teaching Idea
Name | Description |
What's Your Sign: Integer Addition | This video offers a quick and easy way for math students to add numbers with positive and negative signs by modelling with colored stickers. The teacher used red stickers for negative numbers, orange as a neutral, and green for positives in order to give the students a visual learning tool to help tackle the world of integer addition. |
Tutorials
Name | Description |
Adding and Subtracting Numbers in Different Formats | In this example, we will work with three numbers in different formats: a percent, a decimal, and a mixed number. |
Simplifying Expressions with Rational Numbers | In this tutorial, you will simplify expressions involving positive and negative fractions. |
Rational Number Word Problem with Decimals | This video demonstrates adding and subtracting decimals in the context of an overdrawn checking account. |
Substitution with negative numbers | Practice substituting positive and negative values for variables. |
Finding the absolute value as distance between numbers | In this video, we will find the absolute value as distance between rational numbers. |
Creating equivalent expressions with positive and negative numbers | This video will demonstrate how to create quivalent expressions with positive and negative numbers. |
Even More Negative Number Practice | This video uses the number line to find unknown values in subtraction statements with negative numbers. |
Adding Negative Numbers on Number Line Examples | This video asks you to select the model that matches the given expression. |
Negative Number Word Problem | Use a number line to solve a word problem that includes a negative number. |
Finding Initial Temperature from Temperature Changes | In this video, we figure out the temperature in Fairbanks, Alaska by adding and subtracting integers. |
Adding and Subtracting Fractions | This video demonstrates how to add and subtract negative fractions with unlike denominators. |
Adding Negative Numbers | This video demonstrates use of a number line and absolute value to add negative numbers. |
Adding Numbers with Different Signs | This video demonstrates use of a number line to add numbers with positive and negative signs. |
Subtracting a Negative = Adding a Positive | Find out why subtracting a negative number is the same as adding the absolute value of that number. |
Negative Number Practice | This video demonstrates adding and subtracting integers using a number line. |
Pre-Algebra - Commutative & Associative Properties of Addition | A look behind the fundamental properties of the most basic arithmetic operation, addition |
Adding Integers | Students will be able to see examples of addition of integers while watching a short video, and practice adding integers using an online quiz. |
Video/Audio/Animations
Name | Description |
Interpreting Integer Expressions on the Number Line | This video contains three examples of interpreting integer expressions in the context of a number line. |
Interpreting Negative Number Statements | Explore negative numbers to represent real world situations in this tutorial. |
Virtual Manipulative
Name | Description |
Math Match - Concepts Review Game | This interactive game allows students to review math concepts, including shapes, shape names, addition, multiplication, negative numbers, and equivalent expressions. |
Student Resources
Original Student Tutorial
Name | Description |
Amazing Adventures: | Learn how to explain the meaning of additive inverse, identify the additive inverse of a given rational number, and justify your answer on a number line in this original tutorial. |
Educational Game
Name | Description |
Integers Jeopardy Game: | This interactive game has 4 categories: adding integers, subtracting integers, multiplying integers, and dividing integers. Students can play individually or in teams. |
Problem-Solving Tasks
Name | Description |
Distances on the Number Line 2: | The purpose of this task is meant to reinforce students' understanding of rational numbers as points on the number line and to provide them with a visual way of understanding that the sum of a number and its additive inverse (usually called its "opposite") is zero. |
Comparing Freezing Points: | In this task, students answer a question about the difference between two temperatures that are negative numbers. |
Operations on the Number Line: | The purpose of this task is to help solidify students' understanding of signed numbers as points on a number line and to understand the geometric interpretation of adding and subtracting signed numbers. There is a subtle distinction between a fraction and a rational number. Fractions are always positive, and when thinking of the symbol ab as a fraction, it is possible to interpret it as a equal-sized pieces where b pieces make one whole. |
Tutorials
Name | Description |
Adding and Subtracting Numbers in Different Formats: | In this example, we will work with three numbers in different formats: a percent, a decimal, and a mixed number. |
Simplifying Expressions with Rational Numbers: | In this tutorial, you will simplify expressions involving positive and negative fractions. |
Rational Number Word Problem with Decimals: | This video demonstrates adding and subtracting decimals in the context of an overdrawn checking account. |
Substitution with negative numbers: | Practice substituting positive and negative values for variables. |
Finding the absolute value as distance between numbers: | In this video, we will find the absolute value as distance between rational numbers. |
Even More Negative Number Practice: | This video uses the number line to find unknown values in subtraction statements with negative numbers. |
Adding Negative Numbers on Number Line Examples: | This video asks you to select the model that matches the given expression. |
Negative Number Word Problem: | Use a number line to solve a word problem that includes a negative number. |
Finding Initial Temperature from Temperature Changes: | In this video, we figure out the temperature in Fairbanks, Alaska by adding and subtracting integers. |
Adding and Subtracting Fractions: | This video demonstrates how to add and subtract negative fractions with unlike denominators. |
Adding Negative Numbers: | This video demonstrates use of a number line and absolute value to add negative numbers. |
Adding Numbers with Different Signs: | This video demonstrates use of a number line to add numbers with positive and negative signs. |
Subtracting a Negative = Adding a Positive: | Find out why subtracting a negative number is the same as adding the absolute value of that number. |
Negative Number Practice: | This video demonstrates adding and subtracting integers using a number line. |
Pre-Algebra - Commutative & Associative Properties of Addition: | A look behind the fundamental properties of the most basic arithmetic operation, addition |
Adding Integers: | Students will be able to see examples of addition of integers while watching a short video, and practice adding integers using an online quiz. |
Parent Resources
Problem-Solving Tasks
Name | Description |
Distances on the Number Line 2: | The purpose of this task is meant to reinforce students' understanding of rational numbers as points on the number line and to provide them with a visual way of understanding that the sum of a number and its additive inverse (usually called its "opposite") is zero. |
Comparing Freezing Points: | In this task, students answer a question about the difference between two temperatures that are negative numbers. |
Operations on the Number Line: | The purpose of this task is to help solidify students' understanding of signed numbers as points on a number line and to understand the geometric interpretation of adding and subtracting signed numbers. There is a subtle distinction between a fraction and a rational number. Fractions are always positive, and when thinking of the symbol ab as a fraction, it is possible to interpret it as a equal-sized pieces where b pieces make one whole. |
Tutorial
Name | Description |
Adding Integers: | Students will be able to see examples of addition of integers while watching a short video, and practice adding integers using an online quiz. |