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
Numbers in items must be nonnegative rational numbers. One-variable linear equations and inequalities. An equation or inequality should be given if a context is included. Inequalities are restricted to < or >. Lists of numbers should not use set notation.
No
Allowable
Sample Test Items (4)
Test Item # | Question | Difficulty | Type |
Sample Item 1 | An equation is shown. x + 5 = 14 Which of the values can be substituted for x to make the equation true?
|
N/A | MC: Multiple Choice |
Sample Item 2 | An equation is shown. What value of 3x makes the equation true? |
N/A | EE: Equation Editor |
Sample Item 3 | An inequality is shown. Select all the values of n that make the inequality true.
|
N/A | MS: Multiselect |
Sample Item 4 | Select the values of x that make each equation or inequality true.
|
N/A | MI: Matching Item |
Related Courses
Course Number1111 | Course Title222 |
1205010: | M/J Grade 6 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 - 2024, 2024 and beyond (current)) |
1205020: | M/J Accelerated Mathematics Grade 6 (Specifically in versions: 2014 - 2015, 2015 - 2020, 2020 - 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)) |
7812015: | Access M/J Grade 6 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2022, 2022 and beyond (current)) |
7912110: | Fundamental Explorations in Mathematics 1 (Specifically in versions: 2013 - 2015, 2015 - 2017 (course terminated)) |
Related Resources
Educational Games
Name | Description |
Solving Equations: Same Variable, Both Sides, One Solution | In this challenge game, you will be solving equations with variables on both sides. Each equation has a real solution. Use the "Teach Me" button to review content before the challenge. After the challenge, review the problems as needed. Try again to get all challenge questions right! Question sets vary with each game, so feel free to play the game multiple times as needed! Good luck! |
Timed Algebra Quiz | In this timed activity, students solve linear equations (one- and two-step) or quadratic equations of varying difficulty depending on the initial conditions they select. This activity allows students to practice solving equations while the activity records their score, so they can track their progress. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet. |
Algebra Four | In this activity, two students play a simulated game of Connect Four, but in order to place a piece on the board, they must correctly solve an algebraic equation. This activity allows students to practice solving equations of varying difficulty: one-step, two-step, or quadratic equations and using the distributive property if desired. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the Java applet. |
Formative Assessments
Name | Description |
Finding Solutions of Inequalities | Students are given three inequalities and asked to determine if any numbers from a given set are solutions. |
Solutions of Inequalities | Students are asked to explain what it means for a number to be a solution of an inequality. |
Solutions of Equations | Students are asked to explain what it means for a number to be a solution of an equation. |
Finding Solutions of Equations | Students are given three equations and asked to determine if any numbers from a given set are solutions. |
Lesson Plans
Name | Description |
Gather Data For Distribution by Programming an App | This lesson allow students to gather, calculate, and plot data using both computer code and mathematical equations. In this lesson students will create a pedometer app to demonstrate the understanding of algorithms, components (such as buttons, textboxes, sensors, etc.), and If/Then statements. This lesson uses algebraic equations and random data to access the needed components to store data in a spreadsheet. |
Data Sets Represented in Computers | This lesson shows how data can be represented by computers, in relation to everyday activities we may not be aware that we use computer. It gives an overview of graphing data by creating a histogram based on population data. Using the data collected, students will get a chance to hand write code to show what structure is needed for computers to collect, analyze and distribute such data. This lesson is lesson 1 of the Data Set and Deviation Statistics Unit and bridges statistical concepts of data collection, graphing and analysis with programming a computer using coding language while reinforcing foundational algebraic skills. |
How Much was Lunch? | This lesson explores using substitution to solve one-step equations. Each real world problems involves discussion and students are expected to support their solutions. |
Solving One-Step Equations Using Mental Math | In this lesson students will solve one-step equations using mental math and guess-and-check. Students will use number cubes to generate random numbers to test as solutions to the equations. |
Original Student Tutorials
Name | Description |
Dr. E. Quation Part 2: One Step Multiplication & Division Equations | Learn how to solve 1-step multiplication and division equations with Dr. E. Quation in Part 2 of this series of interactive tutorials. You'll also learn how to check your answers to make sure your answer is the solution to the equation. |
Dr. E. Quation Part 1: One Step Addition & Subtraction Equations | Learn how to solve and check one-step addition and subtraction equations with Dr. E. Quation as you complete this interactive tutorial. Click here to open Dr. E. Quation Part 2: One-Step Multiplication and Division Equations |
Perspectives Video: Expert
Name | Description |
Improving Hurricane Scales | Meteorologist, Michael Kozar, discusses the limitations to existing hurricane scales and how he is helping to develop an improved scale. Download the CPALMS Perspectives video student note taking guide. |
Problem-Solving Task
Name | Description |
Log Ride | Students are asked to solve an inequality in order to answer a real-world question. |
Teaching Idea
Name | Description |
True, False, and Open Sentences | "Students first explore arithmetic sentences to decide whether they are true or false. The lesson then introduces students to sentences that are neither true nor false but are algebraic equations, also called open sentences, such as x + 3 = 7 or 2 x = 12." from Math Solutions. |
Tutorials
Name | Description |
How to Test Solutions to Inequalities | Learn how to test if a certain value of a variable makes an inequality true in this tutorial. |
How to Test Solutions to Equations Using Substitution | Learn how to test if a certain value of a variable makes an equation true in this tutorial. |
How to evaluate an expression with variables | Learn how to evaluate an expression with variables using a technique called substitution (or "plugging in"). |
Video/Audio/Animations
Name | Description |
Why Do We Divide Both Sides? | This short video provides a clear explanation why we perform the same steps on each side of an equation when solving for the variable/unknown. |
Solving Simple Equations | This short video provides a clear explanation about the "why" of performing the same steps on each side of an equation when solving for the variable/unknown. |
Virtual Manipulative
Name | Description |
Pan Balance - Numbers | This tool helps students better understand that equality is a relationship and not an operational command to "find the answer." The applet features a pan balance that allows the student to input each half of an equation in the pans, which responds to the numerical expression's value by raising, lowering or balancing. |
Student Resources
Original Student Tutorials
Name | Description |
Dr. E. Quation Part 2: One Step Multiplication & Division Equations: | Learn how to solve 1-step multiplication and division equations with Dr. E. Quation in Part 2 of this series of interactive tutorials. You'll also learn how to check your answers to make sure your answer is the solution to the equation. |
Dr. E. Quation Part 1: One Step Addition & Subtraction Equations: | Learn how to solve and check one-step addition and subtraction equations with Dr. E. Quation as you complete this interactive tutorial. Click here to open Dr. E. Quation Part 2: One-Step Multiplication and Division Equations |
Educational Games
Name | Description |
Solving Equations: Same Variable, Both Sides, One Solution: | In this challenge game, you will be solving equations with variables on both sides. Each equation has a real solution. Use the "Teach Me" button to review content before the challenge. After the challenge, review the problems as needed. Try again to get all challenge questions right! Question sets vary with each game, so feel free to play the game multiple times as needed! Good luck! |
Timed Algebra Quiz: | In this timed activity, students solve linear equations (one- and two-step) or quadratic equations of varying difficulty depending on the initial conditions they select. This activity allows students to practice solving equations while the activity records their score, so they can track their progress. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet. |
Algebra Four: | In this activity, two students play a simulated game of Connect Four, but in order to place a piece on the board, they must correctly solve an algebraic equation. This activity allows students to practice solving equations of varying difficulty: one-step, two-step, or quadratic equations and using the distributive property if desired. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the Java applet. |
Problem-Solving Task
Name | Description |
Log Ride: | Students are asked to solve an inequality in order to answer a real-world question. |
Tutorials
Name | Description |
How to Test Solutions to Inequalities: | Learn how to test if a certain value of a variable makes an inequality true in this tutorial. |
How to Test Solutions to Equations Using Substitution: | Learn how to test if a certain value of a variable makes an equation true in this tutorial. |
How to evaluate an expression with variables: | Learn how to evaluate an expression with variables using a technique called substitution (or "plugging in"). |
Video/Audio/Animations
Name | Description |
Why Do We Divide Both Sides?: | This short video provides a clear explanation why we perform the same steps on each side of an equation when solving for the variable/unknown. |
Solving Simple Equations: | This short video provides a clear explanation about the "why" of performing the same steps on each side of an equation when solving for the variable/unknown. |
Virtual Manipulative
Name | Description |
Pan Balance - Numbers: | This tool helps students better understand that equality is a relationship and not an operational command to "find the answer." The applet features a pan balance that allows the student to input each half of an equation in the pans, which responds to the numerical expression's value by raising, lowering or balancing. |
Parent Resources
Problem-Solving Task
Name | Description |
Log Ride: | Students are asked to solve an inequality in order to answer a real-world question. |