Cluster 1: Understand solving equations as a process of reasoning and explain the reasoning. (Algebra 1 - Major Cluster) (Algebra 2 - Major Cluster)Archived

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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.

General Information
Number: MAFS.912.A-REI.1
Title: Understand solving equations as a process of reasoning and explain the reasoning. (Algebra 1 - Major Cluster) (Algebra 2 - Major Cluster)
Type: Cluster
Subject: Mathematics - Archived
Grade: 912
Domain-Subdomain: Algebra: Reasoning with Equations & Inequalities

Related Standards

This cluster includes the following benchmarks.

Related Access Points

This cluster includes the following access points.

Access Points

MAFS.912.A-REI.1.AP.1a
Solve equations with one or two variables and explain the process.
MAFS.912.A-REI.1.AP.2a
Solve simple rational and radical equations in one variable.

Related Resources

Vetted resources educators can use to teach the concepts and skills in this topic.

Formative Assessments

Does It Follow?:

Students are asked if one linear equation follows from another that is assumed to be true.

Type: Formative Assessment

Equation Logic:

Students are given a linear equation and are asked to solve the equation, explaining and justifying each step. Students are then asked to explain how confident they are in their solution.

Type: Formative Assessment

Justify the Process - 2:

Students are asked to justify each step in the process of solving an equation.

Type: Formative Assessment

Justify the Process - 1:

Students are asked to justify each step in the process of solving an equation.

Type: Formative Assessment

Lesson Plans

Sticks and Stones May Break My Bones:

In this Model Eliciting Activity, MEA, "Sticks and Stones May Break My Bones", teams of students work as forensic anthropologists and use equations to determine the height and gender of persons to whom a series of newly discovered bones may belong.

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.

Type: Lesson Plan

Radical Mathematical:

In this lesson students will solve radical equations, showing how extraneous solutions may arise. Students will solve radical equations that model real-world relationships.

Type: Lesson Plan

Method to My Mathness:

In this lesson, students will complete proof tables to justify the steps taken to solve multi-step equations. Justifications include mathematical properties and definitions..

Type: Lesson Plan

Rainbow Lab: Investigating the Visible Spectrum:

This activity will explore the connection between wavelength and frequency of colors in the visible light using web sites, hand-spectroscopes, spectral tubes and CSI type investigations.

Type: Lesson Plan

A Rational Representation:

Students will tackle a real-world situation regarding starting a business that requires a rational equation to evaluate the plan. Students will determine a method and set of steps for solving rational equations and then revisit the original scenario and solve using the new method they have synthesized. Students will also explore, through collaborative learning structures, the concept of extraneous solutions.

 

Type: Lesson Plan

Justly Justifying:

Students will review the properties used in solving simple equations through a quiz-quiz-trade activity. As a class, they will then associate these properties with individual steps in solving equations. The students will then participate in a Simultaneous Round Table to practice their justifications. Finish the lesson with a discussion on the different methods that students could use to acquire the correct answer. The following day, students will take a short quiz to identify misconceptions.

Type: Lesson Plan

Original Student Tutorials

Solving Rational Equations: Using Common Denominators:

Learn how to solve rational functions by getting common denominators in this interactive tutorial.

Type: Original Student Tutorial

Solving Rational Equations: Cross Multiplying:

Learn how to solve rational linear and quadratic equations using cross multiplication in this interactive tutorial.

Type: Original Student Tutorial

Justifiable Steps:

Learn how to explain the steps used to solve multi-step linear equations and provide reasons to support those steps with this interactive tutorial.

Type: Original Student Tutorial

Problem-Solving Tasks

Radical Equations:

To engage this task meaningfully, students must be aware of the convention that the square root of "a" for a positive number "a" refers to the positive square root of "a". The purpose of this task is to show students a situation where squaring both sides of an equation can result in an equation with more solutions than the original one.

Type: Problem-Solving Task

How does the solution change?:

The purpose of this task is to continue a crucial strand of algebraic reasoning begun at the middle school level. By asking students to reason about solutions without explicitly solving them, we get to the heart of understanding what an equation is and what it means for a number to be a solution to an equation. The equations are intentionally simple; the point of the task is not to test techniques in solving equations, but to encourage students to reason about them.

Type: Problem-Solving Task

Same Solutions?:

The purpose of this task is to provide an opportunity for students to reason about equivalence of equations. The instruction to give reasons that do not depend on solving the equation is intended to focus attention on the transformation of equations as a deductive step.

Type: Problem-Solving Task

Basketball:

This task provides a simple but interesting and realistic context in which students are led to set up a rational equation (and a rational inequality) in one variable, and then solve that equation/inequality for an unknown variable. It seems likely to be direct and relevant enough to be used for assessment purposes, either in part or in whole. Alternatively, this task could be used as a motivation for studying equations of this form in general, as while students might be able to solve the first part by trial and error, this becomes rather tedious for the later parts. Teachers might also find this task could be used to illustrate standard A-REI.A.1 if some more emphasis were placed on the reasoning behind the algebraic manipulations provided in the solutions.

Type: Problem-Solving Task

Tutorials

Simplifying Square Roots Containing Variables:


This video will demonstrate how to simplify square roots involving variables.

Type: Tutorial

Solving Radical Equations:

This video will demonstrate how to solve radical equations with additional practice problems.

Type: Tutorial

Solving a literal equation:

Students will learn to solve a literal equation. 

Type: Tutorial

Unit/Lesson Sequence

Sample Algebra 1 Curriculum Plan Using CMAP:

This sample Algebra 1 CMAP is a fully customizable resource and curriculum-planning tool that provides a framework for the Algebra 1 Course. The units and standards are customizable and the CMAP allows instructors to add lessons, worksheets, and other resources as needed. This CMAP also includes rows that automatically filter and display Math Formative Assessments System tasks, E-Learning Original Student Tutorials and Perspectives Videos that are aligned to the standards, available on CPALMS.

Learn more about the sample Algebra 1 CMAP, its features and customizability by watching the following video:

Using this CMAP

To view an introduction on the CMAP tool, please .

To view the CMAP, click on the "Open Resource Page" button above; be sure you are logged in to your iCPALMS account.

To use this CMAP, click on the "Clone" button once the CMAP opens in the "Open Resource Page." Once the CMAP is cloned, you will be able to see it as a class inside your iCPALMS My Planner (CMAPs) app.

To access your My Planner App and the cloned CMAP, click on the iCPALMS tab in the top menu.

All CMAP tutorials can be found within the iCPALMS Planner App or at the following URL: http://www.cpalms.org/support/tutorials_and_informational_videos.aspx

Type: Unit/Lesson Sequence

Student Resources

Vetted resources students can use to learn the concepts and skills in this topic.

Original Student Tutorials

Solving Rational Equations: Using Common Denominators:

Learn how to solve rational functions by getting common denominators in this interactive tutorial.

Type: Original Student Tutorial

Solving Rational Equations: Cross Multiplying:

Learn how to solve rational linear and quadratic equations using cross multiplication in this interactive tutorial.

Type: Original Student Tutorial

Justifiable Steps:

Learn how to explain the steps used to solve multi-step linear equations and provide reasons to support those steps with this interactive tutorial.

Type: Original Student Tutorial

Problem-Solving Tasks

Radical Equations:

To engage this task meaningfully, students must be aware of the convention that the square root of "a" for a positive number "a" refers to the positive square root of "a". The purpose of this task is to show students a situation where squaring both sides of an equation can result in an equation with more solutions than the original one.

Type: Problem-Solving Task

How does the solution change?:

The purpose of this task is to continue a crucial strand of algebraic reasoning begun at the middle school level. By asking students to reason about solutions without explicitly solving them, we get to the heart of understanding what an equation is and what it means for a number to be a solution to an equation. The equations are intentionally simple; the point of the task is not to test techniques in solving equations, but to encourage students to reason about them.

Type: Problem-Solving Task

Same Solutions?:

The purpose of this task is to provide an opportunity for students to reason about equivalence of equations. The instruction to give reasons that do not depend on solving the equation is intended to focus attention on the transformation of equations as a deductive step.

Type: Problem-Solving Task

Tutorials

Simplifying Square Roots Containing Variables:


This video will demonstrate how to simplify square roots involving variables.

Type: Tutorial

Solving Radical Equations:

This video will demonstrate how to solve radical equations with additional practice problems.

Type: Tutorial

Solving a literal equation:

Students will learn to solve a literal equation. 

Type: Tutorial

Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this topic.

Problem-Solving Tasks

Radical Equations:

To engage this task meaningfully, students must be aware of the convention that the square root of "a" for a positive number "a" refers to the positive square root of "a". The purpose of this task is to show students a situation where squaring both sides of an equation can result in an equation with more solutions than the original one.

Type: Problem-Solving Task

How does the solution change?:

The purpose of this task is to continue a crucial strand of algebraic reasoning begun at the middle school level. By asking students to reason about solutions without explicitly solving them, we get to the heart of understanding what an equation is and what it means for a number to be a solution to an equation. The equations are intentionally simple; the point of the task is not to test techniques in solving equations, but to encourage students to reason about them.

Type: Problem-Solving Task

Same Solutions?:

The purpose of this task is to provide an opportunity for students to reason about equivalence of equations. The instruction to give reasons that do not depend on solving the equation is intended to focus attention on the transformation of equations as a deductive step.

Type: Problem-Solving Task