**Subject Area:**Mathematics

**Grade:**912

**Domain-Subdomain:**Algebra: Reasoning with Equations & Inequalities

**Cluster:**Level 3: Strategic Thinking & Complex Reasoning

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

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.

**Date Adopted or Revised:**02/14

**Date of Last Rating:**02/14

**Status:**State Board Approved - Archived

**Assessed:**Yes

**Assessment Limits :**

Items will not require the student to recall names of properties from memory.**Calculator :**

Neutral**Clarification :**

Students will complete an algebraic proof of solving a linear equation.Students will construct a viable argument to justify a solution method

**Stimulus Attributes :**

Items should be set in a mathematical context. Items may use function notation.Items should be linear equations in the form of ax + b = c, a(bx + c) = d, ax + b = cx + d, or a(bx + c) = d(ex + f), where a, b, c, d, e, and f are rational numbers. Equations may be given in forms that are equivalent to these.

Coefficients may be a rational number or a variable that represents any real number.

Items should not require more than four procedural steps to reach a solution.

**Response Attributes :**

Items may ask the student to complete steps in a viable argument.Items should not ask the student to provide the solution.

**Test Item #:**Sample Item 1**Question:**Some of the steps in Raya's solution to 2.5(6.25x +0.5) = 11 are shown.

Select the correct reason for line 4 of Raya's solution.

**Difficulty:**N/A**Type:**SHT: Selectable Hot Text

## Related Courses

## Related Access Points

## Related Resources

## Formative Assessments

## Lesson Plans

## Original Student Tutorial

## Problem-Solving Tasks

## Tutorial

## Unit/Lesson Sequence

## STEM Lessons - Model Eliciting Activity

Students will reaffirm their knowledge about linear equations. Will be able to apply the concept to real life situations.

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.

## MFAS Formative Assessments

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

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.

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

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

## Original Student Tutorials Mathematics - Grades 9-12

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

## Student Resources

## Original Student Tutorial

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

The purpose of this task is to continue a crucial strand of algebraic reasoning begun at the middle school level (e.g, 6.EE.5). By asking students to reason about solutions without explicitly solving them, we get at 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 very simple; the point of the task is not to test technique in solving equations, but to encourage students to reason about them.

Type: Problem-Solving Task

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

## Tutorial

## Parent Resources

## Problem-Solving Tasks

The purpose of this task is to continue a crucial strand of algebraic reasoning begun at the middle school level (e.g, 6.EE.5). By asking students to reason about solutions without explicitly solving them, we get at 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 very simple; the point of the task is not to test technique in solving equations, but to encourage students to reason about them.

Type: Problem-Solving Task

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