### Clarifications

**Examples of Opportunities for In-Depth Focus**

When students write equations of the form x + p = q and px = q to solve real-world and mathematical problems, they draw on meanings of operations that they are familiar with from previous grades’ work. They also begin to learn algebraic approaches to solving problems.

^{16}

^{16}For example, suppose Daniel went to visit his grandmother, who gave him $5.50. Then he bought a book costing $9.20 and had $2.30 left. To find how much money he had before visiting his grandmother, an algebraic approach leads to the equation x + 5.50 – 9.20 = 2.30. An arithmetic approach without using variables at all would be to begin with 2.30, then add 9.20, then subtract 5.50. This yields the desired answer, but students will eventually encounter problems in which arithmetic approaches are unrealistically difficult and algebraic approaches must be used.

**Subject Area:**Mathematics

**Grade:**6

**Domain-Subdomain:**Expressions & Equations

**Cluster:**Level 2: Basic Application of Skills & Concepts

**Cluster:**Reason about and solve one-variable equations and inequalities. (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

**Assessed:**Yes

**Assessment Limits :**

Numbers in items should not require students to perform operations with negative rational numbers or result in answers with negative rational numbers. Items must be one-step linear equations with one variable.**Calculator :**No

**Context :**Allowable

**Test Item #:**Sample Item 1**Question:**An equation is shown.

8x = 35

What is the value for x that makes the equation true?

**Difficulty:**N/A**Type:**EE: Equation Editor

**Test Item #:**Sample Item 2**Question:**Suzie buys a salad for $5.12 and is given $14.88 as change.Which equation represents the situation if ???? is the amount Suzie had before she bought the salad?

**Difficulty:**N/A**Type:**MC: Multiple Choice

**Test Item #:**Sample Item 3**Question:**This question has

**two**parts.Syrilla sells homemade scarves for $4 each.

**Part A.**Which equation could be used to find the number of scarves, x, Syrilla needs to sell in order to earn $200?**Part B.**How many scarves does Syrilla need to sell?**Difficulty:**N/A**Type:**MC: Multiple Choice

## Related Courses

## Related Access Points

## Related Resources

## Assessments

## Formative Assessments

## Lesson Plans

## Original Student Tutorials

## Problem-Solving Tasks

## Student Center Activity

## Tutorials

## Video/Audio/Animations

## Virtual Manipulative

## MFAS Formative Assessments

Students are asked to solve a real-world problem by writing and solving an equation.

Students are asked to solve a real-world problem by writing and solving an equation.

Students are asked to solve a real-world problem by writing and solving an equation.

Students are asked to solve a real-world problem by writing and solving an equation.

## Original Student Tutorials Science - Grades K-8

Use models to solve balance problems on a space station in this interactive, math and science tutorial.

## Original Student Tutorials Mathematics - Grades 6-8

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**

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.

## Student Resources

## Original Student Tutorials

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.

Type: Original Student Tutorial

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**

Type: Original Student Tutorial

Use models to solve balance problems on a space station in this interactive, math and science tutorial.

Type: Original Student Tutorial

## Problem-Solving Tasks

The purpose of this task is to give students an opportunity to solve a challenging multistep percentage problem that can be approached in several different ways. Students are asked to find the cost of a meal before tax and tip when given the total cost of the meal. The task can illustrate multiple standards depending on the prior knowledge of the students and the approach used to solve the problem.

Type: Problem-Solving Task

Students are asked to write and solve an equation in one variable to answer a real world question.

Type: Problem-Solving Task

In this task students are asked to write an equation to solve a real-world problem.

Type: Problem-Solving Task

Students are asked to write an equation with one variable in order to find the distance walked.

Type: Problem-Solving Task

## Student Center Activity

Students can practice answering mathematics questions on a variety of topics. With an account, students can save their work and send it to their teacher when complete.

Type: Student Center Activity

## Tutorials

Here's an introduction to basic algebraic equations of the form ax = b. Remember that you can check to see if you have the right answer by substituting it for the variable!

Type: Tutorial

Learn how to solve equations in one step by multiplying or dividing a number on both sides. These problems involve decimals and fractions.

Type: Tutorial

This video demonstrates how to write and solve a one-step addition equation.

Type: Tutorial

To find the value of a variable, you have to get it on one side of the equation alone. To do that, you'll need to do something to BOTH sides of the equation.

Type: Tutorial

This video provides a conceptual explanation of why one needs to divide both sides of an equation to solve for a variable.

Type: Tutorial

This lesson introduces students to linear equations in one variable, shows how to solve them using addition, subtraction, multiplication, and division properties of equalities, and allows students to determine if a value is a solution, if there are infinitely many solutions, or no solution at all. The site contains an explanation of equations and linear equations, how to solve equations in general, and a strategy for solving linear equations. The lesson also explains contradiction (an equation with no solution) and identity (an equation with infinite solutions). There are five practice problems at the end for students to test their knowledge with links to answers and explanations of how those answers were found. Additional resources are also referenced.

Type: Tutorial

The video describes how to multiply fractions and state the answer in lowest terms.

Type: Tutorial

Introduction to solving one variable multiplication equations of the form px = q.

Type: Tutorial

## Video/Audio/Animations

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.

Type: Video/Audio/Animation

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.

Type: Video/Audio/Animation

## Virtual Manipulative

This virtual manipulative allows the learners to solve simple linear equations through the use of a balance beam. Unit blocks and* x*-boxes are placed on the pans of a balance beam to balance it.

Type: Virtual Manipulative

## Parent Resources

## Problem-Solving Tasks

The purpose of this task is to give students an opportunity to solve a challenging multistep percentage problem that can be approached in several different ways. Students are asked to find the cost of a meal before tax and tip when given the total cost of the meal. The task can illustrate multiple standards depending on the prior knowledge of the students and the approach used to solve the problem.

Type: Problem-Solving Task

Students are asked to write and solve an equation in one variable to answer a real world question.

Type: Problem-Solving Task

In this task students are asked to write an equation to solve a real-world problem.

Type: Problem-Solving Task

Students are asked to write an equation with one variable in order to find the distance walked.

Type: Problem-Solving Task

## Tutorials

The video describes how to multiply fractions and state the answer in lowest terms.

Type: Tutorial

Introduction to solving one variable multiplication equations of the form px = q.

Type: Tutorial

## Virtual Manipulative

This virtual manipulative allows the learners to solve simple linear equations through the use of a balance beam. Unit blocks and* x*-boxes are placed on the pans of a balance beam to balance it.

Type: Virtual Manipulative