Unit 3: Equations and Inequalities

Students write and solve equations of the forms p(x+q)=r and px+q=r and inequalities of the forms px+q>r and p(x+q)<r, building on grade 6 work with one-step equations.

Worksheets

Every sheet has an answer key. Free to print, no login.

Unit

📝 Worksheet ✅ Answer guide

Concept

📝 Worksheet ✅ Answer key

Practice

Set 1

📝 Worksheet ✅ Answer key

Set 2

📝 Worksheet ✅ Answer key

Advanced

Set 1

📝 Worksheet ✅ Answer key

Set 2

📝 Worksheet ✅ Answer key

What this unit covers

A Representing Situations of the Form p(x+q)=r and px+q=r · 5 lessons

Goals

• Create diagrams and equations in the form p(x+q)=r and px+q=r to represent situations.

Lessons

1. Relationships between Quantities
2. Reasoning about Contexts with Tape Diagrams
3. Reasoning about Equations with Tape Diagrams
4. Reasoning about Equations and Tape Diagrams (Part 1)
5. Reasoning about Equations and Tape Diagrams (Part 2)

B Solving Equations of the Form p(x+q)=r and px+q=r and Problems That Lead to Those Equations · 6 lessons

Goals

• Solve equations of the form p(x+q)=r and px+q=r, including those that involve fractions, decimals, and negative numbers, and explain the solution method.

Lessons

1. Reasoning about Solving Equations (Part 1)
2. Reasoning about Solving Equations (Part 2)
3. Dealing with Negative Numbers
4. Different Options for Solving One Equation
5. Using Equations to Solve Problems
6. Solving Problems about Percent Increase or Decrease

C Inequalities · 6 lessons

Goals

• Draw and label a graph on a number line that represents all the solutions to an inequality.
• Solve an inequality of the form px+q>r or px+q<r or p(x+q)>r or p(x+q)<r including any of the four inequality symbols, <, >, ≤, or ≥.

Lessons

1. Writing and Graphing Inequalities
2. Solutions of Inequalities
3. Finding Solutions to Inequalities in Context
4. Efficiently Solving Inequalities
5. Interpreting Inequalities
6. Modeling with Inequalities

D Let’s Put It to Work · 1 lesson

Lessons

1. Using Equations to Solve for Unknown Angles (Optional)

Helpful to know first

The curriculum says this unit builds on these.

Grade 6 Accelerated · Unit 4 Equations and Expressions

Open unit →