Multiplying and Dividing Fractions
Models, meaning, and methods
Math workbook
Expressions and One-Variable Equations: Variables, equivalence, and balance
Grades 6–8Level 3
About this book
Turn words into algebra, keep both sides equal, and check it.
This workbook helps learners in grades 6–8 move from words and pictures to algebra. They define variables with units, write and evaluate expressions, and rewrite expressions with the distributive property and like terms. Then they solve one- and two-step equations by doing the same thing to both sides, and check every answer by substitution. The last module asks whether an answer makes sense in the story. Each module follows the same seven steps, from a readiness check to independent practice and review. An explanatory answer key at the back gives reasons, common errors and reteaching cues.
- Tape diagrams, tables and balance steps
- Worked examples with every step visible
- Spaced and cumulative review built in
- Error-analysis pages with student-style work
- Explanatory answer key for adults
For learners in grades 6–8 who are comfortable with fractions and negative numbers.
Look inside
What this book covers
Covered
In this book: variables, coefficients and constants; evaluating expressions, including squares; the distributive property; like terms; one- and two-step equations; equations with parentheses; checking answers in context.
Not covered
Not in this book: variables on both sides, inequalities and graphs.
Before you start
If fractions or negative numbers feel shaky, Multiplying and Dividing Fractions and Integer Operations: From Number Lines to Rules will help first.
Things to have
Use a pencil.
Notice
Pictures in this book are simplified learning models. Check answers with the explanations at the back of the book.
The steps in this book
- Step 1: Get Ready
Check the skills you need before you begin. If something feels tricky, an adult can help you start in the right place.
- Step 2: Learn It
Read a short, clear explanation of the new idea and the words that go with it.
- Step 3: See It
Watch the idea being used, one step at a time, in a worked example.
- Step 4: Try It Together
Practice with prompts and help cues. The help gets smaller as you get stronger.
- Step 5: On Your Own
Practice on your own with different kinds of questions, and explain your thinking.
- Step 6: Look Back
Look back at earlier learning so it stays strong, then check where to go next.
- Step 7: Check and Fix
Check your answers. Each answer explains why, names a common mistake, and shows how to fix it.
What is in the book
The modules
- Module 1: Expressions name quantitiesPages 5–14
- Module 2: Equivalent expressionsPages 15–24
- Module 3: Solve while preserving equalityPages 25–34
- Module 4: Model, solve, and critiquePages 35–44
Contents
- Readiness check, pp. 3–4. Before Module 1. Its table tells you where to start.
- Modules, pp. 5–44
- Checkpoints, pp. 14, 24, 34, 44. The last page of each module.
- Mixed review, pp. 45–48. Questions from across the book, mixed together.
- Exit check, pp. 49–50. A last check across the book.
- Reflect and repair, p. 51
- Try again, p. 52. Fresh questions like those in the exit check.
- Further practice, pp. 53–55. More pages of step 5, On Your Own.
- Extra practice, pp. 56–57
- Answers and explanations, pp. 58–68. Notes in this part are headed “Why”, “Common mistake” and “Help”.
Other books it mentions
Before this book
Integer Operations: From Number Lines to Rules
Number lines, counters, and patterns
Adding and Subtracting Fractions
Like Units, Common Units, Mixed Numbers
After this book
Linear Equations and Graphs
Tables, slopes, equations and systems