Multiplication
Groups, Arrays, and Facts
About this book
Know when to multiply, when to divide, and why it works.
This workbook helps learners in grades 6–8 multiply and divide fractions and mixed numbers with understanding. Three models carry the work: equal groups for a fraction of a quantity, area models for a fraction times a fraction, and number lines for “how many groups fit?” division. Learners then estimate, compute, check with the inverse operation, and decide what an answer means in a real task. Every module follows the same seven steps, from a readiness check to worked examples, guided and independent practice, spaced review, and an explanatory answer key for adults.
- Readiness check with routes to earlier skills
- Worked examples that link each model to the symbols
- Error analysis pages built on common mix-ups
- Spaced and cumulative review across all four modules
- Answer key with reasons, common errors and reteach cues
For learners in grades 6–8 who can find equivalent fractions and add fractions with unlike denominators.
Look inside
What this book covers
Covered
- This book is about multiplying and dividing fractions.
- You will find a fraction of a whole number, multiply a fraction by a fraction, divide by a fraction, share a fraction equally, and work with mixed numbers in real tasks.
Not covered
Not in this book: negative numbers, decimals, and ratio tables.
Before you start
Before you start, you should know what a fraction is, find equivalent fractions, multiply whole numbers, and add fractions with unlike denominators.
Things to have
Work in 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: A fraction of a quantityPages 5–14
- Module 2: Products on area modelsPages 15–24
- Module 3: How many groups fit?Pages 25–34
- Module 4: Mixed quantities and decisionsPages 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. 56–58
- Answers and explanations, pp. 59–68. Notes in this part are headed “Why”, “Common mistake”, “Help” and “Look for”.
Other books it mentions
After this book
Ratios and Unit Rates
Tables, diagrams, and fair comparisons
Percentages in Everyday Problems
Parts, wholes, change, and claims