Decimals
Place Value, Compare, and Calculate
About this book
Find the whole first. Then every percent makes sense.
Percentages are everywhere: sale tags, survey results, recipe changes and headlines. This workbook shows learners how to read them carefully. Each module starts with a hundred grid, bar or tape model, then moves to equations and multipliers. Learners convert between fractions, decimals and percents, find a percent of a quantity, work out percent change, markups and successive discounts, recover an original amount, and find percent error. Every module follows the same steps, from a skills check to error analysis and review. The key at the back explains each answer and names common mistakes.
- Name the reference whole before you calculate
- Estimate with 10%, 5% and 1%, then find exact values
- See why +20% then −20% does not return to the start
- Undo a discount by dividing by the remaining multiplier
- Check percent claims in fictional surveys and posters
For learners in grades 6–8 who can already use ratio tables, multiply decimals and find equivalent fractions.
Look inside
What this book covers
Covered
- This book is about percentages in everyday problems.
- You will learn to name the whole, change between fractions, decimals and percents, find a percent of an amount, work out percent change, find an original amount when you know only part of it, and work with markups and percent error.
Not covered
Not in this book: interest over many years, loans and probability.
Before you start
Before this book: you should be able to use ratio tables, multiply and divide decimals, and find equivalent fractions.
Things to have
- Work in pencil.
- You may check with a calculator after you have tried on paper.
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: One whole, one hundred partsPages 5–14
- Module 2: Find a percentage amountPages 15–24
- Module 3: Increase, decrease, and sequencePages 25–34
- Module 4: Recover and evaluate the wholePages 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. 53–54. More pages of step 5, On Your Own.
- Extra practice, p. 55
- Answers and explanations, pp. 56–64. Notes in this part are headed “Why”, “Common mistake” and “Help”.
Other books it mentions
Before this book
Ratios and Unit Rates
Tables, diagrams, and fair comparisons
Fractions
Parts, Sets, and Number Lines
After this book
Money skills workbook
Personal Finance: Credit, Interest, and Borrowing Costs
Compare Borrowing Offers by Total Cost