Ratios and Unit Rates
Tables, diagrams, and fair comparisons
Math workbook
Probability: Model Chance and Evaluate Risk: Chance models, conditional data and risk
Grades 9–12Level 4
About this book
Count carefully, check the condition, then judge the claim.
This workbook helps learners in grades 9–12 build chance models and read risk claims with care. Four modules move from model versus observed frequency, to trees and tables for combined events, to conditional probability and base rates, to expected value and responsible claims. A readiness check comes first. Each module then gives a plain explanation, worked examples, guided practice, independent practice, spaced review and a checkpoint. All data and stories are fictional. An explanatory answer key at the back gives each answer, why it works, a common error and a reteaching cue.
- Compare a chance model with real or simulated trials
- Use trees, tables and complements for compound events
- Choose the right denominator for conditional chances
- See why rare events can produce many false alarms
- Use expected value without treating it as a promise
For learners in grades 9–12 who can already work with fractions, percents, ratios and simple tables.
Look inside
What this book covers
Covered
In scope: sample spaces, relative frequency, simulation, complements, the addition rule, independent and dependent events, two-way tables, base rates, expected value, and absolute versus relative change, plus counting codes and mutually exclusive versus independent events.
Not covered
Not in scope: counting formulas for arrangements, binomial and normal distributions, and formal inference.
Before you start
Before you start, you should be comfortable with fractions, percents and ratios.
Things to have
Access: a calculator is fine.
Notice
Every data set and story is fictional. Nothing here is financial, medical or legal advice.
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: Readiness Check
Check the skills you need before you begin. If something feels tricky, an adult can help you start in the right place.
- Step 2: Concept
Read a short, clear explanation of the new idea and the words that go with it.
- Step 3: Worked Example
Watch the idea being used, one step at a time, in a worked example.
- Step 4: Guided Practice
Practice with prompts and help cues. The help gets smaller as you get stronger.
- Step 5: Independent Practice
Practice on your own with different kinds of questions, and explain your thinking.
- Step 6: Review
Look back at earlier learning so it stays strong, then check where to go next.
- Step 7: Answers and Explanations
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: Models and observed frequencyPages 5–14
- Module 2: Combine events with structurePages 15–24
- Module 3: Conditional probability and base ratesPages 25–34
- Module 4: Expected outcomes and responsible claimsPages 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, p. 53. More pages of step 5, Independent Practice.
- Extra practice, pp. 54–56
- Answers and explanations, pp. 57–66. Notes in this part are headed “Why”, “Common mistake” and “Help”.
Other books it mentions
Before this book
Percentages in Everyday Problems
Parts, wholes, change, and claims
Statistics: Describe and Compare Data
Displays, center, spread, and fair comparisons
After this book
Intro Statistics: Sampling and Inference
Study design, sampling variation, intervals and tests