Math lesson plan · 8th grade (Year 9 in England) · 45 minutes
Two-way tables
Statistics and probability
CCSS 8.SP.A.4England: KS3 StatisticsEngland: GCSE Foundation Statistics
Objective and success criteria
Students will: Two-way tables.
- I can answer questions on today's skill on my own, without help.
- I can explain each step and say why it works.
- I can check my answer and spot a mistake.
Before and after
Needs first: Probability of simple events
Leads to: Conditional probability and independence; Relative frequencies in two-way tables; Joint and conditional relative frequencies in two-way tables
Materials: Squared paper for charts, Class survey data, Sticky notes for a live chart, Mini whiteboards and pens, Printed student sheet (below).
Warm-up · 5 min
- Quick retrieval from earlier learning (Probability of simple events). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- What is the probability of rolling an even number on a fair six-sided dice? Give a fraction in simplest form. → 1/2Prompt: List all the equally likely outcomes.
- The probability a spinner lands on blue is 0.75. What is the probability it does NOT land on blue? Give a decimal. → 0.25Prompt: An event either happens or it does not: the two probabilities add up to 1 (or 100%).
- What is the probability of rolling a number greater than 4 on a fair six-sided dice? Give a fraction in simplest form. → 1/3Prompt: List all the equally likely outcomes.
Hook · 5 min
- Take a quick class survey (favorite fruit, travel to school) and ask what the results tell us.
- Share the objective: Two-way tables. Read the success criteria together.
I do: model it · 10 min
- Work through the example out loud, saying why you do each step, not just what you do.
- Example: A two-way table: Year 7 — cats 8, dogs 7; Year 8 — cats 9, dogs 18. How many students are in the table altogether?
- Step 1: 8 + 7 + 9 + 18 = 42
- Answer: 42
- Pause after each step and ask a student to say what comes next.
We do: guided practice · 10 min
- Do these together. Students try each step on whiteboards before you reveal it.
- Use the hints as prompts rather than giving the answer.
- A two-way table: Year 7 — cats 16, dogs 12; Year 8 — cats 11, dogs 9. How many students are in the table altogether? → 48Prompt: Find the row or column you need.
- Year 7 — cats 11, dogs 6; Year 8 — cats 11, dogs 12. A Year 7 student is picked at random. What is the probability they prefer cats? Give a fraction in simplest form. → 11/17Prompt: Only look at the Year 7 row.
You do: independent practice · 10 min
- Students work on the student sheet. Circulate and check the first two answers of every student early.
- Students who finish: write a question of their own for a partner, with the answer.
The 8 questions are on the student sheet below, with answers in the key.
Exit ticket · 5 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- Year 7 — cats 14, dogs 11; Year 8 — cats 6, dogs 6. A Year 7 student is picked at random. What is the probability they prefer cats? Give a fraction in simplest form. → 14/25Prompt: Only look at the Year 7 row.
- A two-way table: Year 7 — cats 7, dogs 17; Year 8 — cats 17, dogs 20. How many students are in the table altogether? → 61Prompt: Find the row or column you need.
Watch out for
- Forgetting to put data in order before finding the median.
- Reading a bar's height wrongly when the scale goes up in 2s or 5s.
Support and stretch
Support
- Review first: Probability of simple events.
- Use concrete materials: squared paper for charts.
- Give the first step of each question, or a partly worked example to finish.
- Pair with a confident partner for the guided practice.
Stretch
- Move on to: Conditional probability and independence; Relative frequencies in two-way tables; Joint and conditional relative frequencies in two-way tables.
- Explain a common mistake in writing and how to fix it.
- Write a word problem that uses today's skill, then solve a partner's.
Homework and more practice
Free online practice with hints and printable worksheets for this skill: eurekami.com/math/grade-8.
Free lesson plan from eurekami.com/lesson-plan-builder