Math lesson plan · 7th grade (Year 8 in England) · 60 minutes
Experimental probability and expected results
Statistics and probability
CCSS 7.SP.C.6CCSS 7.SP.C.7.BEngland: KS3 ProbabilityEngland: GCSE Foundation Probability
Objective and success criteria
Students will: Experimental probability and expected results.
- 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: Expected value; Compare experimental and theoretical probability
Materials: Squared paper for charts, Class survey data, Sticky notes for a live chart, Mini whiteboards and pens, Printed student sheet (below).
Warm-up · 6 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 picking a vowel from the letters of the word MATHS? Give a fraction in simplest form. → 1/5Prompt: List all the equally likely outcomes.
- The probability a spinner lands on blue is 0.6. What is the probability it does NOT land on blue? Give a decimal. → 0.4Prompt: An event either happens or it does not: the two probabilities add up to 1 (or 100%).
- What is the probability of rolling a prime number on a fair six-sided dice? Give a fraction in simplest form. → 1/2Prompt: List all the equally likely outcomes.
Hook · 6 min
- Take a quick class survey (favorite fruit, travel to school) and ask what the results tell us.
- Share the objective: Experimental probability and expected results. Read the success criteria together.
I do: model it · 12 min
- Work through the example out loud, saying why you do each step, not just what you do.
- Example: Jamal flips a drawing pin 50 times. It lands point up 10 times. What is the relative frequency of landing point up? Give a fraction in simplest form.
- Step 1: 10/50
- Step 2: = 1/5
- Answer: 1/5
- Pause after each step and ask a student to say what comes next.
We do: guided practice · 12 min
- Do these together. Students try each step on whiteboards before you reveal it.
- Use the hints as prompts rather than giving the answer.
- Priya flips a drawing pin 20 times. It lands point up 17 times. What is the relative frequency of landing point up? Give a fraction in simplest form. → 17/20Prompt: Relative frequency = number of times it happened ÷ number of trials.
- The probability of an event is 1/3. The experiment is done 15 times. How many times would you expect the event to happen? → 5Prompt: Expected number = probability × number of trials.
You do: independent practice · 17 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 · 7 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- Ben flips a drawing pin 40 times. It lands point up 31 times. What is the relative frequency of landing point up? Give a fraction in simplest form. → 31/40Prompt: Relative frequency = number of times it happened ÷ number of trials.
- The probability of an event is 1/6. The experiment is done 126 times. How many times would you expect the event to happen? → 21Prompt: Expected number = probability × number of trials.
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: Expected value; Compare experimental and theoretical probability.
- 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-7.
Free lesson plan from eurekami.com/lesson-plan-builder