Experimental probability – Grade 7 math lesson
Lesson 18 of 21 in the Grade 7 math course
US version. US grades, US spelling and dollars ($). · UK Maths Department
A complete 45-minute lesson for grade 7 (ages 12–13) that runs on this page – at school or at home. Every answer is graded right away, with a worked explanation.
- Time
- 45 minutes + 20 min homework
- Grade
- Grade 7 (ages 12–13)
- You need
- Paper, a pencil and this page
- Graded
- Instantly, with explanations
For parents: how to use this lesson
You don't need to know this topic yourself. The lesson explains each step on screen, one tidy step at a time. Every answer is graded straight away with a worked explanation, so you never have to grade anything.
- Read what your child will learn and the big ideas together.
- Press Start the lesson below and sit with your child for the teaching and the worked examples (about 19 minutes).
- Let them do the practice on their own. They choose Getting started, On track or Challenge – start on On track and move up after a few right in a row.
- Finish with the exit ticket and the talk question: “If you flip a coin 10 times and get 7 heads, is the coin biased?”
- Later that day or the next day: the homework (20 minutes), then a practice test.
Watch out for
- Thinking a few trials prove a dice is unfair. Small samples vary: do many more trials.
- Expecting exactly the expected number every time. Expected is an average, not a promise.
Tip for home: Do a quick experiment with a dice and record results together.
What your child will learn
Learning goal: estimate probabilities from experiments and predict expected outcomes.
Success looks like
- I can calculate relative frequency.
- I can predict expected outcomes.
- I can decide whether something might be biased.
Key words
- experimental probability
- how often something happened as a fraction of the trials
- trial
- one go of an experiment
- expected
- the number you would predict
- fair
- all outcomes equally likely
What to have ready
- Paper and a pencil
- This page on a computer, tablet or phone
- For the hands-on part: Flip a coin 50 times, record the results and work out the relative frequency of heads after 10, 20 and 50 flips.
The big ideas (for the adult)
Relative frequency = number of times something happened ÷ number of trials. It estimates the probability.
The more trials, the better the estimate.
Expected number of outcomes = probability × number of trials.
The lesson, step by step
| Part | Time | How it is checked |
|---|---|---|
| Starter: quick recall | 5 min | Graded by Classfern |
| Teaching input | 10 min | Not assessed, self-checked |
| Worked examples and guided practice | 9 min | Not assessed, graded by Classfern |
| Independent practice | 15 min | Graded by Classfern |
| Closure and exit ticket | 6 min | Graded by Classfern, self-checked |
Starter, "your turn", practice and exit ticket are graded by Classfern. Worked examples and teaching are not assessed. The hands-on task and the reflection are self-assessed. Explanations in talk are judged by the parent and not recorded.
The lesson
It runs here on the page. No sign-up and no names – progress is kept only in this browser.
Homework and practice at home
20 minutes: 10 practice questions, 3 multiple-choice questions and 2 to remember from earlier work, then a short reflection. New questions every time, all graded instantly.
More practice
More Grade 7 math lessons
- Ratios
- Percent
- Proportional relationships
- Operations with integers
- Repeating decimals
- Evaluating expressions
- Simplifying expressions
- Expanding expressions
- Solving equations
- Inequalities
- Scale drawings and maps
- Angle relationships
- Area of triangles, parallelograms and trapezoids
- Circles: circumference and area
- Volume and surface area
- Cross sections of 3-D figures
- Probability
- Compound events
- Box plots and interquartile range
- Sampling and making inferences
Curriculum
Common Core State Standards 7.SP.C.6: “Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times.”
Common Core State Standards 7.SP.C.7.b: “Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies?”
Our lessons and questions are our own. They are not written or endorsed by any government department, testing agency or exam board.