Compound events – Grade 7 math lesson
Lesson 19 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: “Why do the probabilities on each set of branches add up to 1?”
- Later that day or the next day: the homework (20 minutes), then a practice test.
Watch out for
- Adding along branches instead of multiplying. Along: multiply. Between routes: add.
- Keeping the same probabilities when items are not replaced. Reduce the total by one on the second set of branches.
Tip for home: Work out the chances in a simple game with two dice.
What your child will learn
Learning goal: find probabilities of combined events with sample spaces and tree diagrams.
Success looks like
- I can list a sample space.
- I can use a tree diagram.
- I can deal with events without replacement.
Key words
- sample space
- a list of all possible outcomes
- tree diagram
- branches showing each stage of events
- independent
- one event does not affect the other
- without replacement
- not put back, so the next probability changes
What to have ready
- Paper and a pencil
- This page on a computer, tablet or phone
- For the hands-on part: Draw a tree diagram for picking two socks from a drawer, with and without putting the first back.
The big ideas (for the adult)
A sample space lists every possible combined outcome, for example a grid for two dice.
On a tree diagram, multiply along the branches to find the probability of one route; add the routes you need.
Without replacement, the second set of branches changes because there is one fewer item.
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
- Experimental probability
- Box plots and interquartile range
- Sampling and making inferences
Curriculum
Common Core State Standards 7.SP.C.8.a: “Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.”
Common Core State Standards 7.SP.C.8.b: “Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., "rolling double sixes"), identify the outcomes in the sample space which compose the event.”
Our lessons and questions are our own. They are not written or endorsed by any government department, testing agency or exam board.