Systematic listing and counting – Year 10 maths lesson
Lesson 1 of 37 in the Year 10 maths course
UK version. UK school years, UK spelling and pounds (£). · US Math Department
A complete 45-minute lesson for Year 10 (ages 14–15) that runs on this page – at school or at home. Every answer is marked straight away, with a worked explanation.
- Time
- 45 minutes + 20 min homework
- Year
- Year 10 (ages 14–15)
- You need
- Paper, a pencil and this page
- Marked
- 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 marked straight away with a worked explanation, so you never have to mark 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: “How many 3-digit codes can be made from the digits 1 to 5 with no repeats? How do you know?”
- Later that day or the next day: the homework (20 minutes), then a practice test.
Watch out for
- Listing in a random order and missing some. Fix one choice at a time and list all the others.
- Adding the choices instead of multiplying. Draw a tree: each starter branches into every main.
Tip for home: Count the possible combinations of outfits or meals at home.
What your child will learn
We are learning to list outcomes systematically and use the product rule for counting.
Success looks like
- I can list outcomes systematically.
- I can use the product rule.
- I can count arrangements without repeats.
Key words
- outcome
- one possible result
- systematic
- in a careful order
- product rule
- multiply the number of choices at each step
- arrangement
- an order of items
What to have ready
- Paper and a pencil
- This page on a computer, tablet or phone
- For the hands-on part: List all the outfits you can make from 3 tops and 2 pairs of trousers.
The big ideas (for the adult)
Listing systematically means working in an order so nothing is missed or repeated: fix the first choice, list all the second choices, then move on.
The product rule: if there are 3 starters and 4 mains, there are 3 × 4 = 12 different meals.
If items cannot be repeated, the number of choices goes down at each step: 5 × 4 × 3 ways to fill three places from five people.
The lesson, step by step
| Part | Time | How it is checked |
|---|---|---|
| Starter: quick recall | 5 min | Marked by Classfern |
| Teaching input | 10 min | Not assessed, self-checked |
| Worked examples and guided practice | 9 min | Not assessed, marked by Classfern |
| Independent practice | 15 min | Marked by Classfern |
| Plenary and exit ticket | 6 min | Marked by Classfern, self-checked |
Starter, "your turn", practice and exit ticket are marked 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 marked instantly.
More practice
More Year 10 maths lessons
- Standard form
- Laws of indices
- Surds
- Fractions, decimals and recurring decimals
- Circles: circumference, area, arcs and sectors
- Volume and surface area
- Pythagoras' theorem
- Trigonometry: SOH CAH TOA
- Transformations
- Similarity and congruence
- Vectors
- Circle theorems
- Bearings
- 3-D shapes, plans and elevations
- Quartiles, box plots and spread
- Histograms
- Pie charts and time series graphs
- Scatter graphs and correlation
- Sampling
- Combined events and tree diagrams
- Simplifying expressions
- Expanding brackets
- Factorising
- Solving linear equations
- Inequalities
- Sequences and the nth term
- Straight-line graphs
- Simultaneous equations
- Quadratic equations
- Functions
- Graphs of functions
- Algebraic proof and identities
- Growth and decay
- Direct and inverse proportion
- Scale drawings and maps
- Rates of change from graphs
Curriculum
National Curriculum for England, Year 10: “apply systematic listing strategies, {including use of the product rule for counting}”
GCSE subject content N5: “apply systematic listing strategies including use of the product rule for counting”
Contains public sector information licensed under the Open Government Licence v3.0.
Our lessons and questions are our own. They are not written or endorsed by any government department, testing agency or exam board.