Substitution – Year 8 maths lesson

Lesson 22 of 35 in the Year 8 maths course

UK version. UK school years, UK spelling and pounds (£). · US Math Department

A complete 45-minute lesson for Year 8 (ages 12–13) 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 8 (ages 12–13)
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: “If x = −2, what is x² − 3x? Explain each step.”
Later that day or the next day: the homework (20 minutes), then a practice test.

Watch out for

Writing 3a as 34 when a = 4. Put in the multiplication sign: 3 × 4.
Squaring a negative without brackets. Write (−3)² = 9.

Tip for home: Use a formula to convert temperatures or cooking times together.

What your child will learn

We are learning to substitute numbers into expressions and formulae.

Success looks like

I can substitute into expressions.
I can use formulae.
I can substitute negative numbers.

Key words

substitute: replace a letter with a number
formula: a rule that links quantities
evaluate: work out the value
expression: terms joined by + or −

What to have ready

Paper and a pencil
This page on a computer, tablet or phone
For the hands-on part: Use a formula from real life, such as cooking time = 20 × mass + 20, and substitute different masses.

The big ideas (for the adult)

Substituting means replacing each letter with its number, then working it out.

Remember the hidden multiplication: if a = 4, then 3a = 3 × 4 = 12, not 34.

Take care with negatives and powers: if x = −3, then x² = 9 but −x² = −9. Use brackets when you substitute.

The lesson, step by step

45 minutes in 5 parts
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

All Year 8 maths lessons and tests · Maths Department

More Year 8 maths lessons

Curriculum

National Curriculum for England, Year 8: “substitute numerical values into formulae and expressions, including scientific formulae”

National Curriculum for England, Year 8: “understand and use standard mathematical formulae; rearrange formulae to change the subject”

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Our lessons and questions are our own. They are not written or endorsed by any government department, testing agency or exam board.