Calculating with negative numbers – Year 8 maths lesson
Lesson 2 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: “Why does subtracting a negative number make the answer bigger?”
- Later that day or the next day: the homework (20 minutes), then a practice test.
Watch out for
- Using the multiplying sign rule for adding (−3 + −4 = 7). Adding two negatives moves further left: −7.
- Thinking 4 − (−2) = 2. Taking away a debt makes you richer: 4 + 2 = 6.
Tip for home: Talk about money owed and paid back, or floors above and below ground in a lift.
What your child will learn
We are learning to add, subtract, multiply and divide with negative numbers.
Success looks like
- I can add and subtract negative numbers.
- I can multiply and divide negative numbers.
- I can solve problems with negatives.
Key words
- negative number
- a number less than zero
- integer
- a whole number, positive or negative
- sign
- the + or − in front of a number
- product
- the answer to a multiplication
What to have ready
- Paper and a pencil
- This page on a computer, tablet or phone
- For the hands-on part: Use two colours of counters as positives and negatives; a pair of one of each makes zero.
The big ideas (for the adult)
Adding a negative number is the same as subtracting: 5 + (−3) = 2. Subtracting a negative is the same as adding: 5 − (−3) = 8.
When multiplying or dividing, two signs the same give a positive answer; two different signs give a negative answer.
Use a number line for adding and subtracting, and the sign rules for multiplying and dividing.
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 8 maths lessons
- Ordering numbers, decimals and negatives
- Prime factors, HCF and LCM
- Rounding and estimation
- Powers and roots
- Written methods with decimals
- BIDMAS: order of operations
- Calculating with fractions
- Units and measures
- Area of triangles, parallelograms and trapeziums
- Circles: circumference, area, arcs and sectors
- Angle facts and parallel lines
- Angles in polygons
- Transformations
- Quadrilaterals and symmetry
- Constructions and loci
- Averages and range
- Scatter graphs and correlation
- Probability
- Relative frequency and expected outcomes
- Algebraic notation
- Substitution
- Simplifying expressions
- Expanding brackets
- Solving linear equations
- Sequences and the nth term
- Straight-line graphs
- Graphs of functions
- Ratio
- One quantity as a fraction or percentage of another
- Percentages
- Direct and inverse proportion
- Speed, density and pressure
- Best buys and exchange rates
- Scale drawings and maps
Curriculum
National Curriculum for England, Year 8: “use the 4 operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative”
National Curriculum for England, Year 8: “use conventional notation for the priority of operations, including brackets, powers, roots and reciprocals”
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.