Year 7 maths: what KS3 adds
Year 7 is the first year of key stage 3. The maths does not start again. It keeps the number work from primary school, then adds two big ideas: numbers below zero, and letters that stand for numbers. This guide shows what changes, what stays, and what to do in the first term.
What KS3 is
Key stage 3 is Years 7, 8 and 9, for ages 11 to 14. The national curriculum sets out the maths for the whole key stage, not for each year. So schools choose their own order. Your child’s school may teach algebra in September, or after Christmas. Both are normal.
Ask the school for the Year 7 topic list. Most schools publish it. Then match it to the lessons on the England Year 7 maths page.
What is new in Year 7
| Strand | Primary school | Year 7 adds |
|---|---|---|
| Number | Whole numbers, decimals, fractions | Directed numbers: adding, subtracting, multiplying and dividing below zero |
| Decimals | To three places | Multiplying and dividing a decimal by a decimal |
| Factors | Multiples and factors | Highest common factor |
| Algebra | A simple formula | Expressions, like terms, expanding brackets, equations with two steps |
| Geometry | Angles in a triangle | Angles on parallel lines, constructions, transformations, congruent triangles |
| Measures | Area of rectangles and triangles | Area of a trapezium, volume with a formula |
| Statistics | The mean | Mode, median, range, frequency tables, scatter diagrams |
| Probability | Not taught | The chance of a simple event |
What stays the same
Multiplication, fractions, decimals and percentages do not go away. Year 7 uses them in every topic. A child who is slow with times tables finds algebra slow too, because every step has a multiplication in it.
If the primary work is shaky, fix that first. The Year 7 page starts with addition, subtraction, long multiplication and long division for this reason.
Worked example 1: directed numbers
Directed numbers are numbers with a sign, above or below zero.
The temperature is 4 degrees. It falls by 7 degrees. What is the temperature now?
4 − 7 = −3. The temperature is 3 degrees below zero.
If the answer is 3, the fall was taken off 7 and not off 4. Draw a number line, mark 4, and move 7 steps down.
Worked example 2: collecting like terms
Simplify 3a + 2b + 4a.
The a terms go together. 3a + 4a = 7a. The b term stays on its own. The answer is 7a + 2b.
The common slip is 9ab. You can only add things of the same kind. Three apples, two bananas and four apples is seven apples and two bananas.
Worked example 3: an equation with two steps
Solve 2x + 3 = 11.
Take 3 from both sides: 2x = 8.
Divide both sides by 2: x = 4.Check: 2 × 4 + 3 = 11.
Always check by putting the answer back in. It takes ten seconds and catches most mistakes.
Five questions to try
- −2 + 5
- −3 − 4
- Simplify 5x + 2x − 3x
- Solve x + 9 = 15
- Find the mean of 4, 6, 8 and 10
Answers
- 3
- −7
- 4x
- x = 6
- 7. Add them to get 28, then divide by 4.
What the wrong answers tell you
- −7 for question 1, or −1 or 1 for question 2. The signs are not secure. Use a number line for every question until they are.
- 4 for question 3. The letter was dropped. The answer is 4 lots of x.
- 24 for question 4. The 9 was added, not taken away. Do the opposite of what the equation does.
- 28 for question 5. The total was found, but not shared out. The mean is the total divided by how many numbers there are.
A plan for the first term
| Weeks | What to work on |
|---|---|
| 1 to 3 | Check the primary methods: long multiplication, long division, fractions |
| 4 to 6 | Directed numbers, with a number line |
| 7 to 9 | Decimals: ordering, adding, subtracting, multiplying |
| 10 to 12 | First algebra: expressions and like terms |
Three sittings a week of twenty minutes is enough. Follow the school’s order if it is different. Use this plan for the gaps.
When to go back a year
Go back if your child:
- cannot say the 6, 7, 8 and 9 times tables without counting,
- adds the tops and the bottoms of fractions,
- cannot line up decimals in columns.
The lessons for those ideas are on the Year 6 maths page. One week on the idea underneath saves a term of confusion on top of it.
This half term
Open Year 7 maths and work through three blocks:
- Larger addition, subtraction and multiplication, until the method is calm.
- Directed numbers, until a negative answer feels ordinary.
- Decimals to two places, until the columns after the point stay in order.
Each lesson is a short video, then questions on that idea. Your child can pause, rewind and try the step again. Algebra is further down the same page when you are ready for it.
Other year groups are on Maths. What the programme includes is on the pricing page.