Year 8 in England

7th grade number sense

17 7th grade number sense skills, each with a worked example, free practice that checks every answer, and a printable worksheet. Start with a mixed review, or jump to the skill you need.

Mixed review

Ten questions drawn from every skill below.

Print a review worksheet Riddle puzzle on screen Bingo

Add and subtract integers

CCSS 7.NS.A.1England: KS3 NumberEngland: GCSE Foundation Number

Example

−9 − (−17) = ?

−9 − (−17) = −9 + 17
= 8

Answer: 8

Builds on: Negative numbers and absolute value

Leads to: Multiply and divide integers, Two-step equations

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Multiply and divide integers

CCSS 7.NS.A.2England: KS3 NumberEngland: GCSE Foundation Number

Example

−10 × 10 = ?

10 × 10 = 100
−10 × 10 = −100

Answer: -100

Builds on: Add and subtract integers, Times tables to 12 × 12

Leads to: Operations with negative fractions and decimals, Expand brackets (distributive property), Laws of exponents (indices), Matrices: operations and determinants

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Fractions as decimals

CCSS 7.NS.A.2.DEngland: Y6 Fractions (including decimals)England: KS3 Number

Example

Write 7/25 as a decimal.

7 ÷ 25 = 0.28

Answer: 0.28

Builds on: Divide decimals, Equivalent fractions

Leads to: Rational and irrational numbers, Recurring decimals to fractions, Terminating and repeating decimals from fractions

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Operations with negative fractions and decimals

CCSS 7.NS.A.1.DCCSS 7.NS.A.2.CCCSS 7.NS.A.3England: KS3 NumberEngland: GCSE Foundation Number

Example

Work out 3/5 + (−4/6). Give your answer as a fraction in simplest form.

3/5 + (−4/6) = 18/30 + (−20/30)
= −2/30
= −1/15

Answer: -1/15

Builds on: Multiply and divide integers, Add and subtract fractions with unlike denominators, Multiply fractions

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Add integers with number-line jumps

CCSS 7.NS.A.1.ACCSS 7.NS.A.1.BEngland: KS3 Number

Builds on: Negative numbers and absolute value, Read and place integers on a number line

Leads to: Add integers using sign rules

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Add integers using sign rules

CCSS 7.NS.A.1.BCCSS 7.NS.A.1.DEngland: KS3 NumberEngland: GCSE Foundation Number

Example

−56 + (−45) = ?

56 + 45 = 101
−56 + (−45) = −101

Answer: -101

Builds on: Add integers with number-line jumps

Leads to: Subtract integers by adding the opposite, Collect like terms with negative coefficients

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Subtract integers by adding the opposite

CCSS 7.NS.A.1.CEngland: KS3 NumberEngland: GCSE Foundation Number

Example

−3 − (−11) = ?

−3 − (−11) = −3 + 11
= 8

Answer: 8

Builds on: Add integers using sign rules

Leads to: Solve integer problems about temperature, height and money, Add and subtract negative decimals, Add and subtract negative fractions

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Solve integer problems about temperature, height and money

CCSS 7.NS.A.1CCSS 7.NS.A.3England: KS3 NumberEngland: GCSE Foundation Number

Example

At night a weather station recorded −11 °C. The next afternoon it recorded 10 °C. By how many degrees did the temperature rise?

10 − (−11) = 21

Answer: 21

Builds on: Subtract integers by adding the opposite

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Multiply integers, including three factors and powers

CCSS 7.NS.A.2.ACCSS 7.NS.A.2.CEngland: KS3 NumberEngland: GCSE Foundation Number

Example

5 × (−12) = ?

5 × 12 = 60
5 × (−12) = −60

Answer: -60

Builds on: Multiply and divide integers

Leads to: Predict the sign of a product or quotient, Order of operations with negative numbers, Multiply and divide negative fractions and decimals, Expand brackets with a negative multiplier

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Divide integers and find missing factors

CCSS 7.NS.A.2.BEngland: KS3 NumberEngland: GCSE Foundation Number

Example

−48 ÷ 8 = ?

48 ÷ 8 = 6
−48 ÷ 8 = −6

Answer: -6

Builds on: Multiply and divide integers

Leads to: Solve two-step equations with negative numbers, Solve one-step inequalities, including dividing by a negative

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Predict the sign of a product or quotient

CCSS 7.NS.A.2England: KS3 Number

Example

Without multiplying: is −4 × 6 × (−6) × (−1) positive or negative?

3 negative factors: odd → negative.

Answer: Negative

Builds on: Multiply integers, including three factors and powers

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Order of operations with negative numbers

CCSS 7.NS.A.3England: KS3 NumberEngland: GCSE Foundation Number

Example

12 + (−1) × (−8) = ?

(−1) × (−8) = 8
12 + 8 = 20

Answer: 20

Builds on: Multiply integers, including three factors and powers, Order of operations with exponents

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Add and subtract negative decimals

CCSS 7.NS.A.1.DEngland: KS3 Number

Example

−4.5 + (−5.9) = ?

−4.5 + (−5.9) = −10.4

Answer: -10.4

Builds on: Subtract integers by adding the opposite, Add and subtract decimals

Leads to: Multi-step problems with positive and negative numbers

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Add and subtract negative fractions

CCSS 7.NS.A.1.DEngland: KS3 Number

Example

Work out −8/11 + 7/11. Give a fraction in simplest form (or a whole number).

−8/11 + 7/11 = −1/11

Answer: -1/11

Builds on: Subtract integers by adding the opposite, Add and subtract fractions with unlike denominators

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Multiply and divide negative fractions and decimals

CCSS 7.NS.A.2.ACCSS 7.NS.A.2.BCCSS 7.NS.A.2.CEngland: KS3 Number

Example

Work out (−6/7) × (−5/7). Give a fraction in simplest form.

30/49

Answer: 30/49

Builds on: Multiply integers, including three factors and powers, Divide fractions by fractions

Leads to: Multi-step problems with positive and negative numbers

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Terminating and repeating decimals from fractions

CCSS 7.NS.A.2.DEngland: KS3 NumberEngland: GCSE Foundation Number

Example

Does 2/3 give a terminating or a repeating decimal?

3 = 3 → another prime factor: repeating
2 ÷ 3 = 0.666666…

Answer: Repeating

Builds on: Fractions as decimals

Leads to: Convert repeating decimals into fractions

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Multi-step problems with positive and negative numbers

CCSS 7.NS.A.3CCSS 7.EE.B.3England: KS3 NumberEngland: GCSE Foundation Number

Example

A diver is at −3 m. She descends 0.75 m every second for 4 seconds. What is her new depth, in m? (Give a negative number.)

4 × (−0.75) = −3
−3 + (−3) = −6

Answer: -6

Builds on: Multiply and divide negative fractions and decimals, Add and subtract negative decimals

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