Year 9 in England

8th grade number sense

15 8th 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

Scientific notation (standard form)

CCSS 8.EE.A.3CCSS 8.EE.A.4England: KS3 NumberEngland: GCSE Foundation NumberEngland: GCSE Higher Number

Example

Write 660 000 in scientific notation (standard form).

The point moves 5 places.
6.6 × 10⁵

Answer: 6.6 × 10⁵

Builds on: Whole-number exponents, Multiply and divide by 10, 100, 1000

Leads to: Write scientific notation as an ordinary number

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Square roots and cube roots

CCSS 8.EE.A.2CCSS 8.NS.A.2England: KS3 NumberEngland: GCSE Foundation Number

Example

What is √256?

16 × 16 = 256
16

Answer: 16

Builds on: Primes, squares and cubes

Leads to: Rational and irrational numbers, Simplify surds (radicals), Pythagoras' theorem, Spread: standard deviation

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Rational and irrational numbers

CCSS 8.NS.A.1CCSS 8.NS.A.2England: GCSE Higher Number

Example

Which of these numbers is irrational: √16 ; √49 ; √2 ; 1.25?

√2 cannot be written as a fraction: its decimal goes on forever without repeating.

Answer: √2

Builds on: Square roots and cube roots, Fractions as decimals

Leads to: Classify numbers as rational or irrational

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Write scientific notation as an ordinary number

CCSS 8.EE.A.3England: KS3 NumberEngland: GCSE Foundation Number

Example

Write 7 × 10³ as an ordinary number.

7 × 1000 = 7000

Answer: 7000

Builds on: Scientific notation (standard form)

Leads to: Write numbers in scientific notation (standard form)

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Write numbers in scientific notation (standard form)

CCSS 8.EE.A.3CCSS 8.EE.A.4England: KS3 NumberEngland: GCSE Foundation Number

Example

Write 16 000 in scientific notation (like 4.5 × 10^6).

Move the point 4 places: 1.6 × 10⁴

Answer: 1.6 × 10⁴

Builds on: Write scientific notation as an ordinary number

Leads to: Compare and order numbers in scientific notation, Multiply and divide in scientific notation

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Compare and order numbers in scientific notation

CCSS 8.EE.A.3England: KS3 NumberEngland: GCSE Foundation Number

Example

Which is larger: 8.9 × 10⁵ or 7.3 × 10⁶?

7.3 × 10⁶ is larger.

Answer: 7.3 × 10⁶

Builds on: Write numbers in scientific notation (standard form)

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Multiply and divide in scientific notation

CCSS 8.EE.A.4England: KS3 NumberEngland: GCSE Foundation Number

Example

Work out (4 × 10⁷) × (1 × 10³). Give the answer in scientific notation.

4 × 1 = 4
10⁷ × 10³ = 10¹⁰
4 × 10¹⁰

Answer: 4 × 10¹⁰

Builds on: Write numbers in scientific notation (standard form), Multiply powers with the same base

Leads to: Compare real quantities in scientific notation

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Compare real quantities in scientific notation

CCSS 8.EE.A.3CCSS 8.EE.A.4England: KS3 NumberEngland: GCSE Foundation Number

Example

A large hard drive holds 5 × 10⁵ bytes. A photo is 4 × 10³ bytes. How many photos fit on the drive?

5 ÷ 4 = 1.25
10⁵ ÷ 10³ = 10²
125

Answer: 125

Builds on: Multiply and divide in scientific notation

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Square roots of fractions and decimals

CCSS 8.EE.A.2England: KS3 NumberEngland: GCSE Foundation Number

Example

Find √(9/4).

√9 = 3, √4 = 2
3/2

Answer: 3/2

Builds on: Square roots and cube roots, Perfect squares and whole-number square roots

Leads to: Estimate square roots between whole numbers, Solve x² = p and x³ = p, Use Pythagoras to find the hypotenuse

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Cube roots, including negatives

CCSS 8.EE.A.2England: KS3 NumberEngland: GCSE Foundation Number

Example

Find ∛1000.

10 × 10 × 10 = 1000

Answer: 10

Builds on: Square roots and cube roots

Leads to: Solve x² = p and x³ = p

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Estimate square roots between whole numbers

CCSS 8.NS.A.2England: KS3 NumberEngland: GCSE Foundation Number

Example

√138 lies between which two consecutive whole numbers? Give the smaller one.

121 < 138 < 144
11 < √138 < 12

Answer: 11

Builds on: Square roots of fractions and decimals

Leads to: Order numbers including square roots and π

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Solve x² = p and x³ = p

CCSS 8.EE.A.2England: KS3 AlgebraEngland: GCSE Foundation Algebra

Example

Solve x² = 121. Give both solutions, separated by a comma.

x = ±√121
x = 11 or x = −11

Answer: x = -11 or x = 11

Builds on: Cube roots, including negatives, Square roots of fractions and decimals

Leads to: Find a missing radius or height from a volume

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Classify numbers as rational or irrational

CCSS 8.NS.A.1England: KS3 NumberEngland: GCSE Foundation Number

Example

Is −5 rational or irrational?

−5 can be written as a fraction: rational.

Answer: Rational

Builds on: Rational and irrational numbers

Leads to: Order numbers including square roots and π

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Convert repeating decimals into fractions

CCSS 8.NS.A.1England: KS3 NumberEngland: GCSE Higher Number

Example

Write 0.333… (3 repeating) as a fraction in simplest form.

10x − x = 3
9x = 3
x = 3/9 = 1/3

Answer: 1/3

Builds on: Terminating and repeating decimals from fractions

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Order numbers including square roots and π

CCSS 8.NS.A.2England: KS3 Number

Example

On a number line, √85 is between 9 and 10. Is it closer to 9 or to 10?

√85 ≈ 9.22
9

Answer: 9

Builds on: Estimate square roots between whole numbers, Classify numbers as rational or irrational

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