Year 7 in England
6th grade number sense
23 6th 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.
Greatest common factor and least common multiple
CCSS 6.NS.B.4England: Y6 NumberEngland: KS3 NumberEngland: GCSE Foundation Number
Example
Find the greatest common factor (highest common factor) of 88 and 55.
- 88 = 11 × 8
- 55 = 11 × 5
- 8 and 5 share no common factor, so the GCF is 11.
Answer: 11
Prime factorisation
CCSS 6.NS.B.4England: KS3 NumberEngland: GCSE Foundation NumberEngland: 11+ Number
Example
Which is 48 written as a product of prime factors?
- Factor tree: 48 → 2 × 2 × 2 × 2 × 3
- 2⁴ × 3
Answer: 2⁴ × 3
Negative numbers and absolute value
CCSS 6.NS.C.5CCSS 6.NS.C.6CCSS 6.NS.C.7England: Y5 Number and place valueEngland: Y6 NumberEngland: KS3 Number
Example
The temperature is −3 °C at noon and −14 °C at night. By how many degrees did it fall?
- −3 − (−14) = 11
Answer: 11
Whole-number exponents
CCSS 6.EE.A.1England: KS3 NumberEngland: GCSE Foundation Number
Example
Evaluate 2⁶.
- 2 × 2 × 2 × 2 × 2 × 2 = 64
Answer: 64
Opposite numbers and zero
CCSS 6.NS.C.6.AEngland: KS3 Number
Example
Simplify −(−(−(−9))).
- The number has 4 minus signs.
- An even number of minus signs gives 9.
Answer: 9
Read and place integers on a number line
CCSS 6.NS.C.6.CEngland: KS3 Number
Compare integers, including two negatives
CCSS 6.NS.C.7.ACCSS 6.NS.C.7.BEngland: KS3 Number
Example
Choose the sign: −12 __ −1
- −12 < −1
Answer: <
Builds on: Read and place integers on a number line
Leads to: Put integers in order, Work with absolute value
Put integers in order
CCSS 6.NS.C.7.AEngland: KS3 Number
Example
Winter morning temperatures: Montreal −5 °C, Helsinki −3 °C, Reykjavik −19 °C, Anchorage −20 °C. Which city is coldest?
- The least temperature is −20 °C: Anchorage.
Answer: Anchorage
Builds on: Compare integers, including two negatives
Work with absolute value
CCSS 6.NS.C.7.CCCSS 6.NS.C.7.DEngland: KS3 Number
Example
|2| + |−15| = ?
- |2| = 2, |−15| = 15
- 2 + 15 = 17
Answer: 17
Distance between two integers
CCSS 6.NS.C.8CCSS 7.NS.A.1.CEngland: KS3 Number
Example
A drone hovers at 31 m above sea level and a submarine robot sits at 22 m below sea level (−22 m). What is the vertical distance between them, in metres?
- 31 − (−22) = 31 + 22 = 53
Answer: 53
Describe real situations with positive and negative numbers
CCSS 6.NS.C.5England: KS3 Number
Example
Write an integer for this: a team loses 188 points.
- It is negative: −188.
Answer: -188
Builds on: Opposite numbers and zero
Test divisibility by 2, 3, 4, 5, 6, 9 and 10
CCSS 6.NS.B.4England: Y5 Multiplication and divisionEngland: KS3 Number
Example
Is 930 divisible by 3?
- 930 ÷ 3 = 310, so yes.
Answer: Yes
Builds on: Factors, multiples, primes
Tell prime numbers from composite numbers
CCSS 4.OA.B.4England: Y5 Multiplication and divisionEngland: KS3 Number
Example
Is 61 prime or composite?
- 61 has no factors except 1 and 61: prime.
Answer: Prime
Find every factor using factor pairs
CCSS 4.OA.B.4CCSS 6.NS.B.4England: Y5 Multiplication and divisionEngland: KS3 Number
Example
How many factors does 24 have?
- 1 × 24, 2 × 12, 3 × 8, 4 × 6
- Factors: 1, 2, 3, 4, 6, 8, 12, 24. That is 8 factors.
Answer: 8
Builds on: Factors, multiples, primes
Write a prime factorisation using powers
CCSS 6.NS.B.4CCSS 6.EE.A.1England: KS3 NumberEngland: GCSE Foundation Number
Example
Write 45 as a product of prime factors in index form (for example 2^3 × 5).
- 3 × 3 × 5
- = 3² × 5
Answer: 3² × 5
Builds on: Prime factorisation
Greatest common factor of two or three numbers
CCSS 6.NS.B.4England: KS3 NumberEngland: GCSE Foundation Number
Example
Find the GCF (highest common factor) of 24 and 15.
- Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
- Factors of 15: 1, 3, 5, 15
- GCF = 3
Answer: 3
Least common multiple of two or three numbers
CCSS 6.NS.B.4England: KS3 NumberEngland: GCSE Foundation Number
Example
Find the LCM (lowest common multiple) of 4 and 2.
- Multiples of 4: 4
- LCM = 4
Answer: 4
Builds on: Greatest common factor and least common multiple
Leads to: Choose GCF or LCM to solve a problem
Choose GCF or LCM to solve a problem
CCSS 6.NS.B.4England: KS3 NumberEngland: GCSE Foundation Number
Example
A club has 27 red tulips and 45 yellow tulips. They make identical kits with nothing left over. What is the greatest number of kits they can make?
- GCF of 27 and 45 = 9
- 9 kits, each with 3 red tulips and 5 yellow tulips.
Answer: 9
Rewrite a sum by taking out the GCF
CCSS 6.NS.B.4England: KS3 NumberEngland: KS3 Algebra
Example
36 + 42 = □ × (6 + 7). What number goes in the box?
- 6 × 6 = 36, 6 × 7 = 42
- The box is 6.
Answer: 6
Use exponent notation for repeated multiplication
CCSS 6.EE.A.1England: KS3 Number
Example
Write 12 × 12 × 12 × 12 as a power (for example 4^3).
- 12 appears 4 times.
- 12⁴
Answer: 12⁴
Builds on: Whole-number exponents
Leads to: Powers of ten and place value, Square and cube fractions and decimals
Powers of ten and place value
CCSS 5.NBT.A.2CCSS 6.EE.A.1England: KS3 Number
Example
Write 10⁶ as an ordinary number.
- 10⁶ = 1 000 000
Answer: 1000000
Square and cube fractions and decimals
CCSS 6.EE.A.1England: KS3 Number
Example
Work out (4/7)². Give a fraction.
- (4/7)² = 4/7 × 4/7
- = 16/49
Answer: 16/49
Perfect squares and whole-number square roots
CCSS 6.EE.A.1CCSS 8.EE.A.2England: Y6 NumberEngland: KS3 Number
Example
Find √49.
- 7 × 7 = 49
- √49 = 7
Answer: 7
Builds on: Primes, squares and cubes
Leads to: Square roots of fractions and decimals
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