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Year 7

Divisibility tests for 6 and 9

I can identify and explain whether a number is or is not a multiple of a given integer.

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New
New
Year 7

Divisibility tests for 6 and 9

I can identify and explain whether a number is or is not a multiple of a given integer.

Download all resources
Share activities with pupils

Lesson details

Key learning points

  1. A number is a multiple of 6 if and only if it also is a multiple of 2 and 3.
  2. For any multiple of 9 the sum of its digits is also a multiple of 9.

Common misconception

Incorrectly summing the digits to identify a multiple of 3 or 9.

Use number bonds to sum large numbers of digits.

Keywords

  • Divisibility - Divisibility is a number’s ability to be exactly divided by another number, leaving no remainder.

Students could come up to the board and create a class version of the multiple of 9 maze. This will give students the opportunity to think about examples and non-examples to ensure that there is only one route through the maze.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Video

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Starter quiz

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6 Questions

Q1.
Divisibility is a number’s ability to be:
squared
divided by another number
Correct answer: exactly divided by another number, leaving no remainder
multiplied by another number
Q2.
A number is a multiple of 3 when the sum of its digits is divisible by
Correct Answer: 3, three
Q3.
Match each number with the correct statement.
Correct Answer:478 374 378,is divisible by 2 and 3

is divisible by 2 and 3

Correct Answer:989 890 484,is divisible by 2

is divisible by 2

Correct Answer:113 890 291,is not divisible by 2 or 3

is not divisible by 2 or 3

Correct Answer:231 321,is divisible by 3

is divisible by 3

Q4.
Is the statement "all common multiples of 2 and 3 are even" sometimes true, always true or never true?
Correct answer: Always true
Sometimes true
Never true
Q5.
Is the statement "all common multiples of 3 and 7 are even" sometimes true, always true or never true?
Always true
Correct answer: Sometimes true
Never true
Q6.
The number 238 839 239 382.33 has a digit sum of 66. Sofia says it is a multiple of 3. Alex says it is also a multiple of 2. Andeep says it is not a multiple of 2 or 3. Who is correct?
Sofia
Alex
Correct answer: Andeep
They are all incorrect.

Exit quiz

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6 Questions

Q1.
All numbers that are divisible by 2 and divisible by 3 are also divisible by 1 and
Correct Answer: 6, six
Q2.
Which of these numbers is divisible by 6?
8992
9374
Correct answer: 34 830
390 021
Q3.
Which of these numbers is divisible by 6?
51 370
Correct answer: 51 372
51 374
51 376
Q4.
Match the divisibility test with the correct summary.
Correct Answer:A divisibility test for 3 ...,states the sum of its digits is a multiple of 3

states the sum of its digits is a multiple of 3

Correct Answer:A divisibility test for 2 ...,states the digits 0, 2, 4, 6 or 8 must be in the ones column

states the digits 0, 2, 4, 6 or 8 must be in the ones column

Correct Answer:A divisibility test for 9 ...,states the sum of the digits is a multiple of 9

states the sum of the digits is a multiple of 9

Q5.
Jun says 340 is a multiple of 6. Jacob says 312 is a multiple of 6. Lucas says 366 is a multiple of 6. Who is incorrect?
All of them
Correct answer: Jun
Jacob
Lucas
Q6.
Which of the following is divisible by both 6 and 9?
328 204 901
367 982 200
422 893 903
Correct answer: 820 082 808