General algebraic forms for specific number properties | Maths

Starter quiz

Which of these are integers?

5 ✓

-1 ✓

$1\over 2$

20.4

0 ✓
A multiple is the product of a number and...

an integer. ✓

any other number.

a positive number.

itself.
Which of these are multiples of 3?

54 ✓

73

125

231 ✓

334
Which of these is an example of consecutive integers?

-5, -4, -3, -2 ✓

-0.5, 0.5, 1.5, 2.5

-1, 0, 1, 2 ✓

0, 2, 4, 6

23, 24, 25, 27
Which of these shows consecutive even integers?

5, 7, 9, 11

10, 11, 12, 13

14, 18, 22, 26

30, 32, 34, 36 ✓
Which shows consecutive square numbers?

2, 4, 6, 8

4, 9, 16, 25 ✓

1, 5, 10, 20

49, 64, 81, 100 ✓

121, 144, 196, 225

Exit quiz

Which of these expressions could be even if $n$ is an integer?

$n$ ✓

$2n$ ✓

$3n$ ✓

$2n + 1$

$10n - 1$
Which of these expressions must be even for any integer $n$ ?

$7n$

$14n$ ✓

$3n + 6$

$4n + 2$ ✓

$9(2n + 3)$
Which of these expressions are always odd for any integer value of $n$ ?

$2n -1$ ✓

$3n$

$4n + 3$ ✓

$5(2n+1)$ ✓

$7n + 1$
Which of these statements are true for the expression $6n + 3$ when $n$ is an integer?

It could be a multiple of 6.

It could be a multiple of 3. ✓

It could be a multiple of 2.

It is always odd. ✓

It is always 3 less than a multiple of 6. ✓
Which of these must represent 3 consecutive odd numbers when $n$ is an integer?

$5n, 7n, 9n$

$n + 1, n + 3, n + 5$

$2n -1, 2n + 1, 2n + 3$ ✓

$2n + 1, 2n + 2, 2n + 3$

$2(2n+1), 2(2n+3), 2(2n + 5)$
Which of these represent any 2 different even numbers?

$2n$ and $2n$ where $n$ is an integer.

$2n$ and $2n + 2$ where $n$ is an integer.

$2n$ and $2m$ where $n$ and $m$ are integers and $n \ne m$ . ✓

$2n$ and $12n$ where $n$ is an integer and $n \ne 0$ .

$2n + 1$ and $2m + 3$ where $n$ and $m$ are integers.

Worksheet

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Lesson Details

Key learning points

The divisibility tests can be used to help write general algebraic forms of multiples.
By understanding the general algebraic form of multiples, other values can be expressed.

Common misconception

Pupils may think it is acceptable to use the same letter for all expressions.

It may be acceptable for the letter to be the same but that depends on what the letter is representing. This is explored in the first learning cycle with chocolates.

Keywords

Multiple - A multiple is the product of a number and an integer.
Integer - An integer is any positive or negative whole number or zero.