Use informal pencil and paper methods to support, record or explain multiplications and divisions. develop and refine written methods for TU x U, TU ÷ U, and find remainders after division. (NNS Framework for teaching mathematics, Supplement of examples, Section 6, pages 56, 66, 68)

Associated knowledge and skills

Errors and misconceptions

Tracking charts

Teaching sequences and spotlights

Know multiplication facts for 2, 3, 4, 5 and 10 times tables.

Is not confident in recalling multiplication facts.

1 Y4
1 Y4
1 Y4

Know the division facts which correspond with multiplication facts listed above.

Understand the inverse relationship connecting multiplication and division.

Is muddled about the correspondence between multiplication and division facts, recording, for example,
3 × 5 = 15 so 5 ÷ 15 = 3.

2 Y4
2 Y4
2 Y4

Understand the effect of multiplying whole numbers less than a thousand by ten.

Describes the operation of multiplying by ten as 'adding a nought'.

3 Y4
3 Y4
3 Y4

Can apply the distributive law (but not by name) to multiplying, using partitioning and recombining, For example:
14 x 3 = (10 x 3) + (4 x 3) = 30 + 12 = 42 so

Know how to record TU × U multiplication by a partitioning method in a grid format.

Does not apply partitioning and recombining when multiplying.
for example, 14 x 3 is calculated as
(10 x 3) + 4 = 34 or
or

14 × 3 = 312,
confusing the value of two-digit numbers.

4 Y4
4 Y4
4 Y4

Recognise that the commutative law holds for multiplication but not for division.

Assumes that commutative law holds for division also. For example, assuming that
15 ÷ 3 = 5 so 3 ÷ 15 = 5.

5 Y4
5 Y4
5 Y4

Understand the idea of remainder, and when to round up or down after division.

Writes a remainder that is larger than the divisor. For example, 36 ÷ 7 = 4 remainder 8.

Discards the remainder, as does not understand its significance.

Does not recognise when a remainder is significant in the decision about whether to round up or down.

6a Y4
6a Y4
6a Y4

6b Y4
6b Y4
6b Y4

6c Y4
6c Y4
6c Y4

Know how to record division as repeated subtraction, with appropriate use of chunking.

Continues to subtract twos when calculating twenty divided by two without using knowledge that two multiplied by 5 equals ten.

7 Y4
7 Y4
7 Y4