Use multiplication to solve addition and subtraction problems.
Number Framework Stage 7
Create two arrays using animal cards to represent 6 _ 8 and 3 _ 8. Ask the students how many animals are in each array. Pose the problem of adding these sets of animals together, that is 48 + 24. Allow the students to present their strategies.
Some students may note that (6 x 8) + (3 x 8) = 9 x 8 = 72 (combining sets of eight).
Provide two similar examples, getting the students to make the arrays then solve theresulting addition problem. Suitable problems include:
(5 x 7) + (4 x 7) = 9 x 7 (3x 6) + (6 x 6) = 9 x 6
(4 x 9) + (6 x 9) = 10 x 9 (7 x 8) + (2 x 8) = 9 x 8
Ask the students to state what these problems have in common (both addends aremultiples of a common number).
Using Imaging
Pose problems for the students to image, beginning with the addends instead of the factors. If necessary, fold back to the materials. Possible examples include:
16 + 24 + 32 as (2 x 8) + (3 x 8) + (4 x 8) = 9 x 8
49 + 28 as (7 x 7) + (4 x 7) = 11 x 7
45 + 27 + 18 as (5 x 9) + (3 x 9) + (2 x 9) = 10 x 9
Extend the imaging to include subtraction problems:
81 – 27 as (9 x 9) – (3 x 9) = 6 x 9 64 – 48 as (8 x 8) – (6x 8) = 2 _ 8
63 – 35 as (9 x 7) – (5 x 7) = 4 x 7 90 – 36 as (10 x 9) – (4 x 9) = 6 _ 9
54 – 36 as (9 x 6) – (6 x 6) = 3 x 6 or (6 x 9) – (4 x 9) = 2 x 9
Using Number Properties
Pose addition and subtraction problems where it is helpful to identify a common factor.
48 + 56 + 24 + 32 = 20 x 8 42 + 35 + 49 + 14 = 20 x 7
72 – 27 + 45 – 36 = 6 x 9 88 – 56 – 16 + 32 = 6 x 8
120 – 54 – 48 – 18 = 0 x 6 77 – 28 + 14 – 35 = 4 x 7