Doubling-and-Halving Strategy to Multiply (with Arrays)

A PowerPoint which introduces the ‘Doubling-and-Halving Strategy for Multiplication’.

This PowerPoint uses an array to show the multiplication strategy of doubling one factor and halving the other factor to help to work out some multiplication problems. Doubling and halving is therefore related to thinking that ‘restructures’ an array to make it more manageable to multiply (e.g. 3 × 18 = ___ can be rewritten as 6 × 9 = ___).

Very visual resource which helps students see that the total number of circles in an array (the product) stays the same when an array is cut and rearranged.

No text: so recommend that the teacher walks through the first couple of example slides and then students verbally explain the following examples to their peers.

Order of animations:

1. Tricky array and sum is shown.
2. Confused smiley bounces in. (explain here that if you don’t know your 15 times table etc. this could be hard)
3. Scissors appear and cut the array - array restructures into simpler array (double of one factor/half of the other)
4. New corresponding sum appears - click & answer is shown
5. Array restructures to first formation and tricky sum is shown again
6. As the total number of circles has remained the same throughout the sequence the answer should be obvious :-)

I use it alongside other strategies so that it is presented as an option for mental computation involving multiplication.