CAMBRIDGE PRIMARY MATHEMATICS 0096 · STAGES 3 TO 6

Arrays & Laws Studio

Rearrange the same counters and the total cannot change. That licence is what the commutative, associative and distributive laws are, and it is what lets you choose the easier way to work a calculation out.

3Ni · the laws of arithmetic and the order of operations, shown by rearranging counters

What can you do to the same counters?

Drag the corner handle to change the rows and columns: the sentence under the array is written from your own counters, so every number in it changes as you drag. Press the turn handle to stand the same counters the other way round, and drag the dashed line to cut the array into two parts.

The array writes its own number sentence. Turning it swaps the rows and the counters in each row while the total stays: the commutative law for multiplication. Cutting it down one line shares the multiplier over the two parts: the distributive law. Further down is a separate example with no counters: its hoop chooses which pair is worked first, the associative law, and with no hoop the order of operations decides.

Practice and challenge checks record the selected pathway and response in this page session. Explore changes are not scored.