Multiplication as repeated addition (age 6+)

Activities to try

1. 1

   Problem playground: model the story, then solve

   Why it works: A word problem's structure (equal groups, array, or sharing/grouping) determines which operation and representation fit; meaning should drive the method rather than grabbing the numbers and operating blindly.

   1. Read a contextual equal-groups or sharing story (e.g. '5 bags with 2 apples in each — how many altogether?').
   2. First decide: is this a multiplication story (combining equal groups) or a division story (splitting into equal parts — by sharing or by grouping)? State your choice before solving.
   3. Choose how to model it: build an array, lay equal jumps on a number line, write it as repeated addition, or use a known fact.
   4. Solve and check that your model actually matches the story (equal groups, the right group size and number of groups).
   5. Repeat with a sharing story (e.g. 'Share 15 sweets equally among 3 children'), a grouping story (e.g. '15 sweets are put into bags of 3 — how many bags?') and an array task (e.g. 'Draw an array for 4 × 3').
2. 2

   Count-all vs known fact: the efficiency race

   Why it works: For a child who knows the fact, recalling it (or using group structure) is much quicker than counting everything in ones — this efficiency gain is the motivation to leave counting-all behind.

   1. Take one problem whose total comes from a fact the child knows (e.g. 2×12 = 24, a 2-times fact) and solve it two ways: once by counting every object in ones, and once by using the recalled fact.
   2. Watch the counting-all method work slowly up to the total while the known fact lands the answer at once.
   3. Say why the fact is quicker, and try the next problem using a fact instead of counting all.
3. 3

   Is it × or ÷? Sort and match the stories

   Why it works: Recognising which operation a word problem needs — and, within division, whether it is sharing or grouping — is a distinct skill from doing the arithmetic.

   1. Read several everyday stories and sort each one: is it a multiplication (combining equal groups) or a division (splitting into equal parts) situation? For each division story, also say whether it is sharing (number of groups known) or grouping (group size known).
   2. Match each story to the number sentence that fits it (e.g. an equal-groups story to 5 × 2, a sharing story to 15 ÷ 3).
   3. For a tricky pair, explain what in the story tells you which operation to use.
   4. Watch for distractors that combine the two numbers with the wrong operation (e.g. 5 + 2 or 15 − 3).