Multiplication and Division Word Problems

Activities to try

1. 1

   Build and partition a bar model to match the story

   Why it works: The operation comes from the structure of the situation, not from the numbers or a scanned key word. 'How many 4-cm pieces fit in 28 cm' is a division even though nothing is shared out — the quotitive/measurement meaning — and both division meanings can share the same equation (28 ÷ 4 = 7) while describing different actions.

   1. Read a word problem such as 'A 28-cm ribbon is cut into 4-cm pieces — how many pieces?' and decide which quantity is unknown: the whole, the group size, or the number of groups.
   2. Draw or build a bar representing the whole (28 cm), then mark the cut lines to make 4-cm segments, and count how many segments result (7).
   3. Write the matching equation using a symbol for the unknown, e.g. 28 ÷ 4 = □, and say in words what the answer counts (pieces, not centimetres).
   4. Repeat with a mixed set of stories — an equal-groups problem (e.g. '6 bags of 8 apples'), an array/area problem, a measurement/quotitive division, and a sharing/partitive division — building a model for each before choosing the operation.
   5. For the sharing story ('28 sweets shared equally among 4 children'), model dealing the whole into 4 equal parts and count the size of one part (7), then compare to the measurement story that also used 28 and 4.
2. 2

   Sort and match problems by structure

   Why it works: Recognising situation type and matching it to equation and model consolidates the difference between the three structures and exposes key-word matching as unreliable.

   1. Sort a set of word stories into equal-groups, array/area, and measurement categories (a consolidation and checking task).
   2. Match each story to the equation that represents it, including a symbol for the unknown.
   3. Choose, from options, the model (bar, array, or number-line of repeated hops) that fits a given story, with wrong options reflecting key-word traps (e.g. 'altogether' nudging toward addition).
3. 3

   Reference gallery of the three structures

   Why it works: Seeing the three situation types side by side with their models and equations gives a reference for how structure maps to representation.

   1. Study one annotated worked example per structure (equal-groups, array/area, measurement), each showing the bar model and its equation with a symbol for the unknown.
   2. Reveal the equation after first predicting which quantity is unknown and how the bar should be partitioned.