Before and after, when one quantity does not change

Your child uses one fixed quantity to connect two stages of a word problem. Only the other amount changes, so the unchanged amount provides a reference for comparing the before and after states. This is a mathematical problem-solving application of the Primary 4 whole-number operations, not a separately named syllabus outcome.

• Identify explicitly which person's or group's amount remains unchanged and which quantity gains, loses, sells or receives items during the story.
• Attach each comparison to its correct time, keeping a statement about the original amounts separate from a relationship after the change.
• Use the fixed quantity to make before and after amounts comparable, so that any equal unit has a consistent value across the calculation.
• Relate the known gain or loss to the difference between the changing quantity's two amounts, then recover the requested original or final amount.
• Check both the direction and the size of the change, since matching a final comparison does not establish the earlier relationship by itself.

The quantity identified as unchanged must have exactly the same numerical value before and after the event. For the other quantity, subtract its smaller state from its larger state and check that the difference equals the stated gain or loss.

Intermediate questions change only one of two quantities. They include an equal starting amount followed by giving away, a comparison that reverses after a loss, a sale that changes a times-as-many relationship and using some items while a known reference count stays fixed. Have your child identify that reference before choosing a unit value. The Challenge question starts with equal shelf counts, then adds to one and removes from the other; compare their net changes to recover the common starting count. Then state which relationship belongs before the change and which belongs afterwards. If the question asks for the amount used or sold, compare the changing quantity's two states. For a fixed-reference task, the final check preserves that count while reproducing the change in the other amount; for the two-shelf task, check both final counts against their stated comparison.

Why is the unchanged amount useful? It gives your child one value that can be trusted across both stages. The changing amount can then be compared with that fixed reference before and after the event. Without identifying it, equal-looking units in two comparisons might be treated as equal even when their values differ.

Does the total stay the same when one quantity is unchanged? If only the other quantity changes by a positive amount, the total changes by that same amount. The difference changes too. Your child should therefore use the fixed individual quantity as the link, rather than assume the combined total or gap is also preserved.

What helps my child separate the two stages of the story? Ask for a spoken description of what was true at first, what happened and what is true afterwards. Include the quantity names in each comparison. Your child can then check that each calculation belongs to the stage where its information is given.