Suppose they were all the same

Your child solves problems involving two kinds of item, a total number of items and a total value or contribution. Supposing that every item is one kind creates a starting total that can be compared with the real one. This is a problem-solving method using Primary 4 arithmetic, rather than a separately listed content outcome.

• Identify the fixed total number of items and the contribution of each kind, such as its cost, number of legs or number of sides.
• Calculate a supposed total by treating every item as the same kind while keeping the overall item count unchanged.
• Find the difference between the supposed and actual totals, deciding whether replacing an item must increase or decrease the contribution.
• Calculate the change caused by replacing one item of the assumed kind with one of the other kind, then divide to find the replacement count.
• Recover the remaining count from the total number of items and check both counts against the actual combined value or contribution.

The two counts found by supposition must add to the given total number of items. Multiplying each count by its own contribution and adding those results must also reproduce the actual total value, so both conditions are checked independently.

Intermediate questions combine a fixed count with two seating capacities, two coin values, two shapes with different side counts, or marks gained and lost in a quiz. The Challenge question finds an item count from total takings before calculating the money received for that kind of item. Your child should name what remains fixed before calculating a supposed total. In the scoring question, replacing a correct response changes the score by both removing its reward and applying the penalty. After finding the replacement count, identify which kind it represents. Check the overall count as well as the combined seating or score, and compare the reasoning with the solution only after your child has attempted those checks. When reviewing the working, ask your child to explain how each replacement changes the supposed total while preserving the overall count.

Is supposition just guessing an answer? The starting assumption is chosen deliberately to make a total easy to calculate. The difference from the actual total then determines how many replacements are needed. Your child does not need to try unrelated guesses, because every replacement changes the total by a known fixed amount.

Why do we divide by the difference between the two contributions? Replacing one item removes its original contribution and adds the other kind's contribution. The net change is their difference. Dividing the total shortfall or excess by that change tells your child how many such replacements account for the full adjustment.

Can my child assume either kind of item? Yes, provided the calculation follows the chosen assumption consistently. Assuming the smaller contribution creates a shortfall, while assuming the larger creates an excess. The replacement count refers to the kind introduced, so your child must identify whose count the division has found.