Two purchases of the same two items

Your child uses two purchases containing the same kinds of item to work out an individual price. This is an application of Primary 4 decimal operations and mathematical problem solving. The key is to compare purchases that contain the same quantity of one item, so the remaining difference has a clear meaning.

• Identify the quantity of each item in each purchase and its total cost, keeping item counts distinct from prices written in dollars and cents.
• Recognise that the same item has the same unit price throughout the problem unless the question explicitly states a different condition.
• Repeat a whole purchase when needed to match one item's count, multiplying both item counts and its total by the same whole number.
• Subtract the matched purchase totals to find the cost of the extra items, then divide by their count to obtain one item's price.
• Use the recovered price in an original purchase to find the other price, and read the final question again before choosing which amount to report.
• Apply comparisons to masses as well as prices, including three pair totals where each of the three objects is counted twice overall.

After finding both unit prices, your child can calculate the cost of each original purchase using its own item counts. Both totals must match the amounts given; fitting just one total is not enough to confirm that the two prices are correct.

This practice set has Intermediate and Challenge questions. Intermediate items include purchases whose item counts already match, a purchase that must be repeated before comparison, three pair masses, and a new combination of containers after individual masses are found. Challenge items add change after finding a price or compare what the same money can buy using a relationship between item prices. Ask your child to identify what is equal before subtracting any totals. For pair-mass questions, discuss how often each object is counted when the three pairs are combined. Once an individual value is known, check the final request carefully: the answer may be another bundle's total or the money remaining.

Does my P4 child need simultaneous equations for this page? No formal algebra is needed for the method described here. Your child works with item counts and purchase totals, repeating a purchase when necessary before comparing. These are applications of multiplication, subtraction and division, with the reason for each calculation stated in words.

Why must both item counts change when a purchase is repeated? Repeating a purchase means buying its entire collection again. Every item count and the total cost therefore change by the same multiplier. Doubling only the item whose count you want to match would create a different purchase whose total is not supplied by the question.

What should I ask if my child subtracts the totals immediately? Ask which items are present in equal numbers in the two purchases. If one item's counts already match, the difference can be useful straight away. If neither matches, your child needs to establish a suitable comparison first so that the difference represents a known number of just one item.