All concepts combined

Your child decides when to use factors, multiples or their relationship in a mixed set of questions. The MOE Primary 4 outcomes cover exact divisibility, common factors and common multiples. Bringing them together helps your child explain what a number represents instead of choosing a method from the subtopic heading.

• Translate a condition such as divides exactly into a test with a remainder, identifying which number is the divisor and which is being divided.
• Separate a request for a shared factor from a request for a shared multiple before beginning a list or a calculation.
• Combine more than one condition, including a numerical interval or a greatest or smallest requirement, without losing the original divisibility test.
• Follow a packing or repeating problem through to the quantity requested, using an earlier factor or multiple result when another calculation is needed.
• Explain why an answer works for every given number and, where required, why other possible answers are excluded by the question.

If an answer is claimed to be a common factor and is greater than the smaller of the two positive given numbers, it cannot be correct. If it is claimed to be a positive common multiple, it must be at least as large as the greater given number, as well as divide exactly by both.

All questions in this mixed set are Intermediate. They connect factor and multiple reasoning with an additional calculation: comparing purchase costs, finding a difference, counting items in identical bags, counting repeated meetings, counting factors or finding complete groups after setting items aside. Your child should label the quantity found at each stage so that a useful common factor or multiple is not mistaken for the final answer. Some questions require the least cost or the smallest difference, which means comparing valid possibilities rather than accepting the first one found. Review the closing instruction after calculating and check whether the answer needs a count, an amount or a comparison.

What should my child say before starting a mixed factor question? Ask your child to complete a sentence about the unknown, such as naming what must divide exactly or what must appear in both lists. That explanation establishes the direction of the relationship. It is more useful than deciding from one isolated word in a longer story.

How can we check that a greatest or smallest answer is justified? First verify that the proposed number meets every condition. Then look for another valid candidate in the direction the question rules out: greater for a greatest answer, smaller for a smallest one. An organised factor or multiple list makes this second check manageable.

What if my child calculates well but chooses the wrong kind of list? Return to what the numbers represent before repeating the arithmetic. Discuss whether the task splits an existing amount or builds up repeated groups. Once your child can explain that distinction, try a different question and ask for the reason behind the chosen list.