Worked Examples in Math: Show One, Then Let Your Child Try

A worked example shows both the steps of a solution and why those steps make sense. It can help when a child does not know how to start. The important next move is to let the child complete some of the reasoning, rather than watching an adult solve every question.

IES recommends alternating worked solutions with problem solving in its instruction and study guide. The three-stage activity below is an original parent example built around that general idea.

Stage 1: Explain one complete solution

Use this problem: “Three identical notebooks cost $12 altogether. What does one notebook cost?”

Draw three equal boxes and label the total $12. Explain: the cost is divided into three equal groups, so 12 ÷ 3 = 4. One notebook costs $4.

Check by multiplying: three notebooks at $4 each cost $12. The answer has a unit, dollars per notebook, and it fits the original total.

Ask your child why the groups must be equal. The word “identical” and the problem's equal-price assumption matter. Without equal prices, the total alone would not identify each price.

Stage 2: Leave a meaningful gap

Now offer: “Four identical pens cost $20 altogether. What does one pen cost?” Draw four equal boxes and write 20 ÷ □ = □.

Let the child fill the gaps and explain them. The completed calculation is 20 ÷ 4 = 5, so each pen costs $5. If needed, return to grouping objects or repeated addition.

Leave a reasoning step missing, not just a decorative label. If every mathematical decision is already supplied, filling in the answer tells you little about independent understanding.

Stage 3: Try a fresh problem

“Five equal packets contain 30 cards altogether. How many cards are in each packet?”

Give a blank page. Your child can draw, use objects, or write an equation. The answer is six cards per packet because 30 ÷ 5 = 6.

If the child asks to see the first example, let them. That means the support is still useful. It is information for your next teaching step, not evidence of cheating during home practice.

Compare the problems after solving

Ask what stayed the same across notebooks, pens, and cards. Each situation gives a total and a number of equal groups, then asks for the amount in one group.

Next, change the structure: “Cards come in packets of six. How many packets make 30 cards?” The answer is five packets, and the unknown is now the number of groups. Discuss the difference rather than assuming all division stories ask the same question.

Know when the model is too advanced

If the child cannot explain the first example even with a drawing, reduce the numbers or revisit the concept with the teacher's materials. More elaborate adult explanations may add confusion.

If they solve all three readily, stop. You can use a more demanding example another day. Completing a manageable task should not automatically trigger extra work.

For assigned homework, follow the after-school routine guide and tell the teacher when substantial help was needed. For optional practice, our learning-task guide explains how to choose a clear endpoint and allow support without changing the bargain midway.