Place Value Games: Helping Children See What the Digits Mean

In thirty-four, the three means thirty. In forty-three, it means three. For an adult, that shift is almost invisible. For a child learning place value, it is the entire problem.

Before practising bigger calculations, spend a little time making that difference visible. These four games focus on whole numbers, tens and ones. They use bundles, drawings and digit cards to connect a written numeral with the quantity it represents.

Make a ten before naming a tens column

Collect thirty or more identical sticks and some elastic bands, or draw groups of ten marks on paper. Bundle exactly ten sticks. A bundle is still ten sticks; the band simply makes the group easier to see. Write “tens” and “ones” on two pieces of paper. Use equipment appropriate for your child’s age and supervise small objects.

Place two bundles on the tens sheet and four loose sticks on the ones sheet. Say “two tens and four ones,” then “twenty-four.” Write 24 = 20 + 4. Avoid saying only “two and four,” which leaves out the value that position gives each digit.

1. Build my number

1. One player chooses a number from 10 to 39 and writes it without showing the other player.
2. Give a clue in tens and ones: “three tens and two ones.”
3. The other player builds the quantity and writes its numeral.
4. Reveal the original number, check together and swap roles. Play six turns total.

For 32, the build needs three ten-stick bundles and two loose sticks. If a child selects three loose sticks and two bundles, ask them to count the actual quantity: twenty-three. The comparison reveals what changed without turning the mistake into a lecture.

2. Swap the digits

Make cards labelled 1 to 9. Draw two different cards, then arrange them into both possible two-digit numbers. Build or sketch each number and decide which is greater. Play five rounds; there is no score.

Drawing 2 and 5 gives 25 and 52. Twenty-five contains two tens; fifty-two contains five. The numbers use the same digits but have different values. Write 25 < 52 and ask which part of the model settled the comparison.

Introduce a zero card afterwards. A 4 and a 0 can make 40 or 04. Explain that 04 represents four, usually written simply as 4; it is not a second two-digit whole number. In 40, zero shows there are no additional ones beyond the four tens.

3. Trade ten ones

Each player starts with no sticks. Roll one six-sided die per turn and collect that many loose sticks. Whenever you have at least ten loose sticks, exchange exactly ten for a bundle. Stop after four turns each and compare totals; a tie is a draw. Have at least fifty sticks available, or use drawings.

A player with eight loose sticks rolls five. They now have thirteen ones and trade ten for one bundle, leaving three loose sticks: thirteen. Count before and after the exchange. The value has not changed, even though the model looks different.

This exchange can later help explain regrouping in addition. For now, let the game establish what a ten is. Do not require the written addition algorithm at the same time.

4. Same number, different build

Build 23 with two tens and three ones. Challenge the other player to show the same amount with only one bundle. They open one bundle, producing one ten and thirteen ones. Count both models to confirm that each represents twenty-three.

Choose three numbers between 20 and 39 and find two builds for each. Record an example as 23 = 20 + 3 = 10 + 13. A child who says thirteen ones is “not allowed” may be remembering the usual column format. Explain that the quantity is valid; trading restores the usual two-tens-and-three-ones form.

Connect the model to the numeral

A review of manipulative-based instruction found average benefits over instruction using abstract symbols alone. It did not test these four games. Our practical aim is to connect each bundle or drawing to its written value, rather than assume handling objects is enough.

The IES intervention guide also supports selecting representations deliberately. Ask your child to point to the thirty in 34, then the four. Try a new number with a drawing and eventually just the numeral. Keep the bundles nearby for checking.

Once tens and ones make sense, explore subtraction games or use the smaller quantities in our dice guide. Our broader number-sense article explains how quantity, comparison and calculation fit together.