How to Teach Place Value with Manipulatives: A Parent-Friendly Guide

Place value tells us that a digit’s value depends on where it sits. In 24, the 2 means two tens; in 42, it means two ones. That idea can feel surprisingly abstract to a child who sees the same digits in both numbers. Manipulatives make the difference visible: children can build each quantity, compare the models, and explain what changed.

Start with tens and ones children can move

Choose two clearly different materials: a length-10 Math Bar to represent one ten and unit bars to represent ones. Physical base-ten blocks, bundled craft sticks, or counters grouped in tens work too. What matters is that one “ten” visibly contains the same quantity as ten ones.

A simple five-minute place-value lesson

1. Build 24. Place two tens together, then add four ones.
2. Name what you see. Say, “Two tens and four ones make twenty-four.”
3. Connect the model to symbols. Write 20 + 4 = 24 beside it.
4. Change one part. Add an extra one, remove a ten, or build a nearby number.
5. Let the child explain. Ask how the model proves the value of each digit.

Try the digit-swap question

Build 24, then build 42 next to it. Ask, “Both numbers use a 2 and a 4, so why are they not equal?” Give the child time to compare before introducing a rule. They may notice that 42 has four groups of ten while 24 has only two.

This comparison helps position carry meaning. The written digit has not changed, but the unit it represents has: tens in one position, ones in another.

Questions that reveal understanding

• How many tens do you see? How many ones?
• What does the 3 mean in 36?
• Can you build the same number another way?
• What happens if we trade one ten for ten ones?
• Which number is greater? How does the model prove it?
• What number is one more, one less, ten more, or ten less?

Make the exchange before teaching “carrying”

Regrouping makes more sense when children first experience the exchange underneath it. Build 28 and add five ones. Once there are at least ten ones, trade ten of them for one ten. The finished model shows three tens and three ones: 33.

Only after the exchange is clear should written notation become the shorthand. The small 1 written above a column is not a mysterious extra number; it records the new group of ten the child already made.

Common place-value pitfalls

• Counting pieces instead of value: two tens are two pieces, but their value is twenty.
• Changing what a piece means: keep each representation consistent within the lesson.
• Moving too quickly to a procedure: let the child build, trade, and explain before using a written shortcut.
• Doing all the moving for the child: ask a question, then let the learner test the idea.

Connect the model to drawings and numbers

Once the child can explain a model, sketch quick lines for tens and dots for ones. Then connect the sketch to expanded form and standard notation: two tens and four ones, 20 + 4, and 24. This movement from objects to pictures to symbols is useful across curricula and mirrors the progression described in our guide to Singapore Math.

Return to the manipulatives whenever a new number or regrouping problem feels confusing. The goal is not to remove the model on a schedule; it is to help the child form a mental picture strong enough to reason without it when ready.

Physical or virtual materials?

Both can support the same conversation. Physical pieces add tactile feedback. Virtual math manipulatives are quick to reset, easy to carry, and useful when curiosity appears away from a desk. Choose the form that keeps the child doing the mathematical thinking.

Further reading

• Understood: Place value with straw bundles
• Understood: Place value disks