Two-digit place value with bundles of ten

Build the number in two parts

Use place-value blocks, bundled craft sticks, or drawn marks suitable for a school-age learner. Make two groups of ten and set three single units beside them. Count the groups as ten, twenty, then twenty-one, twenty-two, twenty-three.

The Institute of Education Sciences identifies well-chosen concrete and semi-concrete representations as supports for understanding mathematical concepts. ^[1] Ask the learner to name the value represented by each group, rather than simply read the digits.

Distinguish digit from value

In 23, the digit 2 is in the tens place, so it represents two tens, or twenty. The digit 3 is in the ones place, so it represents three ones. Together they make twenty-three.

A useful explanation is: “The 2 tells how many tens; the 3 tells how many ones.” This separates the written digit from its place value. If a learner says the 2 means two, ask whether the model shows two single objects or two groups of ten.

Exchange without changing the amount

Trade one bundle of ten for ten single units. The model now has one bundle of ten and thirteen single units. Count the loose units as ten, then eleven through thirteen; with the remaining bundle, the total is still twenty-three.

The exchange changes the form, not the quantity. It is a concrete way to show that one ten is equivalent to ten ones. Keep the two arrangements side by side and ask how they can represent the same number.

Connect the model to writing

Write 23 beside the first model and label it 2 tens + 3 ones. Beside the exchanged model, write 1 ten + 13 ones. Both decompositions equal 23, though the first matches the usual two-digit place-value form.

This distinction supports later work with regrouping. When adding or subtracting, a learner may exchange units between places while preserving the total. Use the language “trade” or “exchange” with the model before expecting the written procedure to carry the meaning alone.

Choose materials with the school

Ask the teacher which representation is used in class, such as base-ten blocks, bundled sticks, or place-value drawings. Familiar materials make it easier to connect home practice with the classroom's vocabulary and notation.

Small loose pieces can be a poor fit for a child who might put them in their mouth. Choose safe, age-appropriate materials and supervise their use. The mathematical idea can also be shown with drawn circles and lines if physical objects are unsuitable.

Build thirty-one next: three bundles of ten and one single counter. Put it beside thirteen, made from one bundle and three singles. The same two written digits can describe different amounts because their places differ. Ask the child to point to each bundle and each single before writing 31 and 13 underneath the models. These are original examples to discuss alongside the school’s chosen representations. ^[1]