Using Base Ten Blocks for Place Value and Regrouping

Base ten blocks turn abstract numbers into objects children can see, touch and rearrange. A small cube represents one, a long rod represents ten, a flat represents one hundred, and a large cube represents one thousand. This physical model helps learners connect written numerals with quantity.

For Australian teachers, parents and homeschoolers, the blocks fit naturally with hands-on mathematics in the Australian Curriculum. They can support lessons about partitioning numbers, addition, subtraction, money and measurement in classrooms from Perth to Brisbane, as well as at home during flexible learning.

Why concrete materials matter

Place value depends on understanding that a digit changes its value according to its position. In 246, the 2 means two hundreds, the 4 means four tens and the 6 means six ones. Children may memorise this language without understanding it, but base ten blocks make each quantity visible.

Begin with free exploration. Invite students to build numbers, compare towers and describe what they notice. Ask them to make 37, then rebuild it using a different combination of tens and ones. This encourages mathematical language such as “three groups of ten”, “seven ones” and “the total is unchanged”.

Preparing a place value lesson

Give pairs or small groups a mat divided into thousands, hundreds, tens and ones. Provide a limited selection of blocks at first so students focus on the target concept rather than constructing elaborate designs. Number cards, whiteboards and small containers for sorting can complete the setup.

A useful warm-up is a “build and say” routine. Call out a number such as 58, and have students build it, draw it and write its expanded form: 50 + 8. Reverse the process by showing a model and asking students to record the numeral. This links concrete, pictorial and symbolic representations.

Building understanding through regrouping

Regrouping becomes meaningful when children see that ten ones can be exchanged for one ten. Place ten unit cubes together, count them aloud and trade them for a rod. Repeat the exchange with ten rods and one hundred flat. Use the terms “compose” and “decompose” alongside “trade” or “regroup”.

For 28 + 7, students build 28, add seven ones and notice that there are fifteen ones. They exchange ten ones for one rod, leaving 35. The written algorithm should come after the physical action, so the carried ten represents a real quantity rather than a mysterious mark above another digit.

Teaching subtraction with exchanges

Subtraction can be modelled by removing blocks, but problems that require an exchange are especially valuable. To solve 42 − 18, students first build four tens and two ones. Since eight ones cannot be removed from two, they exchange one ten for ten ones. The model now shows three tens and twelve ones, allowing eighteen to be removed and leaving 24.

Use precise language throughout the demonstration: “I exchanged one ten for ten ones; the value stayed the same.” This helps prevent a common misconception that a ten has simply disappeared. Ask learners to draw each stage before recording the vertical method.

Activities that encourage mathematical talk

A place value guessing game can build reasoning. Hide a model and give clues such as, “My number has six tens, fewer than five ones and is greater than 62.” Students can use blocks to test possibilities, then explain why their answer works. This activity is suitable for mixed-ability groups because the clues can be adjusted.

For a digital variation, a classroom could pair physical modelling with a short numeracy game. General strategies for pacing, scoring and keeping children focused during online play are outlined in these online bingo tips, which can inspire a place value version using number cards and virtual calls.

Connecting mathematics with Australian contexts

Use Australian coins to connect regrouping with everyday quantities. Students can represent 37 cents as three ten-cent coins and seven one-cent units in a model, while discussing that one-cent coins are no longer used in Australian cash transactions. They can then compare this structure with dollars and cents, keeping the mathematical focus clear.

Australian classrooms can also use familiar contexts such as AFL scores, distances between Sydney and Melbourne, or rainfall readings in a local weather chart. A Year 3 class might represent 1,250 millimetres of rain with one thousand cube, two hundred flats and five tens. These examples make large numbers relevant without relying on worksheets alone.

Hands-on learning can connect numeracy with other subjects and home routines. For example, Roylco’s butter in a jar activity provides a practical setting for counting, measuring and recording changes. Teachers seeking manipulatives, craft resources and classroom materials can browse the Roylco learning collection when planning integrated lessons.

Adapting instruction for every learner

Some students benefit from colour-coded place value mats, larger blocks or raised outlines that define each column. Others may need fewer digits, repeated demonstrations and sentence frames such as “I have ___ tens and ___ ones, so my number is ___.” Allowing students to explain with speech, drawings or gestures provides more than one route to mathematical thinking.

Extension tasks can involve decimals, four-digit numbers or multiple regroupings. Ask confident learners to solve 398 + 127, predict how many exchanges will occur and justify their prediction. For students still developing confidence, use two-digit numbers and focus on one exchange at a time.

Checking progress and recording learning

Assessment should reveal whether a child understands the value represented by each block. Ask learners to build a number, describe it, write its expanded form and change one digit. Their explanation is often more informative than a correct answer alone.

The following progression can help teachers select an appropriate next step:

Learning stage	What the student can do	Useful prompt
Developing	Builds two-digit numbers with support	“How many tens do you see?”
Secure	Represents, reads and partitions two- and three-digit numbers	“Show this number another way.”
Applying	Regroups during addition or subtraction	“What can you exchange, and why?”
Extending	Explains several strategies and works with larger numbers	“Can you prove your method is efficient?”

Finish with a brief exit task: build 64, subtract 18, draw the exchange and write the answer. Collected responses give a clear record of whether students can connect concrete materials, diagrams and formal place value notation.