A student can name the hundreds, tens and ones in 134. Now ask a different question: “Can you show 134 without using a hundred block?”
The challenge is to keep the number the same while changing the units used to show it. Thirteen tens and four ones still make 134. The number of pieces changes; the value does not.
Why ask for another way?
Renaming two- and three-digit numbers using different groupings is part of Australian Curriculum v9 Year 2 mathematics, AC9M2N02. NSW Department of Education guidance on building place value also emphasises flexible ways of naming numbers.
Use the question as an invitation to explain. A correct answer to one task is a starting point for further checking, rather than a verdict on everything a student understands.
Build it, exchange it, check it
Try this short sequence with base-ten materials. First check that students can show why a ten represents ten ones, and why ten tens match a hundred.
- Build 134. Use one hundred, three tens and four ones. Ask students to name the value represented by each type of piece.
- Remove the hundred block through an equal exchange. Replace it with ten tens. Leave the original three tens and four ones in place.
- Name the new grouping. There are now thirteen tens and four ones: 130 + 4 = 134.
- Reverse the exchange. Gather ten of those tens and replace them with one hundred. Ask what changed and what stayed the same.
A useful follow-up is: “You have more pieces now. How can the total still be 134?” Invite students to point to the materials as they explain. The explanation you are looking for is an equal exchange: the ten tens have the same value as the hundred they replaced.
Use the response to choose the next prompt
If a student counts every unit: ask them to identify one group of ten and count the tens while tracking their value: ten, twenty, thirty. Check the connection between the group and the number it represents before returning to 134.
If a student says there can only be three tens because the tens digit is 3: set the two representations beside each other. Ask, “What happened to the hundred when we exchanged it?” Keep the distinction explicit: 3 is the digit in the tens place of the written numeral; thirteen tens and four ones is another grouping of the whole quantity.
If the three-digit example gets in the way: try 34 as three tens and four ones, then exchange one ten for ten ones. The new grouping is two tens and fourteen ones: 20 + 14 = 34. Moving from two-digit to three-digit work is consistent with the Mathematics Hub’s Year 2 planning outline.
An exit check with a new number
Ask students to show 142 in two ways, including one without a hundred block. One possible pair is one hundred, four tens and two ones; and fourteen tens and two ones.
Then ask: “How do you know both models show 142?” If appropriate, extend to 204: two hundreds and four ones can become one hundred, ten tens and four ones. Check each representation by adding the values, rather than counting the pieces as if they were all ones.
Keep a brief note of the explanation as well as the answer. On the next occasion, change the number and ask students to justify the exchange again.
A resource for further practice
Sukindi’s Year 2 Place Value to 1000 unit includes an editable teaching presentation, five student worksheets and a Place Value Check-In assessment. Its listed learning focus includes partitioning and renaming three-digit numbers. Use it for follow-up practice after the materials-based conversation above; the suggested 134 sequence in this article is not a claim about a particular included worksheet.
You can also browse the Year 2 teaching resources for your wider sequence.