Renaming two-digit numbers
Partition and rename two-digit numbers in standard and non-standard ways (e.g. 34 = 3 tens 4 ones = 2 tens 14 ones) using physical and virtual base-ten materials, recognising that the total stays the same
Lesson
Set out your lesson
“Renaming two-digit numbers means showing the same total in more than one way—standard place value (34 = 3 tens 4 ones) and a non-standard rename (2 tens 14 ones)—without changing how many there are. Physical tens and ones make the trade visible. We will build, rename by unbundling a ten, then try a fresh number.”
Bring to the table
- Base-ten materials: tens sticks/bundles and ones (or drawn tens and ones on paper; parent keeps tiny pieces away from mouths)
- Paper and pencil
Extra for the adult
Worked example. 34 = 3 tens 4 ones = 2 tens 14 ones. Unbundling a ten into ones changes the parts, not the total. Renaming keeps the quantity the same.
Optional challenge. For Renaming two-digit numbers, find three different tens-and-ones names for 47 and explain why each still equals 47. Optional: show a wrong rename (3 tens 7 ones for 47) and fix it.
What to notice. Keep one parent note: numbers tried; standard and non-standard names; “same total” language; support used. A photo of sticks alone cannot record the rename talk. This session samples a few items, not mastery of every rename.
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Teaching approaches
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1 approach
Renaming two-digit numbers means showing the same total in more than one way—standard place value (34 = 3 tens 4 ones) and a non-standard rename (2 tens 14 ones)—without changing how many there are. Physical tens and ones make the trade visible. We will build, rename by unbundling a ten, then try a fresh number.
Spend about 12 minutes partitioning and renaming two-digit numbers with tens and ones materials, writing both names, then checking a new rename.
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Learning resources
Extra practice links — they do not replace Gakuva’s teaching approach.
Illustrative Mathematics · Practice link — not the full lesson
Looking at Numbers Every Which Way
Before you open · source notes
Multiple renamings of a number support renaming two-digit numbers. Not every three-digit subtraction algorithm.
Free, no sign-in. A teacher solution is on the same page, so use the student view with your child.
Before you openAsk the learner to rename one two-digit number in two ways using tens and ones.
Opening this link does not save learning or assess mastery.
Source, access and review notes
Public Illustrative Mathematics task page. The .html address responds HTTP 308 to this URL. An anonymous GET of this URL on 2026-11-12 returned HTTP 200 with no login or payment prompt. Where a teacher solution is present, it is on the same page as the student task; this check did not find a separate locked student view. An adult can use the student view section and should not read a solution aloud. Advertising was not observed in the fetched HTML text; that is not a browser, device, or ad-free guarantee. This is a paper or discussion task, not an automatically marked interactive game. Opening the link does not save practice or assess mastery. Diagrams on the page use missing or filename-only alt text, so they are not an accessible image equivalent. Accessibility still depends on an adult describing the picture.
Illustrative Mathematics. “Looking at Numbers Every Which Way.” Licensed CC BY-NC-SA 4.0. External task; Gakuva does not copy, host, embed, or redistribute it.
CC BY-NC-SA 4.0 — link only
Check understanding
- Show 34 with real base-ten blocks as 3 tens and 4 ones, then trade a ten to show 2 tens and 14 ones
- Partition 52 in three different ways with an on-screen base-ten app (e.g. 5 tens 2 ones, 4 tens 12 ones, 3 tens 22 ones) and record each
- Explain why 4 tens and 6 ones and 3 tens and 16 ones are the same number
“If your child has 34 counters made up of 3 bags of ten and 4 loose ones, can they show the same number another way — like 2 bags of ten and 14 loose ones?”
Curriculum record
- Type
- Conceptual
- Subject
- Mathematics
- Domain
- Number Representation & Place Value
- Age range
- Ages 6–9
Standards