Year 1 Mathematics · AC9M1N02

Partitioning Tens and Ones

Numbers can be partitioned in different ways. Two-digit numbers can always be described using tens and ones

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Learning goalsSay it simply

Numbers can be partitioned in different ways. Two-digit numbers can always be described using tens and ones.

Learning routine: Build → Split → Name parts → Recombine → Explain

Success looks like

  • Partition one-digit numbers
  • Partition tens and ones
  • Use materials
  • Recombine parts
  • Explain different splits
Key conceptTeach from the board

Partition into tens and ones first

5650 + 65 tens + 6 ones

Other partitions are possible, such as 40 + 16, if the total stays 56.

Choose a partition that helps the problem

38 = 30 + 838 = 20 + 1838 = 35 + 3

Good mathematicians can split the same number more than one way.

Explain your thinking: Say what each part of the model represents, then explain why the answer or conclusion follows.

Clean visual examplesOne-page board

Clean one-page examples

AC9M1N02 - Partitioning Tens and Ones
Example 1

56 50 + 6 5 tens + 6 ones

Example 2

38 = 30 + 8 38 = 20 + 18 38 = 35 + 3

Example 3

Tens frame Build 43 and split it into tens and ones. Model: 43 = 40 + 3

Example 4

Many ways Find two different partitions of 29. Model: 29 = 20 + 9 = 10 + 19

Curriculum examplesCurriculum examples

These curriculum examples extend the central model into varied contexts. They are learning contexts, not extra definitions to memorise.

E1

building knowledge and understanding of the part-part-whole facts to 10, using physical and virtual materials; for example, using virtual ten-frames through a digital app or website to identify pairs of numbers that combine to make 10

Try and explain: A ten-frame has six filled spaces. How many empty spaces complete ten? Show the two parts.

Answer and teaching point

Four spaces are empty. Six and four combine to make ten: 6 + 4 = 10.

E2

using physical and virtual materials to partition numbers into counts of tens and ones; for example, recognise 35 as 3 tens and 5 ones or as 2 tens and 15 ones

Try and explain: Build 52 with tens and ones. Open one bundle of ten. How many tens and ones are there now?

Answer and teaching point

Four tens and twelve ones. Opening a bundle changes the grouping, but 40 + 12 still equals 52.

E3

using part-part-whole reasoning and physical or virtual materials to represent 24, then partitioning 24 in different ways and recording the partitions using numbers; for example, 10, 10 and 4 combine to make 24 or 10 and 14 combine to make 24

Try and explain: Show 28 as 20 and 8, then find a different split. How can you check it?

Answer and teaching point

For example, 10 and 18. Recombine the parts: 10 + 18 = 28, just as 20 + 8 = 28.

Different parts, the same whole

Partition a number in more than one way and check that its total stays the same.

Worked example

Can 46 be shown as 3 tens and 16 ones?

Two ways to show 46
RepresentationTensOnesTotal
Before regrouping4646
After opening one ten31646
  1. Start with 4 bundles of ten and 6 singles: 40 and 6 make 46.
  2. Open one bundle. There are now 3 bundles and 16 singles.
  3. The objects have only been regrouped. 30 and 16 still make 46.

Watch for this mistake: Regrouping does not add or remove objects. Count the value of each bundle as ten, not one.

Try it, then explain

  1. Complete: 35 is 2 tens and __ ones.

    Hint

    Open one of the 3 tens in 35.

    Answer and explanation

    15 ones. 20 + 15 = 35.

  2. Which shows 28: 2 tens and 8 ones, or 1 ten and 8 ones? Explain.

    Hint

    Find the total in each representation.

    Answer and explanation

    2 tens and 8 ones. The other representation shows 18.

Questions and answersWith answers

Key idea: Numbers can be partitioned in different ways. Two-digit numbers can always be described using tens and ones.

Remember

  • Partition one-digit numbers
  • Partition tens and ones
  • Use materials
  • Recombine parts
  • Explain different splits

Quick questions

  • Partition 68 into tens and ones.
  • Give another partition of 68.
  • What number is 40 + 9?
  • Why is 6 + 2 not the same as 60 + 2?

Return to the concept model if an answer is uncertain. Use the model to explain, not just to guess.

Practice and reviewReady for practice
  • Only one partition — Tens and ones is useful, but numbers can be split in other ways too.
  • Dropping zero — 50 + 6 is 56; 5 + 6 is only 11.
  • Swapping tens and ones — In 47, the 4 means 4 tens, not 4 ones.
Curriculum alignmentStart here

Numbers can be partitioned in different ways. Two-digit numbers can always be described using tens and ones.

Learning routine: Build → Split → Name parts → Recombine → Explain

Success looks like

  • Partition one-digit numbers
  • Partition tens and ones
  • Use materials
  • Recombine parts
  • Explain different splits

AC9M1N02: partition one- and two-digit numbers in different ways using physical and virtual materials, including partitioning two-digit numbers into tens and ones

Australian Curriculum Version 9.0

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