Year 1 Mathematics · AC9M1N06

Equal Sharing and Grouping

Equal sharing means each group gets the same amount. Equal grouping means making groups of the same size

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Learning goalsSay it simply

Equal sharing means each group gets the same amount. Equal grouping means making groups of the same size.

Learning routine: Read → Decide share/group → Model equally → Count → Check

Success looks like

  • Model sharing
  • Model grouping
  • Use equal groups
  • Count results
  • Explain leftovers
Key conceptTeach from the board

Sharing and grouping ask different questions

12 shared into 3 groups4 in each group12 made into groups of 34 groups

The numbers may match, but the question is different.

Use equal groups before counting

same amountno leftovers unless statedcount each group

If the groups are not equal, the model does not solve the problem.

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

AC9M1N06 - Equal Sharing and Grouping
Example 1

12 shared into 3 groups 4 in each group 12 made into groups of 3 4 groups

Example 2

same amount no leftovers unless stated count each group

Example 3

Share fairly Share 15 counters among 3 plates. Count how many on each plate. Model: 15 shared into 3

Example 4

Make groups Make groups of 4 from 16 counters. Count the groups. Model: 16 grouped by 4

Curriculum examplesCurriculum examples

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

E1

modelling problems involving repeated equal group situations, such as, “How many wheels are needed for 3 cars?”, using materials and drawing a picture to show what they did, and recording the results with a number

Try and explain: Four toy bicycles each need two wheels. How many wheels are needed altogether?

Answer and teaching point

Eight wheels. Show four groups of two and count 2, 4, 6, 8.

E2

modelling practical problems involving equal sharing situations; for example, sharing a set of dominoes between the 2 players in a game, and then counting or subitising to ensure they both have the same number of tiles

Try and explain: Share 14 counters equally between two players. How can you check the sharing?

Answer and teaching point

Each receives seven. Count both shares to check that they are equal and that 7 + 7 accounts for all 14 counters.

E3

modelling money problems involving equal sharing; for example, sorting coins from a money box according to their denominations, sharing the coins equally between 4 people, and using counting or subitising to ensure they have equal amounts of each denomination

Try and explain: Share eight $1 play coins equally among four children. How many coins and how much value does each receive?

Answer and teaching point

Each receives two coins worth $2. Deal one to each child twice; all shares have the same value.

Sharing and grouping ask different questions

Use objects to show whether the unknown is the group size or the number of groups.

Worked example

Twelve counters are shared equally onto three mats. How many go on each mat?

Twelve counters shared equally
Mat 1Mat 2Mat 3
● ● ● ●● ● ● ●● ● ● ●
  1. Draw three mats because the number of groups is known.
  2. Deal the twelve counters one at a time around the mats until none remain.
  3. Each mat has four. Check that all three groups are equal and that 4 + 4 + 4 = 12.

Watch for this mistake: For ‘three mats’, make three groups first. For ‘three in each group’, place three objects together repeatedly instead.

Try it, then explain

  1. Put 12 counters into groups of 3. How many groups can you make?

    Hint

    Here the size of each group is known.

    Answer and explanation

    4 groups, with 3 counters in each.

  2. Ten counters are shared onto two mats as 6 and 4. Is the sharing equal? Repair it.

    Hint

    Move a counter without changing the total.

    Answer and explanation

    It is unequal. Move one counter from the group of 6 to the group of 4 to make 5 and 5.

Questions and answersWith answers

Key idea: Equal sharing means each group gets the same amount. Equal grouping means making groups of the same size.

Remember

  • Model sharing
  • Model grouping
  • Use equal groups
  • Count results
  • Explain leftovers

Quick questions

  • Share 12 counters among 3 groups.
  • Make groups of 5 from 20 counters.
  • What is the difference between sharing and grouping?
  • How do you check the groups are equal?

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

Practice and reviewReady for practice
  • Unequal sharing — Check every group has the same amount.
  • Confusing group size and number of groups — Ask: how many groups, or how many in each group?
  • Stopping before leftovers — If there are leftovers, state them clearly.
Curriculum alignmentStart here

Equal sharing means each group gets the same amount. Equal grouping means making groups of the same size.

Learning routine: Read → Decide share/group → Model equally → Count → Check

Success looks like

  • Model sharing
  • Model grouping
  • Use equal groups
  • Count results
  • Explain leftovers

AC9M1N06: use mathematical modelling to solve practical problems involving equal sharing and grouping; represent the situations with diagrams, physical and virtual materials, and use calculation strategies to solve the problem

Australian Curriculum Version 9.0

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