Mathematics · Year 2

Active learning ideas

Equal Groups and Arrays

Active learning lets students physically build and manipulate equal groups and arrays, making abstract multiplicative ideas concrete. When children arrange counters into neat rows and columns, they connect counting to structure, which builds a strong foundation for multiplication. Movement and collaboration also help shift students away from counting by ones toward efficient grouping strategies.

• ACARA Content Descriptions
• AC9M2N04

• 15–40 min
• Pairs → Whole Class
• 3 activities

Activity 01

• Gallery Walk
• 40 min · Pairs

Gallery Walk: Array Scavenger Hunt

Students explore the classroom or schoolyard to find 'natural' or 'man-made' arrays (e.g., window panes, egg cartons). They take a photo or draw it, then label it with two different repeated addition sentences (rows and columns).

How is an array different from a random pile of objects?

Facilitation Tip

During the Gallery Walk, position yourself near pairs to listen for students describing arrays with precise language like 'rows' and 'columns' rather than 'groups of groups.'

What to look for

Provide students with a picture of an array (e.g., 4 rows of 3 buttons). Ask them to: 1. Write the number of rows and columns. 2. Write two repeated addition sentences for the array.

• Understand
• Apply
• Analyze
• Create
• Relationship Skills
• Social Awareness

Activity 02

• Inquiry Circle
• 30 min · Small Groups

Inquiry Circle: The Array Architect

Groups are given a 'total' number (e.g., 12) and must find all the different ways to arrange that many blocks into a perfect rectangle. They record their findings and compare them with other groups to see who found the most combinations.

How can we describe the same array using two different addition sentences?

Facilitation Tip

For The Array Architect, provide grid paper first so students trace their planned arrays before building with counters, reinforcing planning and precision.

What to look for

Display two arrays on the board, one a rotation of the other (e.g., 2 rows of 5 and 5 rows of 2). Ask students to hold up fingers to show the total number of objects in each array. Then, ask: 'What do you notice about the totals?'

• Analyze
• Evaluate
• Create
• Self-Management
• Self-Awareness

Activity 03

• Think-Pair-Share
• 15 min · Pairs

Think-Pair-Share: The Tilted Array

The teacher shows an array of 4x2 and then rotates it 90 degrees. Students think about whether the total number of dots has changed, discuss with a partner, and then explain why 'rows' and 'columns' are just a matter of perspective.

Why does rotating an array not change the total number of items?

Facilitation Tip

When running The Tilted Array, deliberately tilt one array and ask students how the total could stay the same even if the shape changes.

What to look for

Show students a collection of objects arranged randomly and then the same objects arranged in a clear array. Ask: 'How is the array different from the random pile? Which arrangement helps you count faster? Why?'

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

A few notes on teaching this unit

Teach this topic by starting with physical materials and moving to visual representations before any symbols appear. Avoid rushing to abstract notation; let students experience the shift from additive to multiplicative thinking through guided discovery. Research shows that students who build arrays themselves develop stronger conceptual understanding than those who only see pre-made examples. Keep discussions focused on 'How many groups?' and 'How many in each group?' rather than jumping to multiplication facts too soon.

By the end of these activities, students should confidently describe arrays using rows and columns, write repeated addition sentences, and explain why an array is more useful than a random pile for counting. They should also begin to rotate arrays and recognise that 3 rows of 2 is the same total as 2 rows of 3, just arranged differently.

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Watch Out for These Misconceptions

• During Gallery Walk: Array Scavenger Hunt, watch for students counting individual items one-by-one instead of using rows and columns.

  Pause the walk and ask students to point to a row and say how many are in that row. Then have them count by rows rather than by ones, modelling the skip counting process.

• During Collaborative Investigation: The Array Architect, watch for students building arrays with unequal rows or overlapping counters.

  Prompt them to adjust their structure so each row has the same number of counters and no objects touch across rows. Use the grid paper to redraw and rebuild, reinforcing the importance of equal groups.

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Methods used in this brief

• Gallery Walk
• Inquiry Circle
• Think-Pair-Share