Mathematical Explorers: Building Foundations · 2nd Class

Active learning ideas

Arrays and Equal Groups

Active learning works well for arrays and equal groups because students need to see, touch, and manipulate equal groups to build true understanding. When students build and count arrays themselves, they move from abstract symbols to concrete evidence of multiplication. This hands-on approach creates lasting connections between visual models and number sentences.

• NCCA Curriculum Specifications
• NCCA: Junior Cycle - Geometry and Trigonometry - G.1.2

• 20–45 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Experiential Learning
• 30 min · Pairs

Manipulative Build: Array Creator

Provide counters and trays divided into grids. Students create arrays for given facts like 2 × 5 by placing equal rows and columns, then write the number sentence. Partners swap trays to verify and rotate the array to show commutativity.

What is an array, and how does it show a multiplication fact?

Facilitation Tip

During Manipulative Build, ask students to rotate their arrays physically to prove that 3 × 4 equals 4 × 3.

What to look for

Provide students with a small grid paper. Ask them to draw an array for 2 × 5 and write the matching number sentence. Then, ask them to draw an array for 5 × 2 and write that number sentence.

• Apply
• Analyze
• Evaluate
• Self-Awareness
• Self-Management
• Social Awareness

Activity 02

• Stations Rotation
• 45 min · Small Groups

Stations Rotation: Array Challenges

Set up stations with egg cartons, linking chains, dot paper, and number cards. At each, students build or draw arrays matching facts, record observations, and solve extension problems like finding missing factors. Rotate every 7 minutes.

How can you use rows and columns in an array to find a total?

Facilitation Tip

At Station Rotation, place one completed array at each station and have students write the matching number sentence before building their own version.

What to look for

Display an array of 12 objects (e.g., 3 rows of 4 dots). Ask students to write down the number of rows, the number of items in each row, and the multiplication number sentence it represents.

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

Activity 03

• Experiential Learning
• 20 min · Whole Class

Whole Class: Array Hunt Game

Display real-world images like windows or fences on the board. Students identify rows and columns in pairs, shout out facts, and justify with sketches. Tally class scores for most arrays found.

Can you draw an array for a multiplication fact like 3 × 4 and write the matching number sentence?

Facilitation Tip

For the Array Hunt Game, provide clipboards with blank grid paper so students can sketch the arrays they find around the room.

What to look for

Pose the question: 'How does an array help us understand multiplication?' Encourage students to use terms like 'rows,' 'columns,' and 'equal groups' in their explanations, referencing arrays they have built or drawn.

• Apply
• Analyze
• Evaluate
• Self-Awareness
• Self-Management
• Social Awareness

Activity 04

• Experiential Learning
• 25 min · Individual

Individual: Array Drawing Gallery

Students draw arrays for six multiplication facts on grid paper, label rows, columns, and totals. Display on walls for a gallery walk where peers add sticky notes with matching sentences.

What is an array, and how does it show a multiplication fact?

Facilitation Tip

In the Array Drawing Gallery, ask students to label each array with the matching number sentence and a short explanation of how they counted.

What to look for

Provide students with a small grid paper. Ask them to draw an array for 2 × 5 and write the matching number sentence. Then, ask them to draw an array for 5 × 2 and write that number sentence.

• Apply
• Analyze
• Evaluate
• Self-Awareness
• Self-Management
• Social Awareness

A few notes on teaching this unit

Teach arrays by starting with small facts like 2 × 3 before moving to larger ones, using concrete materials students can count. Avoid rushing to symbols; instead, give students time to arrange and rearrange counters to see the groups. Research shows that students who build arrays themselves develop stronger number sense and fewer errors with multiplication facts.

Successful learning looks like students confidently building arrays from any multiplication fact up to 10 × 10. They should explain their arrays using terms like rows, columns, and equal groups, and switch between horizontal and vertical arrangements without prompting. By the end, students should write correct number sentences for any array they create.

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Watch Out for These Misconceptions

• During Manipulative Build, watch for students who insist arrays must only go left to right.

  Give each pair of students 12 counters and ask them to build an array for 3 × 4, then rotate the entire array 90 degrees to build 4 × 3. Have them compare the two shapes and discuss whether the total changed.

• During Station Rotation, watch for students who count only the rows and ignore the columns.

  At each station, ask students to write down the number of rows, the number of items in each row, and the total before writing the number sentence. Circulate and prompt them to recount using both dimensions.

• During Array Drawing Gallery, watch for students who avoid odd-number facts like 3 × 3.

  Provide dot paper with a 3 × 3 grid and ask students to draw and label the array. Encourage them to compare this odd array to even ones like 2 × 4 to see that arrays work for any equal grouping.

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Methods used in this brief

• Experiential Learning
• Stations Rotation