Mathematics · Grade 3

Active learning ideas

Patterns in the Multiples

Active learning transforms abstract patterns in multiples into visible, touchable ideas. When students move, color, and construct, the regularity of numbers becomes something they can see and feel, not just memorize. This topic thrives when students investigate patterns firsthand rather than passively absorb rules.

• Ontario Curriculum Expectations
• 3.OA.D.9

• 20–35 min
• Pairs → Whole Class
• 3 activities

Activity 01

• Gallery Walk
• 35 min · Small Groups

Gallery Walk: Pattern Detectives

Groups are assigned a specific multiple (e.g., 3s or 9s) and color in those numbers on a large hundreds chart. They post their charts around the room, and the class walks around to identify and record 'secret patterns' they see in the shapes or digits.

Analyze why certain multiples always end in specific digits.

Facilitation Tip

During the Gallery Walk, position yourself near a poster to overhear discussions and gently prompt students to explain their observations aloud.

What to look for

Provide students with a list of number sequences (e.g., 3, 6, 9, ___, 15; 7, 14, ___, 28, 35). Ask them to fill in the missing number and explain the pattern they used.

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

Activity 02

• Inquiry Circle
• 30 min · Small Groups

Inquiry Circle: The Doubling Tree

Students work in groups to show how the multiples of 2 can be doubled to find the multiples of 4, and doubled again for 8. They create a visual 'tree' or diagram to show these connections.

Explain how knowing the multiples of 2 can help us find the multiples of 4 and 8.

Facilitation Tip

For The Doubling Tree, model the first branch step-by-step, then step back to let pairs debate the next doubling connection.

What to look for

Display a hundreds chart with multiples of 3 colored in. Ask students: 'What do you notice about the ones digits in the multiples of 3? Predict the ones digit for the next multiple of 3.'

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

Activity 03

• Think-Pair-Share
• 20 min · Pairs

Think-Pair-Share: The Magic of 9

Students look at the first ten multiples of 9. They think about what happens when they add the two digits of each multiple together (e.g., 1+8, 2+7). They share their 'discovery' with a partner and then the whole class.

Predict how patterns can help us solve multiplication problems we haven't memorized yet.

Facilitation Tip

In The Magic of 9, pause after the first example to ask students to turn and talk about what they notice before sharing with the class.

What to look for

Pose the question: 'How does knowing the multiples of 2 help you with the multiples of 4?' Facilitate a discussion where students share their reasoning, perhaps using examples or drawings.

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

A few notes on teaching this unit

Teachers approach this topic by starting with what students already know, like skip counting, and building connections to multiplication. Concrete tools like hundred charts and number lines help students visualize patterns, while open-ended questions encourage them to test predictions. Avoid rushing to formal multiplication facts before students see the relationships. Research shows that students who discover patterns themselves retain them longer and apply them more flexibly.

Successful learning looks like students confidently predicting multiples, explaining their reasoning, and recognizing how one pattern connects to another. They should move from saying, 'I see a pattern,' to sharing, 'This is why the pattern works.' Collaboration and concrete examples help move beyond surface-level observations.

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Watch Out for These Misconceptions

• During the Gallery Walk: Pattern Detectives, watch for students who dismiss patterns as random rather than structural.

  After they record their observations, ask them to extend the pattern for one more term. If they cannot, prompt them to use the colored hundreds chart to see how the multiples form a predictable shape.

• During Collaborative Investigation: The Doubling Tree, watch for students who confuse doubling with adding the same number twice.

  Ask them to trace the branch with their finger, saying the multiplication equation aloud as they go. For example, '4 jumps of 2 is 8,' linking the skip count to the product.

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Methods used in this brief

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