Mathematics · 3rd Year

Active learning ideas

Patterns in Multiples (2, 3, 4, 5, 10)

Active learning helps students see number patterns in multiples as visible and tactile experiences rather than abstract facts. When students move, highlight, and discuss, they build mental models of sequences and relationships that stick longer than memorized tables.

• NCCA Curriculum Specifications
• NCCA: Primary - Algebra
• NCCA: Primary - Number

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

Activity 01

• Decision Matrix
• 35 min · Small Groups

Hundred Square Hunt: Multiples Highlighting

Provide printed hundred squares to small groups. Assign one multiple per group (2, 3, 4, 5, or 10) and have them color all instances. Groups then share observations, like positions of fives or fours as doubles of twos. Discuss patterns as a class.

Analyze why all multiples of five end in either zero or five.

Facilitation Tip

During Hundred Square Hunt, ask students to whisper their next multiple in sequence before highlighting it to keep everyone engaged.

What to look for

Provide students with a hundred square. Ask them to highlight the multiples of 3. On the back, they should write two observations about the patterns they see in the highlighted numbers.

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management

Activity 02

• Decision Matrix
• 25 min · Pairs

Pairs Relay: Skip Counting Race

Pairs line up at a board. First student writes the first five multiples of their assigned number (e.g., 3), tags partner who adds next five. Switch numbers midway. Debrief on sequences and relationships, such as fours from twos.

Explain how to use the 2 times table to help learn the 4 times table.

Facilitation Tip

In Pairs Relay, stand close to the skip counting line to model quick corrections and cheer for smooth transitions.

What to look for

Ask students: 'If you know that 7 x 2 = 14, how can you figure out 7 x 4?' Students write or verbally explain their reasoning, focusing on doubling.

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management

Activity 03

• Decision Matrix
• 30 min · Whole Class

Whole Class: Pattern Prediction Game

Project a partially highlighted hundred square. Students predict and justify the next multiples for 5 or 10. Call on volunteers to explain, then reveal and vote on pattern rules like 'fives end in 0 or 5.'

Construct a list of patterns found on a hundred square when highlighting multiples.

Facilitation Tip

For Pattern Prediction Game, pause after each round to ask students to explain their reasoning before revealing the next prediction.

What to look for

Pose the question: 'Why do all the numbers in the 10 times table end in zero?' Facilitate a class discussion where students share their ideas, encouraging them to use terms like 'multiple' and 'grouping'.

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management

Activity 04

• Decision Matrix
• 20 min · Individual

Individual: Multiples Chain Cards

Give students cards with numbers. They chain multiples of 2, 3, 4, 5, 10 in sequence, noting patterns like even numbers for twos. Swap chains with a partner to verify and extend.

Analyze why all multiples of five end in either zero or five.

Facilitation Tip

When using Multiples Chain Cards, circulate to listen for students describing the doubling rule aloud as they link cards.

What to look for

Provide students with a hundred square. Ask them to highlight the multiples of 3. On the back, they should write two observations about the patterns they see in the highlighted numbers.

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management

A few notes on teaching this unit

Teach this topic by moving from concrete to abstract in short steps. Start with hands-on tools like hundred squares and counters to build visual patterns, then guide students to articulate the rules in their own words. Avoid rushing to memorization before students have experienced the patterns through movement and talk.

Successful learning shows when students can describe and explain patterns using clear language and visual evidence from their work. They should connect the numbers to real objects or grids and justify their observations with reasoning.

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Watch Out for These Misconceptions

• During Hundred Square Hunt, watch for students who only highlight multiples of five that end in five and miss those ending in zero.

  Circulate during Hundred Square Hunt and gently point to a highlighted zero-ending multiple, asking: 'Is this a multiple of five? How do you know?' Encourage students to recount by fives to see both endings appear naturally.

• During Pairs Relay, listen for students who say the four times table is unrelated to the two times table.

  During Pairs Relay, pause the game after one round and ask students to pair up the cards for 2 x 3 and 4 x 3, guiding them to notice 4 x 3 is double 2 x 3 before continuing.

• During Hundred Square Hunt, watch for students who describe patterns as random or unclear.

  After students finish Hundred Square Hunt, ask them to stand back and describe the shapes or lines they see, prompting them to name 'columns,' 'diagonals,' or 'blocks' before moving to the next step.

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Methods used in this brief

• Decision Matrix