Mathematics · Grade 4

Active learning ideas

Prime and Composite Numbers

Active learning turns abstract number properties into tangible, visual experiences that students can manipulate and discuss. For prime and composite numbers, hands-on work with arrays and charts builds deeper understanding than worksheets alone. The activities connect multiplication facts to classification, reinforcing Grade 4 place value while addressing common misconceptions directly through concrete examples.

• Ontario Curriculum Expectations
• CCSS.MATH.CONTENT.4.OA.B.4

• 20–40 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Think-Pair-Share
• 35 min · Small Groups

Small Groups: Array Builder Challenge

Provide each group with counters and number cards from 1 to 50. Students build all possible arrays for a number, list factor pairs, and classify it as prime or composite. Groups share one example with the class, justifying their classification. Conclude with a quick hundreds chart update.

Differentiate between prime and composite numbers using examples.

Facilitation Tip

During Array Builder Challenge, circulate and ask groups to explain why their arrays show only one or multiple factor pairs, focusing on the language of factors.

What to look for

Provide students with a list of numbers (e.g., 13, 15, 17, 21). Ask them to write each number's factor pairs, then classify it as prime or composite. Include the number 1 and ask why it doesn't fit either category.

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

Activity 02

• Think-Pair-Share
• 25 min · Pairs

Pairs: Factor Pair Race

Pair students and give each duo a set of numbers 10-30. They race to list all factor pairs on mini whiteboards, then check arrays with linking cubes. Switch roles if one finishes first. Discuss why 1 and primes have limited pairs.

Justify why the number 1 is neither prime nor composite.

Facilitation Tip

During Factor Pair Race, listen for pairs to name all factors in order; pause if students skip numbers to reinforce completeness.

What to look for

Display a hundreds chart on the board. Ask students to identify and circle all the prime numbers up to 30. Then, ask them to describe any patterns they observe in the placement of these prime numbers.

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

Activity 03

• Think-Pair-Share
• 40 min · Whole Class

Whole Class: Sieve the Hundreds Chart

Project a hundreds chart. Students call out multiples of 2, then 3, crossing them off as a class. Continue to 7. Identify remaining primes and discuss patterns. Students replicate on personal charts.

Analyze patterns in prime numbers using a hundreds chart.

Facilitation Tip

During Sieve the Hundreds Chart, ask students to describe patterns aloud as they mark numbers, using phrases like 'every other number' or 'all numbers ending in 5' to build reasoning.

What to look for

Pose the question: 'If you were explaining prime and composite numbers to someone who had never heard of them, what would be the most important things you would tell them? Use examples of numbers and arrays in your explanation.'

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

Activity 04

• Think-Pair-Share
• 20 min · Individual

Individual: Prime Hunt Journal

Students receive a hundreds chart and color primes one color, composites another, noting why 1 is neither. They journal three patterns observed and one justification for a chosen number.

Differentiate between prime and composite numbers using examples.

Facilitation Tip

During Prime Hunt Journal, remind students to sketch arrays next to each number to connect visuals to written explanations.

What to look for

Provide students with a list of numbers (e.g., 13, 15, 17, 21). Ask them to write each number's factor pairs, then classify it as prime or composite. Include the number 1 and ask why it doesn't fit either category.

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

A few notes on teaching this unit

Teachers should model array building with counters or grid paper first, emphasizing that 1 always counts as a factor. Avoid rushing students to conclusions; instead, ask them to prove their classifications with arrays and factor lists. Research shows that students who articulate their thinking while building models retain concepts longer. Use peer discussion to resolve disagreements, not the teacher as the sole authority.

Students will confidently classify numbers as prime or composite by generating all factor pairs and modeling them with arrays. They will explain why 1 is neither prime nor composite and why 2 is the only even prime. Conversations will focus on factors, not guesses, with clear justifications for each classification.

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Watch Out for These Misconceptions

• During Array Builder Challenge, watch for students to classify 1 as prime because it has only one factor.

  Have students build an array for 1 using counters and ask them to describe the rectangle’s dimensions. Remind them that prime numbers need exactly two distinct factors, so 1 must be modeled with a single row of 1 counter, showing it does not meet the definition.

• During Factor Pair Race, watch for students to assume numbers like 4 or 6 are prime because they are small.

  Ask groups to build all possible arrays for these numbers and list all factor pairs. Point out that even small evens greater than 2 always have more than two factors, especially 2 as a factor.

• During Sieve the Hundreds Chart, watch for students to skip 1 when marking primes, thinking it is prime by default.

  Pause the activity and ask students to explain why 1 is not circled. Have them build a 1x1 array and discuss that it has only one factor, so it belongs in its own category.

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Methods used in this brief

• Think-Pair-Share