Mathematics · 4th Grade

Active learning ideas

Factors, Multiples, and Primes

Active learning builds students’ number sense concretely. When learners physically arrange arrays, sort cards, or race to find factors, they turn abstract definitions into tangible experiences. These kinesthetic and visual tasks help fourth graders internalize the relationships between factors, multiples, and primes before moving to symbolic notation.

• Common Core State Standards
• CCSS.Math.Content.4.OA.B.4

• 20–30 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Stations Rotation
• 30 min · Pairs

Format: Array Factor Hunt

Give each pair a set of square tiles or grid paper and assign them a number (e.g., 24). They build every possible rectangle with that many squares and record each dimension pair as a factor pair. Pairs share their factor lists and the class compares numbers with many factor pairs to numbers with only one, introducing composite vs. prime.

Analyze what determines if a number can be broken down into equal smaller groups.

Facilitation Tip

During Array Factor Hunt, circulate with a checklist to note which students are starting arrays at 1 and moving up, rather than guessing.

What to look for

Provide students with a list of numbers (e.g., 12, 17, 24, 29). Ask them to write down all factor pairs for the composite numbers and to circle the prime numbers, writing 'prime' next to them.

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

Activity 02

• Stations Rotation
• 20 min · Small Groups

Format: Factor/Prime/Composite Sort

Small groups receive number cards 1-30 and sort them into categories: prime, composite, and (as a discussion challenge) the special case of 1. Groups compare their sorts and discuss any disagreements. Post a class anchor chart defining each category based on students' language from the discussion.

Differentiate between factors and multiples of a given number.

Facilitation Tip

While students sort Factor/Prime/Composite cards, listen for precise language like 'exactly two factors' when they describe primes.

What to look for

On one side of an index card, write a number (e.g., 18). Ask students to list all its factors. On the other side, write a different number (e.g., 13) and ask them to explain if it is prime or composite and why.

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

Activity 03

• Stations Rotation
• 25 min · Pairs

Format: Multiple Patterns on a Hundreds Chart

Each student colors multiples of an assigned number on a 1-100 chart. Pairs compare their charts and identify shared colored squares, which are common multiples. Discussion questions: What do the patterns look like? Why do some numbers appear on more charts than others? What do you notice about multiples of prime numbers?

Justify why prime numbers are considered the building blocks of all other numbers.

Facilitation Tip

On the Hundreds Chart for Multiple Patterns, ask students to describe the visual pattern they see before they color, to connect skip-counting with multiples.

What to look for

Pose the question: 'If a number is a multiple of 6, what else do you know about its factors?' Guide students to discuss how multiples relate to the factors of the original number.

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

Activity 04

• Stations Rotation
• 20 min · Small Groups

Format: Factor Pair Relay Race

Teams of four race to find all factor pairs for a given number by passing a recording sheet: each student adds one factor pair and passes it on. The first team to correctly list all factor pairs wins, but any team that misses a pair must keep working. Post-game discussion: how did you know you had found them all?

Analyze what determines if a number can be broken down into equal smaller groups.

Facilitation Tip

In the Factor Pair Relay Race, stand at the finish line to watch students cross off found factors on their number cards to avoid duplicates.

What to look for

Provide students with a list of numbers (e.g., 12, 17, 24, 29). Ask them to write down all factor pairs for the composite numbers and to circle the prime numbers, writing 'prime' next to them.

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

A few notes on teaching this unit

Teach this topic through structured, systematic exploration first. Avoid rushing to rules like 'a number is prime if…' before students experience what primes look like through arrays and sorting. Use consistent vocabulary: factors go in, multiples come out. Research shows that repeated exposure to visual models and partner talk strengthens retention and corrects misconceptions before they take root.

By the end of these activities, students should confidently identify all factor pairs for numbers 1–100, classify numbers as prime or composite with reasons, and explain how factors and multiples connect. Clear vocabulary use and systematic strategies will be evident in their work and discussion.

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Watch Out for These Misconceptions

• During Array Factor Hunt, watch for students who create only one array per number or stop searching once they find a pair.

  Prompt students to ask, 'Have I found all the rectangles?' and guide them to start at 1 and increment systematically, recording each array. Ask them to point to the missing arrays on their grid paper.

• During Factor/Prime/Composite Sort, watch for students who place 1 in the prime category or misclassify 2 as composite.

  Pause the sort and ask, 'How many factors does 1 have? How many does 2 have?' Use the card labels to remind them: primes have exactly two distinct factors, and composites have more than two.

• During Factor Pair Relay Race, watch for students who stop listing pairs once they reach a factor larger than 10, missing larger pairs.

  Have students use a whiteboard to track pairs and remind them to stop when the factors would cross (e.g., for 24, stop after 4 x 6 because 5 x 4.8 is not whole). Ask, 'How do you know you have them all?'

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Methods used in this brief

• Stations Rotation