Mathematics · Year 7

Active learning ideas

Negative Numbers and the Number Line

Active learning helps students grasp negative numbers by giving them physical and visual ways to see how numbers move and relate to each other. Moving along a number line or sorting numbers in groups makes abstract ideas concrete and memorable.

• National Curriculum Attainment Targets
• KS3: Mathematics - Number

• 25–40 min
• Pairs → Whole Class
• 3 activities

Activity 01

• Inquiry Circle
• 30 min · Small Groups

Inquiry Circle: The Sieve of Eratosthenes

In small groups, students work on a large 1-100 grid to systematically cross out multiples. They discuss why certain numbers remain and identify the patterns of primes, specifically looking at why 1 is neither prime nor composite.

Justify the necessity of negative numbers for describing real-world situations.

Facilitation Tip

During the Sieve of Eratosthenes, have students mark multiples in different colors to see patterns emerge quickly.

What to look for

Present students with a list of numbers: 5, -3, 0, 8, -10, 2. Ask them to arrange these numbers in ascending order on a mini-whiteboard and hold it up. Observe for common errors in ordering negative numbers.

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

Activity 02

• Peer Teaching
• 25 min · Pairs

Peer Teaching: Factor Tree Challenge

Pairs are given different large composite numbers. One student creates a factor tree while the other checks the prime status of each branch; then they swap roles to find the HCF of their two numbers using a shared Venn diagram.

Compare the operations of addition and subtraction with positive and negative integers.

Facilitation Tip

When students build factor trees, insist they label each branch with the correct prime factor to reinforce accuracy.

What to look for

Give each student a card with a scenario: 'A diver descends 20 meters below sea level, then ascends 12 meters.' Ask them to write the calculation using negative numbers (e.g., -20 + 12) and state the final depth.

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

Activity 03

• Gallery Walk
• 40 min · Whole Class

Gallery Walk: Prime Art

Students create visual representations of numbers using their prime factors (e.g., using different colours for 2, 3, and 5). They display their work, and the class moves around to identify the original numbers based only on the prime factor 'DNA' shown.

Predict the outcome of multiplying two negative numbers.

Facilitation Tip

Ask students to write a short reflection after the Gallery Walk to articulate what makes a number prime or composite.

What to look for

Pose the question: 'If you add two negative numbers, is the answer always smaller than the original numbers? Explain your reasoning using the number line.' Facilitate a class discussion where students share their justifications.

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

A few notes on teaching this unit

Teach negative numbers by starting with real-world contexts like temperature or elevation so students see negatives as meaningful, not arbitrary. Use consistent language: call -3 'negative three,' not 'minus three,' to avoid confusion with subtraction. Research shows students benefit from multiple representations, so pair number lines with counters or digital tools to build flexible understanding.

Students should confidently place negative numbers on a number line, perform simple calculations, and explain their reasoning using correct terminology. They should also recognize patterns like why adding two negatives always gives a more negative result.

---

Watch Out for These Misconceptions

• During the Sieve of Eratosthenes, watch for students marking 9, 15, or 21 as prime because they are odd.

  As students work, pause the activity and ask them to check if each odd number they marked has more than two factors. Have them cross out these composites immediately and explain why they don’t belong.

• During the Factor Tree Challenge, watch for students including 1 as a prime factor.

  When reviewing factor trees, ask students to list all factor pairs for their starting number. Guide them to see that 1 only pairs with itself, so it cannot be a prime factor.

---

Methods used in this brief

• Inquiry Circle
• Peer Teaching
• Gallery Walk