Integers Benchmarks

Overview

In this lesson, students consolidate their understanding of comparing and ordering integers by using benchmarks and number lines. They will solve ordering problems under specific conditions and justify their reasoning.

Learning intentions

• Students will compare integers and decide which is greater or less using benchmarks.
• Students will order sets of integers from least to greatest (and greatest to least).
• Students will justify ordering decisions with clear reasoning linked to number-line positions.
• Students will consolidate strategies for reasoning about negative and positive integers.

Success criteria

• I can explain how a benchmark helps me compare integers.
• I can correctly order integers using a number line or logical reasoning.
• I can state whether an integer is greater/less than another and support it with an explanation.
• I can justify my ordering when a condition is given (for example, “two are greater than −3”).

Curriculum links

• Compare and order integers using number lines and reasoning.
• Solve problems involving integers, including those requiring justification.
• Communicate mathematical thinking using words, diagrams, and equations.

Lesson structure (40 minutes)

1. 2 min — Launch + goal

• Display the learning target: “Compare and order integers using benchmarks and justify.”
• Quick prompt: “What does it mean if −5 is greater than −7?”

2. 6 min — Benchmark recap (whole class)

• Teacher models: choose a benchmark (commonly 0, −5, or −10 depending on the integers).
• Show comparisons using a number line:
• Example: Compare −8 and −5 using benchmark −5 (−8 is farther left of −5).
• Emphasise key idea: for negatives, “closer to zero is greater.”

3. 8 min — Worked example with justification

• Present: “Order these integers: −12, −3, 0, 5. Explain your method.”
• Teacher thinks aloud:
• Place benchmarks: 0 and maybe −5.
• Reason about each value: numbers less than −5 go left; −3 sits between −5 and 0; 0 is the origin; positives are to the right.
• Conclude with final order and a brief justification statement.

4. 10 min — Guided practice: ordering under conditions

• Students work in pairs on a task with constraints (teacher provides or writes on board):
• “Three integers are: one is less than −6, one is between −6 and −1, and one is greater than −1. Which ordering is possible?”
• Students must:
• Choose/confirm an order.
• Write a justification referencing where each integer lies relative to benchmarks.
• Teacher circulates, prompts for reasoning: “How do you know it’s between these two benchmarks?”

5. 8 min — Independent task (show reasoning)

• Students complete a short set of 3–4 questions:
• A: “Compare: −9 and −4. Explain using a benchmark.”
• B: “Order from least to greatest: −2, −10, 7, −1.”
• C: “True/False: If a number is less than −3, it is also less than −10. Justify.”
• Students include either a small number line sketch or written comparisons.

6. 4 min — Share-out and checking

• Select 2–3 students (or pairs) to share their reasoning for one question.
• Teacher highlights common strengths (clear benchmark use) and corrects misconceptions (especially about negative comparisons).

7. 2 min — Exit ticket

• Exit ticket: “Which is greater: −6 or −9? Explain in one sentence.”
• Collect to inform next lesson review or reteach areas.

Resources

• Board/markers or interactive display with a number line template
• Integer cards or a small set of integer strips for quick ordering (optional)
• Student worksheet with benchmark prompts and space for justification
• Pair work recording sheet (Order → Benchmark used → Reasoning)
• Digital or paper number line (marked at key benchmarks like −10, −5, 0, 5)
• Pens/pencils and rulers for drawing number lines
• Teacher-prepared example steps (benchmark → compare → order → justify)

Assessment

• Formative: Teacher observation during pair and guided practice, listening for benchmark-based justification.
• Formative: Review independent task and specifically check for:
• Correct order
• Correct greater/less than comparisons
• Quality of explanation (benchmark reference or number-line logic)
• Exit ticket: Quick check of negative comparison reasoning.

Differentiation

• Support:
• Provide number lines pre-marked at 0 and at one negative benchmark (for example, −5) to reduce drawing load.
• Offer sentence starters: “I know ___ is greater because it is to the right of ___ on the number line.”
• Allow students to use a small set of benchmark options (0, −5, −10) rather than choosing freely.
• Extension:
• Add a conditional challenge: “Order these integers under the condition that exactly two are less than −4.” Students must produce one valid ordering and explain why others cannot work.
• EAL:
• Encourage students to use diagrams alongside short written explanations.
• Use consistent language stems for comparisons (greater than, less than, between).
• SEN:
• Reduce the number of items per question while keeping the same reasoning requirement.
• Provide a partially completed comparison table (integer → relative position to benchmark → conclusion).