Inequality Detectives

Overview

This is lesson 2 of 10 in Algebra Detectives: Solve, Simplify, Share. Students compare and complete number sentences involving all four operations and the inequality symbols <, >, ≤ and ≥, building on prior work with accurate calculation and mathematical reasoning.

Learning intentions

• WALT use <, >, ≤ and ≥ correctly.
• WALT calculate and compare both sides of a number sentence.
• WALT explain and justify whether an inequality is true.
• WALT communicate mathematical thinking clearly using examples.

Success criteria

• I can choose the correct inequality symbol.
• I can calculate both sides accurately, including decimal calculations.
• I can explain how I know my comparison is true.
• I can check another person’s reasoning and improve my own explanation.

Curriculum links

• Mathematics and Statistics: mathematical reasoning, problem solving and communicating mathematical thinking.
• Number and algebra: using the four operations to calculate, compare and justify relationships between quantities.
• Mathsteasers: challenging higher-order questions that deepen understanding for advanced learners.
• Mathsteasers / Alignment: connecting challenge questions with familiar mathematical ideas and classroom learning.

Lesson structure (45 minutes)

1. 0–6 min · Hook: human number line. Open with the inequality hook slides and place a physical number line across the room, with students holding <, >, ≤ or ≥ cards. Read statements such as 7 __ 4, 3 __ 3 and 2.5 __ 2.05; students move to show the symbol they think belongs between the numbers, then explain their choice to a partner.

2. 6–13 min · Make the thinking visible. Model the example 0.8 × 12 ≤ 8 × 0.5 + 8 using the worked comparison slides. Calculate each side separately, record 9.6 and 12, and discuss why ≤ is true even though the two sides are not equal. Students use a think-pair-share routine to identify common errors, such as comparing digits without considering place value.

3. 13–27 min · Collaborative inequality investigation. Organise 11 students into three groups of three or four. Give each group the inequality investigation worksheet and the inequality symbols and number line cards. Students solve comparison questions involving whole numbers first, then decimals and all four operations; they match suitable symbols and number-line representations where appropriate. Require each group to record both calculations and a written reason for at least three answers.

4. 27–35 min · Research and refine. Display the investigation prompts from the group challenge slides. Each group chooses one statement to test, checks calculations using a place-value grid or calculator, and looks for a way to prove the result rather than relying on a single estimate. Students prepare a two-minute presentation showing the original statement, calculations for both sides, the chosen symbol and a clear explanation.

5. 35–42 min · Mini-presentations and feedback. Invite each group to present its example. The audience uses “notice, question, suggest”: one accurate feature, one clarifying question and one suggestion for making the reasoning stronger. Students compare methods and identify how brackets, operation order and decimal place value affect accuracy.

6. 42–45 min · Exit check and preview. Return to the plenary and exit-check slides. Students independently complete: 1.2 × 5 __ 3 + 2; explain their choice; and write one rule for checking an inequality. Collect responses to identify who needs further support before the next lesson.

Resources

• the inequality lesson slide deck
• the inequality investigation worksheet
• the inequality symbols and number line cards
• Large floor number line
• Inequality symbol cards
• Mini-whiteboards and pens
• Place-value grids
• Calculators for checking
• A3 paper and coloured pens for presentations

Assessment

• Listen during the human number line and ask students to justify, rather than simply name, their symbol.
• Check group worksheets for separate, accurate calculations of both sides and explanations that use mathematical language.
• Use the exit check to assess symbol choice, calculation accuracy and the ability to justify a comparison.

Differentiation

• Begin with whole-number comparisons and use the physical number line and visual comparison mats before introducing decimals.
• Provide place-value grids, worked examples, multiplication tables and sentence starters such as “The left side is…”, “The right side is…”, and “Therefore…”.
• Allow calculators for checking decimal calculations, while requiring students to show an estimate or written method first.
• Pair students strategically and offer oral rehearsal, reduced question sets, enlarged print and a reader/scribe where needed. Encourage manaaki and aroha through respectful feedback and invite atamai, thoughtful explanations.
• For advanced learners, replace the missing symbol or number with a variable: find all possible values for a missing number and prove whether the solution set is finite or infinite. Students must represent their reasoning symbolically, on a number line or with a table.