Checking Number Truths

Overview

This 60-minute lesson introduces Year 7 students to checking the truth of number sentences involving all four operations (addition, subtraction, multiplication, division) and inequalities. It aligns with the New Zealand Curriculum Refresh for Mathematics and Statistics, particularly the Phase 3 Algebra strand focusing on equations and relationships.

Students will develop conceptual understanding and fluency with number sentences – including true/false judgments – using equality and inequality symbols. They will also practise representing and explaining their reasoning using appropriate mathematical vocabulary and symbols.

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Curriculum References

Te Mātaiaho | Mathematics and Statistics in the New Zealand Curriculum (Years 0-8), Phase 3

• Achievement Objective:
• Form and solve true or false number sentences and open number sentences involving all four operations, using an understanding of equality or inequality (Year 7)
• Key Competencies:
• Thinking: reasoning with number sentences, justifying arguments
• Using language, symbols and text: mathematical representing and communicating
• Disciplinary Knowledge:
• Operations with whole numbers and integers
• Use of the equal sign as equivalence, inequality symbols <, >
• Inverse operations to check and solve number sentences.
• Teaching considerations:
• Use of a number line and counters for integers
• Connect language and symbols to meanings clearly
• Use worked examples, step-by-step with one equal sign per line
• Employ the mnemonic GEMA (grouped, exponents, multiplicative, additive) for order of operations
• Mathematical content focus:
• Equality, inequality, truth of statements
• Checking results by inverse operations and estimation
• Connecting algebraic thinking to numeric operations and reasoning with equivalence.

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Learning Intentions

• We are learning to check if number sentences involving addition, subtraction, multiplication and division are true or false.
• We are learning to use inequality symbols (<, >, =) appropriately to compare values.
• We are learning to explain our reasoning using inverse operations and estimation to verify answers.
• We are learning to write and interpret true/false number sentences using all four operations and inequalities.

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Resources Needed

• Whiteboard and markers
• Individual mini whiteboards and pens for students
• Number line posters
• Counters or two-sided counters (red/blue) for integer exploration
• Pre-prepared number sentence cards (involving all operations and inequalities)
• Calculator (optional, for checking)
• Worksheet with number sentences for individual or pair work

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Lesson Breakdown (60 minutes)

1. Introduction & Activation (10 minutes)

• Goal: Connect prior knowledge of operations and equalities to today's learning.
• Discuss the equal sign as "the same as" rather than just an operator to calculate answers.
• Introduce the idea that number sentences can be true or false. Explain this with simple examples on the board:
• 8 + 4 = 12 (True)
• 7 × 3 = 20 (False)
• Introduce inequality symbols < (less than), > (greater than) with intuitive examples using counters or context (e.g., 5 < 8) and show on number line.
• Use a few verbal statements translated into number sentences, e.g. "Ten is less than fifteen," → 10 < 15

Teacher Tip: Use the Frayer model (Definition, Characteristics, Examples, Non-examples) to establish understanding of ‘=’, ‘<’, ‘>’ symbols and vocabulary.

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2. Guided Whole-Class Exploration (15 minutes)

• Model checking truth of number sentences involving all four operations.
• Use simple sentences and demonstrate on board:
• E.g. Is 6 × 4 = 24 true? Calculate 6 × 4, check if equals 24.
• E.g. Is 18 ÷ 3 = 7 true? Calculate; since 18 ÷ 3 = 6, sentence is false.
• E.g. 15 + 7 > 20? Calculate left side, compare to 20 using > symbol.
• Emphasise inverse operations for checking (e.g., If 12 + 8 = 20, check by 20 - 8 = 12).
• Reference the order of operations briefly (GEMA) where needed for multi-step sentences (e.g., 3 + 4 × 2 = 14?).
• Use mini whiteboards: call out sentences, students hold up T or F.

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3. Collaborative Paired Activity (15 minutes)

• Hand out number sentence cards and worksheets with mixed true/false sentences including inequalities.
• Students work in pairs to:
• Evaluate the truth of number sentences.
• Use inverse operations, estimation, or number lines/counters to justify answers.
• Annotate answers with explanations or calculations.
• Teacher circulates to scaffold reasoning, prompt peer discussion, and provide extension challenges for more capable learners (e.g., create their own true or false number sentences involving negative numbers or multi-step operations).

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4. Differentiation for More Capable Learners (5 minutes)

• Challenge students to write number sentences that are deliberately tricky to evaluate, for example:
• Sentences mixing positive and negative integers: -5 + 8 > 3
• Multi-step equations requiring order of operations: (2 + 3) × 4 = 20?
• Use digital tools (exploration with calculators or spreadsheet formulas) to check truth for complex sentences.
• Encourage these learners to verbally explain patterns or rules they discover about true/false sentences and inequalities.

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5. Sharing & Class Discussion (10 minutes)

• Invite selected pairs or individuals to share examples of true and false sentences they checked, and how they verified them.
• Discuss the importance of understanding equality vs inequality signs.
• Clarify any misconceptions observed during activities.
• Reinforce connection to real life: checking correctness of calculations, comparing values in daily life or commerce, problem-solving contexts.

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6. Formative Assessment & Plenary (5 minutes)

• Quick quiz on mini whiteboards: True or False number sentences and inequalities, including some that require multiple steps or inverse checking.
• Use thumbs up/down or T/F signs for quick visual feedback.
• Summarise key learning points:
• Truth of number sentences depends on correct calculations and comparisons.
• Equal sign means equivalence, not just "calculate answer."
• Inverse operations help to check answers.
• Inequalities express relationships of less than or greater than.

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Summary

This introductory algebra exploration session supports students in confidently checking the truth of number sentences and inequalities, building a foundation for solving equations and understanding relationships. It is designed to connect with their prior knowledge, scaffold reasoning with practical tools, and provide extension pathways for advanced thinking, fully aligned with New Zealand’s refreshed curriculum expectations.

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If you require further lesson plans or adaptations, feel free to ask!