True or False Equations

Overview

Students investigate equality and inequality by comparing number sentences using <, > and =. They decide whether addition and subtraction statements are true, explain their reasoning, and solve open number sentences with a missing number.

Learning intentions

• WALT use <, > and = to compare numbers and number sentences.
• WALT check whether an addition or subtraction number sentence is true or false.
• WALT find a missing number in an open number sentence.
• WALT explain how I know my answer is correct.

Success criteria

• I can read <, > and = correctly.
• I can calculate or use a strategy to check a number sentence.
• I can find the missing number in an addition or subtraction sentence.
• I can explain my thinking using numbers, words, drawings or materials.

Curriculum links

• Mathematics and Statistics — Mathsteasers: higher-order thinking questions that challenge learners and deepen understanding.
• Mathematics and Statistics — Mathsteasers / Alignment: connecting mathematical challenge with familiar textbook learning.
• Mathematics and Statistics — Mathsteasers / Additional resources for advanced learners: opportunities to reason, justify and solve non-routine problems.

Lesson structure (30 minutes)

1. 0–4 min · Hook and revisit. Display the hook and learning intention slides and write 7 + 3 = 12 on the board. Ask, “Is this sentence true or false? How do you know?” Students silently decide, then show thumbs up or down and explain to a partner. Revisit that = means “has the same value as”, not simply “the answer comes next”.

2. 4–9 min · Teach the symbols. Use the comparison symbols slides to model <, > and = with two quantities, such as 8 and 5, then with number sentences: 6 + 2 > 7. Teacher emphasises reading the complete sentence: “Eight is greater than five.” Students compare two examples using mini-whiteboards, first calculating each side when needed.

3. 9–15 min · Reasoning together. Display the true-or-false discussion slides with statements such as 14 - 6 = 9, 20 + 5 < 30, and 18 - 8 = 10. Students work in pairs to calculate, decide true or false, and correct one false statement. Invite several explanations, including counting on, partitioning, using known facts, and checking with the inverse operation.

4. 15–24 min · Independent practice. Distribute the open number sentences worksheet. Students complete comparison, true-or-false and missing-number questions. Core questions use accessible numbers within the class’s current range, including 420 - □ = 401 and □ + 36 = 80; a challenge section includes larger numbers such as 8205 - 4721 = 3484 and asks students to explain whether the statement is true or false. Teacher circulates, asking, “What does the equal sign tell you?” and “How could you check?”

5. 24–28 min · Partner challenge and share. Display the partner challenge and discussion slide: “Make a true number sentence using 36, 20, 16 and one symbol. Can you make a different one?” Partners create, check and read their sentences aloud. Select examples that show equality on either side of the equation and discuss more than one possible answer.

6. 28–30 min · Plenary and exit check. Use the plenary slide and ask students to complete orally or on the back of the worksheet: 53 - □ = forty (write 40 rather than the word if appropriate) and 27 + 8 □ 40. Students show answers, then state one way they checked their work.

Resources

• the complete comparison and equations slide deck
• the open number sentences worksheet
• Mini-whiteboards, pens and erasers
• Counters or place-value equipment
• Large cards or board symbols for <, > and =
• Pencils and highlighters

Assessment

• Listen for whether students interpret = as equivalence and can read comparison statements in the correct direction.
• During the worksheet, record who can calculate both sides, identify false statements, and use an inverse operation or another checking strategy.
• Use the final two questions to identify students needing follow-up with comparison symbols, subtraction or missing-number reasoning.

Differentiation

• Support: provide counters, a number line, place-value equipment and sentence frames such as “I know this is true because ___ has the same value as ___.” Reduce the number size while retaining the same structure.
• Dyslexia-friendly options: use a clear sans-serif font, large print, generous spacing, uncluttered questions and symbols separated from surrounding text. Read instructions aloud, allow students to answer orally or draw their reasoning, and avoid requiring copying.
• Pair students strategically for discussion; allow extra processing time and check understanding one question at a time.
• Extension: ask advanced learners to find all missing numbers that make □ + 24 > 50 true, create a false sentence that looks convincing, or solve and justify 8205 - 4721 = 3484 using an efficient written or mental strategy.