Prove Number Sentences

Overview

This final lesson in the five-part unit brings together solving, checking and explaining open number sentences and truth statements to 120. Learners work collaboratively, choosing practical materials, drawings, number lines or equations to prove their thinking before creating a puzzle for a classmate.

Learning intentions

• WALT solve mixed open number sentences involving addition, subtraction, multiplication and division.
• WALT decide whether a number sentence is true or false and explain why.
• WALT choose a useful representation and check an answer.
• WALT communicate mathematical thinking clearly with a partner.

Success criteria

• I can accurately solve or judge a number sentence.
• I can choose a helpful representation, such as materials, a drawing, number line or equation.
• I can explain and justify my thinking.
• I can check my answer using a different strategy.

Curriculum links

• NZC Mathematics and Statistics — Number: use and communicate number knowledge and strategies with numbers to 120.
• NZC Mathematics and Statistics — mathematical problem solving and communication.
• Mathsteasers — higher-order thinking questions that challenge learners and deepen understanding.
• Key competencies: thinking, managing self, and relating to others.

Lesson structure (60 minutes)

1. 0–10 min · Review and hook. Display the opening puzzle and review prompts and ask, “Can both sides of an equals sign be the same?” Model a truth statement such as 36 + 8 = 40 + 4, then show an open sentence such as __ − 17 = 25. Students solve mentally or with materials, compare methods with a partner, and explain how they checked.

2. 10–25 min · Strategy workshop. Use the strategy workshop examples to demonstrate one problem in several ways: build 42 + 15 with tens and ones, show it on a number line, draw it, and record the equation. Think aloud when checking a statement such as 6 × 4 = 28; ask students to identify the operation, estimate the answer and prove whether it is true. Students practise one example on mini-whiteboards, then share which representation was most useful and why.

3. 25–30 min · Trail briefing. Introduce the challenge-trail instructions and organise 10 pairs. Distribute the differentiated challenge trail and provide each pair with a tray of counters, linking cubes, number lines and place-value equipment. Explain that partners must take turns as solver and checker, record a representation or explanation for each challenge, and ask for a teacher conference when they reach a marked check point.

4. 30–50 min · Differentiated challenge trail. Pairs complete the trail at an appropriate level, using the worksheet challenges and available materials. The teacher conferences with groups, asking, “What do you know?”, “How could you prove it another way?” and “Does your answer make sense?” Students solve open sentences, judge true or false statements, correct errors, and check with a second strategy. Encourage spoken, drawn or written explanations.

5. 50–60 min · Create, share and reflect. Display the puzzle-design and reflection prompts. Each learner designs one number-sentence puzzle for a classmate, including a missing number or truth statement and a small clue showing how it can be checked. Partners swap, solve and explain the puzzle. Invite two pairs to share different methods, then students complete the worksheet reflection: “My best strategy was…”, “I checked by…”, and “Next time I will…”.

Resources

• the complete 60-minute teaching deck
• the differentiated challenge trail
• Mini-whiteboards, pens and erasers
• Counters or small connecting cubes
• Tens-and-ones/place-value equipment
• Number lines to 120
• Paper, pencils and crayons
• 10 pair work trays
• Teacher conference checklist

Assessment

• Listen during the review and workshop for accurate operation language, understanding of the equals sign and sensible estimation.
• During the trail, record whether each learner can solve or judge a statement, select a representation, justify their answer and check independently or with prompting.
• Collect the final puzzle and reflection as an exit check. Look for a solvable question, a correct solution and an explanation or checking strategy.

Differentiation

• Support learners with colour-coded operation prompts, partially completed examples, number lines, concrete materials and a reduced number range where needed.
• Offer choice of counters, cubes, place-value equipment, drawings or equations; accept spoken, drawn or written explanations.
• Pair learners thoughtfully and use short teacher conferences with sentence starters such as “I know this because…” and “I checked by…”.
• Extend advanced learners to create a multi-step puzzle with more than one possible solution and explain the conditions that make each solution valid.