Number Operations

Overview

In this lesson, you will build fluency with addition, subtraction, multiplication, and squares by using clear strategies, mental estimation, and written methods. You will connect these operations to problem-solving contexts and to recognising patterns involving square numbers.

Learning intentions

Students will be able to:

• WALT solve addition and subtraction problems using efficient strategies and check reasonableness
• WALT use multiplication to solve problems and justify the method
• WALT calculate and interpret squares (e.g., (n^2)) and use them in simple equations and patterns

Success criteria

Students can:

• I can choose an appropriate strategy (mental, written, or calculator) for addition/subtraction and explain why it works.
• I can use multiplication to find totals accurately and show working.
• I can calculate squares correctly and explain what a square represents.

Curriculum links

• Mathematics — addition and subtraction using strategies (Stage 4 outcomes)
• Mathematics — use strategies for addition and apply strategies for subtraction (language and reasoning)
• Mathematics — extend number sense to multiplication and square relationships using clear written methods and checks
• General cross-curriculum competence: understanding and applying mathematical thinking (reasoning, representing, and communicating)

Lesson structure (45 minutes)

1. 0–5 min · Warm-up recall (mental). Teacher writes: “Estimate then calculate: 47 + 56, 120 − 68.” Student gives a quick estimate, calculates, and explains one strategy used.

2. 5–12 min · Mini direct teach (choosing strategies). Teacher models two methods for addition/subtraction: partitioning (e.g., split into tens/ones or hundreds/tens/ones) and compensation (adjust then correct). Student copies a worked example and answers: “Which method is faster here and why?”

3. 12–20 min · Guided practice (addition + subtraction). Teacher provides a short set (student chooses which 2 questions to do fully, showing steps):

• 368 + 245
• 901 − 376
• 512 + 189 − 250 (one line method allowed, but show checks) Student solves chosen items and includes a brief “check” line (estimate or inverse operation).

4. 20–28 min · Multiplication application (arrays/partition). Teacher explains two strategies: repeated groups/area model (arrays) and partitioning (e.g., (23 \times 14 = 23 \times (10+4))). Student solves:

• 23 × 14
• 105 × 6 (at least one check using estimation) Student writes the method chosen and a reason for it.

5. 28–37 min · Squares (meaning + computation). Teacher introduces: “A square number is ‘number of rows = number of columns’ in a grid.” Student works through:

• Calculate: (12^2), (15^2), (9^2)
• Explain in words what (n^2) means. Teacher prompts pattern noticing: “What changes when the base increases by 1?”

6. 37–43 min · Mixed problem set (reasoning). Teacher gives one multi-step task (student solves with clear working):

• A student buys 3 packs of cards. Each pack costs $7. The student already has $20. (a) How much more money is needed? (b) Is the final amount closer to $30 or $50? Explain using estimation. Student answers using addition/subtraction and at least one multiplication step ((3 \times 7)).

7. 43–45 min · Exit ticket (quick assessment). Student completes on paper:

• (48 + 67 =)? (show strategy)
• (73 − 28 =)? (include a check)
• (14^2 =)? (one method)

Resources

• Printed worksheet with the problem set and blank lines for working
• Squared paper or grid paper for arrays and squares
• Number line (for subtraction support)
• Calculator (optional, only after attempting mental/written strategy first)
• Coloured pens/pencils (for partitioning: tens/ones or hundreds/tens/ones)
• Dyslexia-friendly reading support: a teacher-read audio track or screen reader text plus simplified font worksheet (larger font, spacing)

Assessment

• Formative: teacher observes which strategy the student selects and whether checks are used for addition/subtraction
• Formative: review square calculations and whether the student can explain what squaring means (not only compute)
• Exit ticket: accuracy and presence of strategy + check for at least one addition/subtraction item

Differentiation

• Support for students with reading difficulties (dyslexia-friendly):
• Read all instructions aloud; provide a shorter, chunked worksheet with one question at a time
• Use larger font (at least 14–16pt), generous line spacing, and bold key numbers
• Provide sentence starters: “I chose this method because…”, “I checked by…”, “(n^2) means…”
• Support for conceptual gaps:
• Use grid paper for (n^2) (draw (n) by (n) squares) before using number-only methods
• Provide a blank strategy box on the worksheet: Partition / Compensation / Array / Inverse-check
• Extension for advanced learners (keep as optional):
• Solve: (x^2 = 144). Find (x) and explain how you know.
• Create a set: “Make a subtraction problem where estimation tells you the answer is between 200 and 250.” Then solve and justify.
• If needed (extra scaffolding):
• Reduce the number of practice questions (choose 2 instead of 3) while keeping the mixed reasoning task