Exploring Area Skills

WALT (We Are Learning To)

• Calculate the area of rectangles and squares using the formulas A = length × width and A = side × side.
• Apply multiplication skills to find areas.
• Solve real-life problems involving area.
• Decompose composite shapes into rectangles and squares to calculate area.
• Solve and justify multi-step problems using area.

Curriculum Links

• Mathematics and Statistics, Level 3 (Years 7-8), Geometry and Measurement.
• Develop understanding of area as multiplication of length and width for rectangles and squares.
• Explore composite shapes by decomposing into simpler shapes.
• Apply multiplication and problem-solving skills in measurement contexts.
• Use strategies to justify reasoning and answers.
• Communicate mathematical thinking clearly.

(References align with Te Mātaiaho Maths 0-8, NZ Curriculum Phase 3)

---

Success Criteria

• I can calculate the area of rectangles and squares using the correct formulas.
• I can break down composite shapes into smaller rectangles or squares.
• I can apply multiplication skills accurately in area calculations.
• I can solve multi-step, real-life problems involving area.
• I can explain and justify my solution methods clearly.
• I can compare different methods of calculating area and choose the most efficient.

---

Resources

• Rulers, graph paper, scissors, tape
• Pre-prepared composite shape templates (cut-outs)
• Whiteboard, markers
• Worksheets with area problems and real-life contexts (e.g., garden designs, floor plans)
• Calculators (optional)
• Interactive digital app or spreadsheet for area calculations (extension)

---

Lesson Overview (60 minutes)

Time	Activity	Description	Differentiation/Notes
0-10	Introduction & Review	- Recap formulas for area of rectangles and squares (A = l × w; A = s × s). - Model calculating area with examples. - Quick mental warm-up multiplying pairs of numbers (e.g., 7×8, 23×5).	Use visual models (area grids) for students needing concrete support.
10-20	Guided Practice: Simple Shapes	- Given rectangles and squares, calculate area. - Pair work to complete a set of 4 problems with varying sizes. - Share and compare answers and methods.	Challenge higher learners with larger numbers and mental calculation.
20-35	Composite Shapes: Decomposition	- Introduce composite shapes made from rectangles/squares. - Demonstrate breaking down shapes into known parts. - Students work in small groups to cut and label composite shapes - Calculate total area by summing component areas.	Provide templates; support with sketches or graph paper for spatial learners.
35-50	Real-Life Problem Solving	- Present 2-3 real-life problems (e.g., garden plot planning). - Students apply their area knowledge to solve multi-step problems. - Encourage using different methods (e.g., breaking down shapes, unit squares, equations).	Scaffold word problems for diverse learners; encourage extension with digital tools.
50-58	Justification and Discussion	- Students explain their reasoning and justify answers. - Discuss which methods were easiest/most efficient. - Compare different approaches used by peers.	Use sentence stems to help students articulate mathematical reasoning.
58-60	Plenary and Exit Ticket	- Quick quiz on formulas and concepts. - Students write one new thing they learnt and a question for next time.	Collect exit tickets for assessment and future planning.

---

Detailed Activity Notes

Introduction & Review (0-10 mins)

• Use diagrams on the whiteboard showing rectangles and squares labelled with length and width or side.
• Reinforce area = multiplication of two dimensions.
• Mental multiplication drill (using times tables knowledge).

Guided Practice (10-20 mins)

• Provide rectangles/squares with integer dimensions.
• Students calculate area individually or in pairs.
• Encourage clear presentation and checking work.

Composite Shapes (20-35 mins)

• Demonstrate by drawing a composite shape on board.
• Show how to split into rectangles/squares, calculate each area, then add.
• Groups use cut-outs to physically manipulate shapes.
• Reinforce labelling sides and units.

Real-Life Problems (35-50 mins)

• E.g., “You want to put new turf in a backyard that is shaped like an L. Work out how much turf you need if one metre squared costs $4.”
• Provide scaffolded prompts for solving.
• Encourage selection of appropriate strategies.
• Use multiplication, addition, and area formulas.

Justification and Discussion (50-58 mins)

• Ask students to share how they solved the last problem.
• Prompt peer feedback and comparison.
• Highlight efficiency and accuracy.

Plenary (58-60 mins)

• Exit ticket questions:
  • What formula did you use to find the area of a square?
  • How can we find the area of an L-shaped garden?
• Collect responses to guide next steps.

---

Differentiation Strategies

• For students needing support:
  • Use physical models and manipulatives.
  • Step-by-step scaffolding in problem-solving.
  • Pair with stronger peers for peer support.
• For advanced learners:
  • Extend to exploring area of triangles or parallelograms.
  • Challenge with including decimals or fractions in dimensions.
  • Use digital tools like spreadsheets to create formulas and automate area calculations for complex shapes.
  • Investigate different methods to prove that area formulas work (e.g., algebraic reasoning with distributive property).

---

Extension Activities

• Design a floor plan using composite shapes and calculate total flooring cost given price per square metre.
• Explore simplifying algebraic expressions related to area (e.g., expressing area as an expanded expression for a shape composed of (x+3) by (x+2)).
• Use programming or spreadsheet models to automate area calculations from inputted measurements.
• Investigate unusual composite shapes (including triangles and circles) and estimate area.

---

This lesson plan embeds the New Zealand Curriculum focus on applying multiplication, solving real-life problems, comparing different methods, and decomposing shapes to calculate area in a collaborative and engaging way. It emphasises mathematical communication and justification, supporting critical thinking and deeper understanding for Year 7-8 students.

If you would like, I can also provide printable student worksheets or digital resources to complement this lesson!