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- 1Identify and recall the properties of circles (radius, diameter, circumference) and explain why understanding circumference helps us find area. This objective matters because learners must activate their prior knowledge of circle parts and the circumference formula before they can understand how to derive the area formula
- 2Activity 1: Circle Properties Recall — Display a large hand-drawn circle on the board. Mark and label the radius (r), diameter (d), and write the word 'circumference' above the edge. Ask learners: What do we call the distance from the centre to the edge? (radius). What is the distance all the way across the circle through the centre? (diameter). What do we call the distance around the circle? (circumference). Show a worked example: If the radius of a circular plate used in a chop bar in Makola Market is 10 cm, what is the diameter? Learners write their answers in exercise books (diameter = 20 cm). Ask a volunteer to explain how they found it. Confirm: diameter = 2 × radius
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- DERIVING THE FORMULA FOR AREA OF A CIRCLE FROM CIRCUMFERENCE AND RADIUS
- 1Main Activity: Circle-to-Rectangle Conversion Model — Explain to learners that mathematicians discovered that if you cut a circle into many thin slices (like cutting a pie into 32 or 64 pieces) and rearrange them, they almost form a rectangle. Draw this on the board step-by-step: first, show a circle with the radius marked as 'r'. Then show the same circle divided into 8 slices radiating from the centre. Next, show those slices rearranged side-by-side to form a shape that looks like a rectangle. Write on the board: Length of rectangle = half the circumference = πd/2 = π(2r)/2 = πr. Width of rectangle = radius = r. Therefore, Area = length × width = πr × r = πr². Write this formula clearly in a box on the board and ask learners to copy it into their exercise books with a labelled diagram. Say: This is the key formula we use to find the area of ANY circle
- 2Sub-activity 1: Formula Explanation in Ghanaian Context — Provide a concrete example using local context. Write on the board: Kwame is a farmer near Techiman who wants to fence a circular fish pond. The radius is 7 metres. But first, he wants to know the area to calculate how much fertiliser to put in the water. Using the formula A = πr², where π = 22/7, show the working step-by-step on the board: A = 22/7 × 7 × 7 = 22/7 × 49 = 22 × 7 = 154 m². Ask learners: Why did we square the radius? (because area is always measured in square units, and we multiply length × width). Have learners repeat the calculation in their exercise books using the ruler and graph board to draw the circle and mark the radius. Invite a learner who found this easy to come to the board and show one step of the calculation to the class
- 3Sub-activity 2: Guided Practice with Calculator Support — Provide learners with a second worked example using a different radius. Write on the board: A circular mat used at a naming ceremony in Accra has a radius of 14 cm. Find its area (use π = 22/7). Guide the class through the steps: Step 1: Write the formula (A = πr²). Step 2: Substitute the values (A = 22/7 × 14 × 14). Step 3: Calculate using the calculator if needed (22/7 = 3.14., or use 22 × 14 ÷ 7 = 616 cm²). Learners work in their exercise books. Circulate and check three learners' working. Ask the group that finished first to present their answer (616 cm²). Say: Notice we get a whole number because 14 is divisible by 7 — this is not always the case
- 4Differentiation: Struggling learners — provide a partially-filled template with the formula already written and only require them to substitute and calculate using the calculator. Average learners — complete the full worked example as described. Fast finishers — challenge them to find the area of a semi-circle with radius 7 cm (A = πr²/2 = 22/7 × 7 × 7 ÷ 2 = 77 cm²) and explain why it is half the full circle's area. Extension: Ask fast finishers to calculate the area of a circular garden plot if its diameter (not radius) is 20 metres and π = 3.14. They must first find the radius (10 m), then apply the formula (A = 3.14 × 10 × 10 = 314 m²). Invite them to present this challenge to a peer.
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- 1Textbook (showing diagrams of circle-to-rectangle conversion and worked area examples)
- 2Exercise book (for learners to copy diagrams, formulas, and work through calculations)
- 3Ruler and graph board (to draw circles and mark radius/diameter accurately)
- 4Calculator (for efficient computation, especially with non-whole-number π values)
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- 1Plenary Activity 1: Formula Chant and Recall — Display the formula A = πr² on the board in large writing. Ask the class to read it aloud three times together: 'A equals pi r squared'. Then say: I will give you a circle with a radius. You tell me the formula step. Show a circle drawn on the board with radius labelled 5 cm. Ask: What do we multiply? (π × r²). What is r² here? (5 × 5 = 25). If π = 3.14, what is the area? (3.14 × 25 = 78.5 cm²). Ask learners to show thumbs up if they feel confident with this process, thumbs sideways if they are unsure, and thumbs down if they need more help. Acknowledge those with thumbs down and note them for one-on-one support in Day 2
- 2Plenary Activity 2: Real-World Problem Consolidation — Present a new scenario: Yaw's mother is a chop bar operator in Kaneshie Market and wants to paint a circular section of her floor. The radius is 3 metres. If one tin of paint covers 20 m², will one tin be enough? (A = 22/7 × 3 × 3 = 22/7 × 9 ≈ 28.3 m². No, she needs more than one tin.) Ask pairs to work through this together and discuss whether one tin is enough. Call on one representative from each pair to share their answer and reasoning. Confirm: Understanding the area of circles helps us solve real market and household problems every day in Ghana
Exercise
- 1Written Exercise — Ama is a tailor in Accra who is designing a circular fabric patch. The radius of the patch is 10.5 cm. Find the area of the patch in square centimetres (use π = 22/7). Show all your working. Model answer: A = πr² = 22/7 × 10.5 × 10.5 = 22/7 × 110.25 = 22 × 15.75 = 346.5 cm² (or 345.75 cm² depending on rounding of 10.5²). Accept answers between 345–347 cm² as correct if all steps are shown. This exercise directly assesses the Phase 1 objective (Identify and recall circle properties and apply the derived formula) and the Day 1 lesson objective (Use the relationship between radius and the area formula to solve a problem) in their exercise books.
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- 1Learners will recall the relationship between diameter, radius, and circumference of a circle, and identify why this relationship is essential for deriving and applying the area formula A = πr². This objective matters because understanding the foundational relationship between circumference and area helps learners see WHY the formula works—not just memorise it—making problem-solving more confident and transferable
- 2Quick Recall Starter: Draw a large circle on the board. Ask learners: 'What is the distance from the centre of a circle to the edge called?' (Expected: radius). 'What is the distance across the circle through the centre called?' (Expected: diameter). 'If the radius is 5 cm, what is the diameter?' Ask a volunteer to write the answer on the board (10 cm). Ask the class: 'How many radii fit into one diameter?' (Answer: 2). Learners write their working in exercise books. This activates their understanding of radius and diameter relationships
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- DEDUCING AND APPLYING THE CIRCLE AREA FORMULA USING THE DIAMETER–CIRCUMFERENCE RELATIONSHIP
- 1Main Activity — Deriving the Area Formula from a Rectangle Model: Explain to learners: 'Imagine we cut a circle into many thin strips (like pizza slices). If we arrange these strips end-to-end, they form almost a rectangle.' Draw this on the board step by step. Label the rectangle: 'The length of this rectangle equals half the circumference (because we use both sides of the circle). Half of C = 2πr ÷ 2 = πr. The width of the rectangle equals the radius (r).' Write on the board: 'Area of rectangle = length × width = πr × r = πr².' Ask learners: 'What shape did we start with? What shape did we form? How did the dimensions change?' Learners write the derived formula A = πr² in their exercise books and draw the rectangle model next to it. Use the textbook diagram (page reference in Teachers Resource Pack) to confirm the model if available. This activity uses Understand level (Bloom's): learners explain why the formula works
- 2Sub-activity 1 — Guided Problem: Kofi's Well (Understand → Apply): Write on the board: 'Kofi's family dug a circular well in their compound in Ashanti. The well has a radius of 3.5 metres. What is the area of the well cover needed?' Guide learners step-by-step: Step 1: 'Write down the formula.' (A = πr²). Step 2: 'What is r?' (r = 3.5 m). Step 3: 'Substitute into the formula: A = 22/7 × (3.5)² = 22/7 × 12.25.' Step 4: 'Use a calculator to divide: 22/7 ≈ 3.14, then 3.14 × 12.25 ≈ 38.5 m².' Write the full working on the board. Ask: 'Who can explain step 2 to the class?' (Understanding the substitution). Learners copy this worked example into their exercise books. This uses Apply level (Bloom's): learners use the formula to solve
- 3Sub-activity 2 — Semi-circle Problem (Apply → Analyse): Write: 'Ama's shop in Makola Market has a semi-circular display table with radius 2 metres. What area of the table can she display goods on?' Learners work in pairs using rulers and graph boards to draw a semi-circle with radius 2 cm (scaled). Ask: 'Is a semi-circle half of a circle? If the full circle area is A = πr², what is the semi-circle area?' Guide them: 'Area of semi-circle = πr²/2 = 22/7 × 2² ÷ 2 = 22/7 × 4 ÷ 2 = 22/7 × 2 = 44/7 ≈ 6.3 m².' Pairs check their calculations with a calculator. Ask the group that finished first to present their working. This uses Apply/Analyse level (Bloom's): learners decompose the circle into a semi-circle and recalculate. Reference the Learners Resource Pack semi-circle exemplar (page provided in Pack)
- 4Differentiation: Struggling learners—provide a step-by-step formula card to carry during the lesson. Write: 'A = πr² | Step 1: Find r | Step 2: Multiply r × r | Step 3: Multiply by π | Step 4: Calculate.' Pair them with a stronger learner for sub-activities 1 and 2. Average learners—follow the main activity and complete sub-activities 1 and 2 as described. Fast finishers—extend with: 'Kwesi has a circular plot of land with diameter 28 metres. He wants to plant cassava in half the plot. What area will have cassava? Use π = 22/7.' Learners should draw the plot on their graph board, show all working, and present to the class. Ensure all learners use the ruler and graph board at least once to draw and measure a circle.
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- 1Textbook (circle area section)
- 2Exercise book
- 3Calculator
- 4Ruler and graph board
- 5Teachers Resource Pack (diagram of rectangle from circle strips)
- 6Learners Resource Pack (semi-circle exemplar)
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- 1Consolidation Question Round: Ask the class: 'If I tell you the radius of any circle, what two things must you do before you can find the area?' (Answer: 1) Square the radius, 2) Multiply by π). Learners whisper their answers to their partner. Then ask: 'Why do we square the radius and not just multiply it by 2?' (Because area is 2-dimensional, so we need r × r, not 2 × r). A volunteer explains this to the class. The class repeats the formula A = πr² chorally three times. This consolidates the 'why' behind the formula
- 2Real-Life Application Reflection: Ask: 'Where in Accra, Kumasi, or your town have you seen circular shapes? (Market tables, wells, roofs, food trays).' Take 2 learner responses. Ask: 'If you were a carpenter and had to build a circular table top with radius 1 metre, how would you know how much wood to buy?' Guide them: 'You would calculate the area using A = πr².' Learners discuss in pairs how they would use this formula in a future job. One representative from each group shares. This evaluates learners' ability to transfer the formula to real contexts (Evaluate level, Bloom's)
Exercise
- 1Written Exercise (Assessment of Phase 1 Objective): 'A circular table in Kejetia Market, Kumasi, has a radius of 7 cm. Calculate the area of the table. (Use π = 22/7). Show all your working.' Model Answer Hint: Learners should: (1) Write the formula A = πr², (2) Substitute r = 7, (3) Calculate A = 22/7 × 49 = 22 × 7 = 154 cm². Full marks require correct formula use, substitution, and final answer. This exercise directly assesses whether learners can recall the relationship between radius and area formula, and apply the formula to a concrete problem (Recall → Apply, Bloom's) in their exercise books.
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