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- 1Recall and identify known measurement conversions (1m = 100cm, 1kg = 1000g) from prior learning. This objective matters because conversion factors are the foundation of ratio reasoning—learners must recognise these relationships before they can apply them to solve real-world measurement problems involving multiplication or division of quantities
- 2Activity 1 — Quick Recall Chart: Write on the board the phrase '1 metre = ___ centimetres' and '1 kilogram = ___ grams'. Ask learners: 'Who has measured something in centimetres at home? What was it? How many centimetres would 2 metres be?' Take 3–4 oral responses. Then reveal the answers (100cm and 1000g). This activates learners' prior knowledge of unit relationships from primary years and connects to their lived experience of measurement
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- IDENTIFYING AND EXPLAINING CONVERSION FACTORS AS RATIOS
- 1Main Activity — Conversion Factor Discovery Using Ruler and Graphboard: Place a ruler and a graphboard on a desk visible to all learners. Say: 'Kwame is a carpenter. He has a piece of wood that measures 2 metres long. His customer wants to know the length in centimetres. Let's use the ruler to understand the relationship.' Point to the ruler and show 1 centimetre, then say: 'We know 1 metre has how many of these?' (Pause for response: 100). Write on the board: '1m = 100cm'. Ask: 'So 2 metres = 2 × 100 = 200 centimetres. What is the multiplication happening here? Yes—we are using the ratio 1:100 to convert.' Write the ratio box: [1m: 100cm]. Ask learners: 'Is this a ratio? Yes, because it compares two quantities in the same situation.' Repeat with 1kg = 1000g using the same structure. Ask a learner who found this easy to explain to the class: 'Why is 1kg called a conversion factor?' (Because it tells us how to change from one unit to another using multiplication.)
- 2Sub-activity 1 — Fill-in-the-Blank Conversion Table: Hand out exercise books. Draw a table on the board with three rows: Metres | Centimetres; 1 | 100; 2 |?; 3 |?. Say: 'Use the ratio 1m = 100cm to complete the table in your exercise book.' Learners fill in 200 and 300. Ask a learner from the middle-ability group to come to the board and write one answer, explaining: '2 metres is 2 times 1 metre, so I multiply 100 by 2 to get 200.' This consolidates the multiplicative structure of ratio conversion
- 3Sub-activity 2 — Reverse Conversion Challenge: Say: 'Yaw buys 5 kilograms of rice from Techiman Market. How many grams of rice does he have?' Write: '1kg = 1000g, so 5kg = 5 × 1000 = 5000g.' Learners copy into exercise books and solve. Struggling learners: work with 1kg and 2kg only, using the ruler or graphboard to visualise the magnification. Fast finishers: create their own scenario (e.g. '7 metres of rope, how many centimetres?') and write the solution on the board. This extends learners' ability to apply the ratio to different scales
- 4DIFFERENTIATION: Struggling learners — use the ruler physically to measure and count: 'See, this 1cm section repeats 100 times in 1 metre.' Pair them with a stronger peer to check their table entries. Average learners — follow the main activity and sub-activities as written. Fast finishers — after completing sub-activity 2, ask them to solve: 'A tailor has 8 metres of kente cloth. She cuts it into 100cm pieces. How many pieces does she have?' (Answer: 8 pieces). This requires division using the conversion factor, extending to the second phase of ratio reasoning.
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- 1Exercise book
- 2Ruler
- 3Graph board
- 4Whiteboard and marker
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- 1Plenary Activity 1 — Choral Repetition and Ratio Consolidation: Stand at the front. Say: 'Let's say together, three times: One metre equals one hundred centimetres.' Learners repeat chorally three times. Then ask: 'Who can tell me: What does the number 100 represent?' (It is the ratio that multiplies metres to get centimetres.) Ask a volunteer to stand and explain to the class in one sentence: 'The conversion factor 1:100 means one unit of metres is the same as one hundred units of centimetres.' This ensures all learners have verbalised the core concept
- 2Plenary Activity 2 — Quick Peer Check: Learners compare answers with the person sitting next to them using their exercise books from Sub-activity 1. Ask: 'Did you both get the same answers for 2 metres and 3 metres? Show thumbs up if yes, thumbs down if no.' Those with thumbs down pair with a peer who has thumbs up to review the ratio logic together. This peer-checking consolidates accuracy before assessment
Exercise
- 1Written Exercise — Application of Conversion Factor: 'Kofi measures a football field and finds it is 12 metres long. Using the conversion factor 1m = 100cm, how many centimetres long is the football field? Show your working in your exercise book.' Model Answer: '1m = 100cm, so 12m = 12 × 100 = 1200cm. The football field is 1200cm long.' This exercise directly assesses the Phase 1 objective (identifying and using the conversion factor in a real-world context) and requires learners to apply multiplication reasoning with the ratio
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- 1Recall and identify what unit rates are in real-life situations (pricing and speed), and explain why knowing the unit rate helps us compare costs and speeds fairly. This objective matters because unit rates are essential for making smart shopping decisions at Makola Market, comparing transport fares on trotros, and understanding motion in everyday life
- 2Activity 1 — Prior Knowledge Recall with Market Context: Display on the board: 'Ama buys 6 exercise books for GH₵18. What is the cost of 1 exercise book?' Ask learners: 'Have you or your parents ever worked out the price of one item when you bought many items together?' Learners turn to a partner and whisper one example from their home (e.g. yam, kenkey, books). Call on three learners (alternating boys and girls) to share aloud. Confirm: finding the cost of ONE item is finding the unit price — this is a unit rate
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- SOLVING UNIT RATE PROBLEMS USING FRACTIONS AND UNIT PRICING (WITH DECIMAL ROUNDING)
- 1Main Activity — Guided Calculation of Unit Pricing at Makola Market: Present this scenario on the board: 'Kwame buys 8 tins of tomato paste at Makola Market for GH₵24. What is the unit price (price of 1 tin)?' Write step-by-step with exact working: (1) Identify: total cost = GH₵24, total tins = 8. (2) Unit rate formula: Unit Price = Total Cost ÷ Number of Items = GH₵24 ÷ 8. (3) Calculate: GH₵24 ÷ 8 = GH₵3 per tin. (4) Round: already a whole number, so GH₵3.00. Now present a second, more complex example: 'Abena buys 7 metres of cloth for GH₵45.50. Find the unit price per metre and round to 2 decimal places.' Work through: GH₵45.50 ÷ 7 = GH₵6.5 (if calculated as a fraction 45.50/7 = 6.5). Ask learners: 'What if the answer was GH₵6.4857.? Which decimal place would we round to?' Guide them to round to 2 d.p. = GH₵6.49. Learners write both worked examples in their exercise books and copy the unit price formula
- 2Sub-activity 1 — Practising Unit Pricing with Ruler and Graph Board: Give learners this task written on the board: 'Yaw sees a poster at the market: 5 loaves of bread cost GH₵12.50. (a) Calculate the unit price. (b) How much would 12 loaves cost? (c) Round your unit price to the nearest pesewa (2 d.p.).' Learners use their exercise books to set out the calculation in the same format as the model. They may use the ruler and graph board to draw a simple table if they wish (columns: Number of Loaves | Cost in GH₵). Struggling learners: work with a partner. Provide them with a partially completed table and ask them to fill in rows 1, 2, and 5 only. Average learners: complete all three parts (a, b, c) independently. Fast finishers: add a fourth part: 'If you had GH₵50, how many loaves could you buy at this unit price?'
- 3Sub-activity 2 — Peer Checking and Real-World Application: Learners swap exercise books with the person sitting next to them. Using an answer key you write on the board, partners check each other's working and mark with a tick or circle any errors. Ask pairs to raise their hands if they got all three parts correct. Call on one representative from each pair that finished to read aloud their unit price answer. Extend: Ask fast finishers to explain to the class why knowing the unit price helps shoppers decide whether to buy larger or smaller packs. Correct answer hint: Unit price = GH₵2.50 per loaf; 12 loaves = GH₵30; rounded to 2 d.p. = GH₵2.50
- 4Differentiation: Struggling learners — provide a worked example card showing the three steps clearly labelled (Step 1: Divide, Step 2: Calculate, Step 3: Round). Allow them to use a calculator. Pair with a stronger peer who can explain each step aloud. Average learners — use the standard task as written; emphasise showing all working. Fast finishers — after part (d), ask them to create their own unit pricing problem using a real price from a local shop (e.g. price of 10 pencils, 6 loaves, 4 exercise books) and pose it to a classmate to solve. Extension Task: Present this challenge: 'At Kejetia Market, Kofi sees two different shops. Shop A: 3 kg of rice for GH₵27. Shop B: 5 kg of rice for GH₵40. Using unit rates, which shop is cheaper? How much is the difference per kg?' Learners calculate both unit rates (GH₵9/kg vs GH₵8/kg), compare, and explain why Shop B is cheaper. Ask: 'How does knowing unit rates help us make smart choices?'
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- 1Exercise book
- 2Ruler and graph board
- 3Whiteboard and marker
- 4Answer key (prepared by teacher)
- 5Worked example card (for struggling learners)
- 6Calculator (optional, for struggling learners)
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- 1Plenary Activity 1 — Consolidation Question with Whole-Class Response: Display on the board: 'Efua bought 9 oranges for GH₵5.40. What is the cost of 1 orange to 2 decimal places?' Learners calculate silently in their exercise books. Then ask: 'Show fingers 1–5: how confident are you that your answer is correct? (1 = not sure, 5 = very sure).' Observe hands. Call on a learner who showed confidence level 4 or 5 to write their answer on the board. Confirm: GH₵5.40 ÷ 9 = GH₵0.60 per orange. Ask the class: 'Who got a different answer? What step did you do differently?' Address any errors by re-working one step together. Thumbs up if you now understand
- 2Plenary Activity 2 — Real-World Reflection with Partner Discussion: Ask: 'Think about your family's shopping. Have you noticed your parents comparing unit prices or sizes?' Learners whisper their answer to their partner (90 seconds). Invite 2–3 learners to share their family example aloud (e.g. 'My mother buys big tins of tomato paste because the unit price is lower'). Close with: 'Unit rates help us be smart shoppers and travellers. On Day 3, we will use unit rates to solve speed problems, like comparing trotro speeds.'
Exercise
- 1Written Assessment Exercise: 'Yakubu buys a pack of 6 exercise books for GH₵4.80. (a) Calculate the unit price per book. (b) At this unit price, how much would 15 books cost? (c) Round your unit price answer to the nearest pesewa (2 decimal places). Show all your working.' Model Answer Hint: (a) GH₵4.80 ÷ 6 = GH₵0.80 per book; (b) GH₵0.80 × 15 = GH₵12.00; (c) Rounded to 2 d.p. = GH₵0.80. Assessment Note: This exercise directly assesses the Phase 1 objective (recall and identify unit rates and solve a unit pricing problem using fractions, division, and decimal rounding). A learner who scores 2/3 or above has met the indicator
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