|
|
- 1Recall and identify ratios and rates in everyday Ghanaian contexts. This objective matters because learners must recognize that unit rates are all around them—at Makola Market when buying yams, on trotro journeys, and in shopping—before they can solve unit rate problems confidently
- 2Ratio Recall from Market Context: Show learners a simple scenario on the board: 'Ama bought 3 yams from Makola Market for GH₵12 total.' Ask: 'If all yams cost the same, how much does ONE yam cost?' Allow learners to whisper their answer to a partner first, then call on a volunteer to share aloud. Repeat with a second example: 'A trotro travels 120 km in 2 hours on the Accra-Kumasi road. How far does it travel in 1 hour?' This activates prior knowledge of equal sharing and simple division, which are the foundation for unit rates
|
- UNDERSTANDING UNIT RATE THROUGH MARKET PRICING
- 1Main Activity — Price Per Single Item (Understand level): Write on the board: 'A market trader in Kejetia Market sells 6 packets of sugar for GH₵18.' Say aloud: 'A unit rate tells us the price of ONE packet. To find the unit rate, we divide the total price by the number of items: GH₵18 ÷ 6 = GH₵3 per packet.' Write this division on the board step by step. Then ask: 'If Kofi wants to buy 1 packet, he pays GH₵3. If he wants 4 packets, he pays 4 × GH₵3 = GH₵12. Does anyone see the pattern?' Allow learners to respond. Repeat with a second example: '8 oranges cost GH₵16. What is the unit price?' Work through it together: GH₵16 ÷ 8 = GH₵2 per orange. Write both examples on the board and leave them visible for the rest of the lesson. Teacher note for struggling learners: Use a drawing on the board showing 6 sugar packets grouped together, then separate one packet. Say: 'We are finding the cost of THIS ONE packet.' For average learners: Ask them to identify the division operation needed before you do it. For fast finishers: Give them a third example to solve independently using their exercise book and ruler to draw the items if needed
- 2Sub-Activity 1 — Finding Unit Rate Using Exercise Books: Distribute exercise books to all learners. Write THREE problems on the board: (1) 5 bundles of firewood cost GH₵25. Find the cost per bundle. (2) A jar of honey weighs 500g and costs GH₵10. Find the cost per gram. (3) 12 eggs cost GH₵9. Find the unit price per egg. Ask learners to copy each problem into their exercise book and solve using the formula: Unit Rate = Total ÷ Number of Items. Circulate the room. After, ask a learner who struggled with the starter to attempt problem (1) while you guide them: 'How many bundles do we have? [5] What is the total cost? [GH₵25] So we divide.' Pairs then check each other's answers using the answers you write on the board
- 3Sub-Activity 2 — Speed and Distance Unit Rate: Tell learners: 'Unit rates are not just about shopping—they also help with travel.' Write on the board: 'A trotro travels 180 km in 3 hours from Accra to Cape Coast. What is the unit rate (distance per hour)?' Work through: 180 km ÷ 3 hours = 60 km per hour. Ask: 'If the trotro keeps the same speed, how far will it travel in 1 hour? [60 km] In 2 hours? [120 km]' Have learners copy this example and the second problem into their exercise books: 'A cyclist travels 24 km in 2 hours. Find the unit rate.' Learners solve independently. Struggling learners may use a ruler and graph board to draw a simple timeline of hours and mark the distance covered. Fast finishers create their own speed problem using Ghana's roads (e.g., STC bus, shared taxi speed) and share with a partner
- 4Differentiation: Struggling learners should work ONLY with unit pricing problems in this section (not speed problems). Pair them with a strong peer who can model the division step aloud. Average learners complete all three sub-activities as described. Fast finishers should be asked to explain to a weaker peer why we divide, or create a third type of unit rate problem (e.g., cost per kilogram of cassava at market). Extension task: Ask fast finishers to solve this challenge: 'If 15 bundles of cassava leaves cost GH₵45, and you have GH₵90, how many bundles can you buy?' They must find the unit rate first, then multiply or count.
|
- 1Exercise book
- 2Ruler and graph board
- 3Whiteboard and marker
- 4Chalkboard (if available)
|
- 1Consolidation Question 1 — Unit Rate Reflection: Ask learners to turn to their partner and answer this question aloud: 'In your own words, what is a unit rate? Give one example from the market or from travel.' After of pair discussion, invite two learners (one boy, one girl if possible) to share their explanation with the whole class. Affirm correct explanations. If a learner struggles, guide them: 'A unit rate is the cost (or distance, or amount) for just ONE item (or ONE hour, or ONE unit). If sugar costs GH₵3 per packet, that is a unit rate.'
- 2Consolidation Question 2 — Quick Check with Thumbs: Write on the board: 'Oranges cost GH₵20 for 4. The unit price is GH₵5 per orange.' Ask learners to show thumbs up if they agree, thumbs down if they disagree, or thumbs sideways if unsure. Count the hands. Work through it aloud: '20 ÷ 4 = 5, so GH₵5 per orange is CORRECT.' Repeat with one false statement: 'If a trotro travels 100 km in 2 hours, the unit rate is 200 km per hour.' Learners show thumbs down. Correct: '100 ÷ 2 = 50 km per hour, not 200.'
Exercise
- 1Written Assessment — Unit Price Problem: Write this question in learners' exercise books or on the board. 'A shopkeeper at Madina Market sells 9 tins of tomato paste for GH₵27. (a) Find the unit rate (cost per tin). (b) If Abena buys 6 tins, how much will she pay?' Model answer hint: (a) GH₵27 ÷ 9 = GH₵3 per tin (unit rate). (b) 6 × GH₵3 = GH₵18. Learners write their working and answers in their exercise books. Circulate and check for correct division and multiplication. This exercise directly assesses the Phase 1 objective: learners must identify the unit rate (GH₵3) and explain/apply it to solve a second part
|
|
|
- 1Identify and recall the key variables (distance, time, speed) and their relationships in real-world travel scenarios involving stops and returns. This objective is critical because learners must extract correct data from story problems before they can plot accurate distance-time graphs; without this foundation, their graphs will be incorrect and misleading
- 2Activity 1 — Quick Recall Using the Exemplar Scenario: Display the trader journey from Buduata to Assin to Adawso on the board. Ask learners: 'The trader travels 8 miles from Buduata to Assin. How long does this take? (Answer:.) Now the trader rests at Assin — what happens to the distance during rest time?' Learners whisper their answer to a partner. Ask a volunteer to share aloud: 'The distance stays the same; no new distance is covered.' Write 'STOP = FLAT LINE' on the board. This activates prior knowledge about the link between movement and graph shape
|
- UNDERSTANDING AND BUILDING A DISTANCE-TIME GRAPH FROM THE TRADER'S JOURNEY
- 1Main Activity — Step-by-Step Graph Construction with the Exemplar: Draw a blank distance-time graph on the board with axes: horizontal axis = Time (minutes) from 0 to 180; vertical axis = Distance from Buduata (miles) from 0 to 20. Write on the board: 'Segment 1: Buduata to Assin — 8 miles.' Ask the class: 'At time 0, where is the trader?' (Answer: Buduata, distance = 0 miles.) 'At time, where is the trader?' (Answer: Assin, distance = 8 miles.) Plot point (0, 0) and point (60, 8) on the board. Draw the connecting straight line. Say: 'This line shows the trader moving at constant speed — no stops.' Now write: 'Segment 2: Rest at Assin —.' Ask: 'If the trader is resting, does the distance change?' (Answer: No.) 'So what does the graph line do?' (Answer: It stays flat/horizontal.) From point (60, 8), draw a horizontal line to point (96, 8)—the line stays at 8 miles for 36 more minutes (60 + 36 = 96). Explain: 'A flat line means the trader is not moving.' Continue with Segment 3: 'Assin to Adawso —. The distance goes from 8 miles to 20 miles.' Plot (96, 8) and (120, 20), then draw the line. Finally, Segment 4: 'Return to Buduata — from distance 20 miles back to 0 miles.' Plot (120, 20) and (168, 0), then draw the line downward. Say: 'Notice the line slopes down—the distance decreases as the trader returns.' Step back and review the complete graph with learners. Ask: 'Which line is the steepest—the Buduata-to-Assin segment or the return segment? Why?' (The return segment because it covers 20 miles vs. 8 miles.) This builds conceptual understanding of how slope relates to speed
- 2Sub-Activity 1 — Guided Plotting on Exercise Books Using Ruler: Give each learner an exercise book and ruler. On the board, draw the same axes again, smaller. Dictate each point slowly: 'Mark a dot at (0, 0). Mark a dot at (60, 8). Use your ruler to draw a straight line connecting them.' Pause. 'Mark a dot at (96, 8). Draw a horizontal line from (60, 8) to (96, 8).' Continue through all four segments. Circulate as learners draw. Correct any misplaced points in real time by asking: 'Check the time on the horizontal axis—is 60 the right spot?' This ensures every learner has an accurate graph in their book for reference
- 3Sub-Activity 2 — Speed Calculation for Each Segment: Write on the board: 'Speed = Distance ÷ Time.' For Segment 1, ask: 'The trader covers 8 miles. What is the speed in miles per minute?' Learners calculate: 8 ÷ 60 = 0.13 miles per minute (round to 2 d.p.). Ask: 'For Segment 3 (8 miles to 20 miles ), what is the distance covered? (12 miles.) What is the speed?' (12 ÷ 24 = 0.5 miles per minute.) Say: 'The steeper the line on the graph, the faster the travel—higher speed equals steeper slope.' Record speeds next to each segment on the board. This links the visual slope to the numerical speed value
- 4Differentiation: Struggling learners—provide a pre-drawn distance-time grid with axes labeled and grid squares already visible; work through Segments 1 and 2 with this group first, then Segments 3 and 4 with teacher support. Average learners—follow the main activity as described. Fast finishers—ask: 'If the trader had not rested for 36 minutes, how much sooner would he have reached Adawso? Recalculate the total journey time without the rest and redraw the graph.' This requires them to recalculate time intervals and apply the concept to a modified scenario.
|
- 1Exercise book
- 2Ruler and graph board
- 3Printed exemplar text (trader journey Buduata–Assin–Adawso)
- 4Board and chalk/marker
- 5Pre-drawn distance-time grid template (for struggling learners)
|
- 1Plenary Activity 1 — Graph Interpretation Question: Display the completed distance-time graph on the board. Ask the class: 'Look at the four segments. Which segment shows the trader travelling fastest? How do you know from the graph?' (The return segment—Segment 4—because the line is steepest, covering 20 miles.) Ask a learner who struggled during Phase 2 to point to this steep line on the board and describe why it is steep. Say: 'A steep line = fast speed. A flat line = no movement (stop). A gentle slope = slow speed.' Have the whole class repeat chorally: 'Steep line, fast speed. Flat line, no movement.' This consolidates the visual-to-speed connection
- 2Plenary Activity 2 — Peer Check and Reflection: Ask learners to hold up their exercise books showing their plotted graphs. Pairs swap books and compare the four segments. Ask: 'Does your partner's graph match the board graph? Check the four points on the horizontal axis: 0, 60, 96, 120, 168. Check the distances: 0, 8, 8, 20, 0. Give your partner a thumbs up if correct, or whisper one point that needs fixing.' Allow for peer feedback. Invite one volunteer from a pair that found an error to explain what was wrong and how they fixed it. This builds collaborative accountability and self-correction
Exercise
- 1Exercise (Written Assessment): A trader, Yakubu, travels from Tema to Accra, a distance of 24 kilometres. He drives at constant speed and arrives in Accra. He rests. He then returns to Tema. On a distance-time graph with Time (0– ) on the horizontal axis and Distance from Tema (0–24 km) on the vertical axis, plot the three segments of Yakubu's journey and draw the lines connecting them. Then calculate Yakubu's speed in km per minute for the outbound journey (Tema to Accra). [Model Answer: Outbound segment: points (0, 0) and (30, 24), straight line; Rest segment: points (30, 24) and (45, 24), horizontal line; Return segment: points (45, 24) and (85, 0), downward sloping line. Speed calculation: 24 km ÷ = 0.8 km/min.] in their exercise books.
|
