|
|
- 1Write 857,386,321 on the board. Ask: How many digits does this number have? Which digit is in the hundred thousands place?
- 2Ask learners: If Kofi earned GH₵12,456.78 from selling kelewele at the market, what is the value of the digit 5? Why does position matter?
|
- UNDERSTANDING PLACE VALUE AND SIGNIFICANT FIGURES
- 1Display the number 857,386,321 using a place value chart with columns: millions, hundred thousands, ten thousands, thousands, hundreds, tens, ones. Ask Ama to point to the ten thousands place and identify its value.
- 2Explain: A significant figure is any digit that carries meaning. In 857,386,321, all 9 digits are significant. Write on the board: 5 significant figures means we keep 5 important digits from left to right, then round. Model: 857,386,321 to 5 s.f. = 85,739,000 (rounded up because the next digit is 8).
- 3Work through a Ghanaian example: A farmer at Techiman harvested 3,456,789 maize cobs. Express this to 4 significant figures. Step 1: Identify first 4 digits = 3,456. Step 2: Check 5th digit (7) - it's ≥5, so round up = 3,457,000. Write answer as 3.457 × 10^6 in standard form.
- 4Significant figures count from the first non-zero digit on the left
- ROUNDING TO DECIMAL PLACES
- 5Show the number 45.6789. Ask: What is the first decimal place? (6) Second decimal place? (7). Explain: Decimal places count digits AFTER the decimal point.
- 6Model rounding 45.6789 to 2 d.p.: Look at the 3rd decimal place (8). Since 8 ≥ 5, round the 2nd decimal place up from 7 to 8. Answer: 45.68. Repeat with 12.3542 to 2 d.p. = 12.35.
- 7Real-life task: Abena's chop bar sales today were GH₵1,234.5678. Round this amount to 2 decimal places (nearest pesewa). Learners work in pairs, show their rounding steps on mini whiteboards.
- 8Use a place value diagram for decimals: ones . tenths hundredths thousandths ten-thousandths
|
- 1Place value chart (laminated or drawn on board)
- 2Mini whiteboards and markers
- 3Calculator (for checking)
- 4Exercise book
|
- 1Ask: In your own words, what is the difference between significant figures and decimal places? Turn to your partner and explain using an example.
- 2One learner volunteers to round 2,456.7834 to 3 s.f. and another to 2 d.p. Discuss how the answers differ.
Exercise
- 1Express 12,345,678 to 4 significant figures. Then express GH₵123.456 to 2 decimal places.
|
|
|
- 1Quick peer review: Show the answers from yesterday's exercise (12,350,000 and GH₵123.46). Ask: Did you round correctly? Raise your hand if you got both right.
- 2Write on the board: I am a 3-digit number. My first digit is 7. My last digit is 2. My middle digit is 5. What am I? (Answer: 752). Say: Today we solve riddles like this using place value.
|
- DECODING NUMBERS USING PLACE VALUE CLUES
- 1Present the puzzle: I am a 6-digit number. My first digit is 5 more than my last digit. My second digit is the third multiple of 3. My fourth digit is the second multiple of 3. Work through step by step: Last digit =?. If first digit = last digit + 5, and we need a 1-digit result, let last digit = 1, first = 6. OR last = 2, first = 7, etc. Third multiple of 3 = 9 (second digit). Second multiple of 3 = 6 (fourth digit).
- 2Scaffold the puzzle: Draw a 6-box template on the board: ___ ___ ___ ___ ___ ___. Label: 1st | 2nd | 3rd | 4th | 5th | 6th. Write clues below. Learners fill in boxes step by step. Guide them: The answer is something like 7 9? 6?. Ask: What operations do we need? (division, multiples, remainders). One possible answer: 796,123 – verify against all clues.
- 3This develops logical reasoning and place value understanding simultaneously
- REAL-LIFE PROBLEM SOLVING WITH PLACE VALUE
- 4Scenario: A trader in Kejetia Market, Kumasi, sells different items. Kente cloth costs GH₵342.89 per yard. Batakari smocks cost GH₵1,567.50 each. Gold beads cost GH₵78.45 per gram. A customer buys 3 yards of kente, 1 batakari, and 50 grams of beads. Calculate the total to 2 decimal places, then round to the nearest whole cedis (0 d.p.).
- 5Learners work in mixed-ability pairs. Kwabena and Yaa are given the problem. They calculate, round to 2 d.p. first, then to 0 d.p. Discussion: Why does the order of rounding matter? What is the most accurate amount to charge the customer?
- 6Connects place value, rounding, and real Ghanaian trading context
- ERROR ANALYSIS AND CORRECTION
- 7Display incorrect work on the board: A student rounded 3,456.7891 to 2 d.p. and wrote 3,456.78. Another rounded 345.6789 to 2 d.p. and wrote 345.67. Ask: Which student is correct? Why did the other make a mistake? (First student: correct - 8 < 5, so 8 stays 8. Second student: wrong - should be 345.68 because the digit after 7 is 8, which is ≥ 5).
- 8In groups of 3, learners are given 4 rounding errors. They identify which ones are wrong, circle the mistakes, and write the correct answer with full working. Share findings with the class. Celebrate correct reasoning.
- 9Builds metacognition and peer learning
|
- 16-box puzzle template (printed or drawn)
- 2Real-life scenario cards with Kejetia Market prices
- 3Error analysis worksheet with 4 examples
- 4Calculator
- 5Exercise book
|
- 1Exit ticket: Write ONE thing you learned about place value today and ONE question you still have. Pass to the teacher.
- 2Ask a volunteer: When would a shopkeeper need to round prices? Why is rounding important in real life?
Exercise
- 1Ama's family farm produced 45,678.456 kg of maize. The government statistician must report the yield to 3 significant figures and also to 1 decimal place. What are both answers? Show your rounding steps.
|
|
|
- 1Speed challenge: Show 5 numbers (e.g. 23.456, 1,234.567, 89.123, 5.6789, 12,345.89). Call out: Round to 1 d.p., round to 2 s.f., round to 3 d.p., etc. Learners write answers on mini whiteboards. First correct answer scores a point.
- 2Ask: What types of numbers have we worked with so far? (Integers, decimals). Today we connect them to something bigger: the rational number system.
|
- INTRODUCTION TO THE RATIONAL NUMBER SYSTEM AND SET RELATIONSHIPS
- 1Draw three overlapping circles on the board (Venn diagram). Label them: Whole Numbers (W), Integers (Z), Rational Numbers (Q). Explain: Whole numbers are 0, 1, 2, 3. Integers include whole numbers AND negative numbers:.-3, -2, -1, 0, 1, 2, 3. Rational numbers are any number that can be written as a fraction p/q where q ≠ 0. Include 1/2, 3/4, -5, 7, 0.25, etc.
- 2Mark key facts: Is 5 a whole number? (Yes, mark in W circle). Is 5 also an integer? (Yes, it overlaps W and Z). Is 5 also rational? (Yes, 5 = 5/1, so it overlaps all three). Is -3 a whole number? (No, it's only in Z and Q).
- 3Show the union (∪) symbol: W ∪ Z means 'all numbers that are in W OR in Z OR in both.' The intersection (∩) symbol: W ∩ Z means 'numbers that are in W AND Z at the same time' (which is W itself, since all whole numbers are integers).
- 4Use concrete, visual Venn diagrams. This is the foundation for the exercise
- CLASSIFYING NUMBERS AND FINDING UNION AND INTERSECTION
- 5List 10 numbers on the board: -7, 0, 2, 1/2, -3.5, 15, 22/7, -4/2, 0.75, 100. Ask learners to sort them into sets: Which are whole numbers only? Which are integers? Which are rational? Work as a class to place each number. Record: W = {0, 2, 15, 100}, Z = {-7, 0, 2, 15, 100, -4/2 = -2}, Q = {all 10 numbers}.
- 6Define: W ∪ Z (union) = all numbers that belong to W or Z = {-7, -2, 0, 2, 15, 100}. Define: W ∩ Z (intersection) = numbers in both W and Z = {0, 2, 15, 100} = W itself. Ask: Why is W ∩ Z = W? (Because every whole number is an integer, so their intersection is exactly W).
- 7Learners may confuse ∪ and ∩; use concrete language: 'OR means union; AND means intersection'
- REAL-LIFE PROBLEM SOLVING WITH THREE SETS
- 8Scenario: A school tuck shop records daily transactions. Set A = {items that cost a whole number of cedis: GH₵1, GH₵2, GH₵5, GH₵10}. Set B = {items priced with fractions or decimals: GH₵0.50, GH₵1.50, GH₵2.50, GH₵3.75}. Set C = {items that Kwesi bought yesterday: GH₵1, GH₵2.50, GH₵5, GH₵0.50}. Find: A ∪ B (all items in the shop), A ∩ B (items in both—none, so ∅), A ∩ C (items Kwesi bought that cost whole cedis = {GH₵1, GH₵5}), B ∩ C (items Kwesi bought with decimals = {GH₵2.50, GH₵0.50}).
- 9Learners work in groups of 3. Each group is given a similar three-set problem (e.g. Set W = whole number prices, Set P = prices Ama can afford on GH₵5, Set M = prices marked on sale this week). They draw their own Venn diagram, list union and intersection, and present one finding to the class.
- 10Connects number classification to familiar Ghanaian shopping context
|
- 1Large Venn diagram template (3 circles, laminated or drawn on board)
- 2Marker pens (different colours for shading regions)
- 3Set notation reference card (∪, ∩, ∈, ∉, ∅)
- 4Three-set problem cards (tuck shop, market, farm scenarios)
- 5Exercise book
|
- 1Celebrate mastery: Invite three learners to share one key insight they learned this week. E.g. 'I learned that whole numbers are inside integers, which are inside rational numbers.' 'I learned ∩ means AND, not OR.'
- 2Confidence check: Using your fingers (1-5), show how confident you feel classifying numbers into W, Z, and Q, and finding unions and intersections. No one is judged—this helps me know who needs more practice.
Exercise
- 1Set W = {whole numbers: 0, 1, 2, 3, 4, 5}, Set Z = {integers: -2, -1, 0, 1, 2, 3, 4, 5}, Set Q = {rational numbers: -2, -1, -1/2, 0, 1/2, 1, 2, 3, 4, 5}. (a) List W ∩ Z. (b) List W ∪ Q. (c) Is 1/2 in W ∩ Z? Explain why or why not. (d) In two sentences, explain the relationship: All whole numbers are integers, and all integers are rational numbers.
|
