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- 1Identify place value positions and read whole numbers greater than 1,000,000,000 correctly
- 2Display the number 2408321 on the board. Ask learners: What does the digit 4 represent in this number? Learners write their answers in exercise books (ones, tens, hundreds, thousands, ten thousands, hundred thousands, or millions). Call on Ama to share. Confirm: the 4 is in the hundred thousands position, so it represents 400,000.
- 3Show learners a phone displaying an image of a Ghana currency note serial number: TD1567451. Ask: Can you read this number aloud to your partner? Learners practise reading 1567451 in pairs. Select Kwame to read it aloud to the class. Confirm: One million, five hundred and sixty-seven thousand, four hundred and fifty-one.
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- READING AND WRITING NUMBERS OVER 1,000,000,000 USING PLACE VALUE
- 1Write the numeral 3,742,805,639 on the board. Point to each digit from left to right and name the place value: 3 (billions), 7 (hundred millions), 4 (ten millions), 2 (millions), 8 (hundred thousands), 0 (ten thousands), 5 (thousands), 6 (hundreds), 3 (tens), 9 (ones). Read aloud: Three billion, seven hundred and forty-two million, eight hundred and five thousand, six hundred and thirty-nine. Learners repeat chorally three times.
- 2Provide each learner with a laptop or phone showing a place value chart (billions to ones). Display the number 5,629,413,178. Ask learners to identify which digit is in the ten millions place (1) and which digit is in the hundred millions place (4). Learners write their answers. Call on Kofi and Abena to share. Confirm both answers.
- 3In pairs, learners are given three numbers: 2,804,560,321; 7,193,245,008; 6,451,089,762. For each number, learners write the number in words in their exercise books. Circulate and check. Select Yaw and Adwoa to write one number and its words on the board. Class verifies correctness.
- 4Use the laptop or phone to display the place value chart continuously so learners reference it visually throughout the section.
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- 1laptop
- 2phone
- 3place value chart (billions to ones)
- 4exercise books
- 5whiteboard and marker
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- 1Learners play Place Value Snap: Call out a place value name (e.g., 'hundred thousands'). Learners hold up fingers showing the position from the right (e.g., 6 fingers for hundred thousands). Do this for five different place values. Evaluate quickly by observation.
- 2Learners stand in a circle. Call out a large number (e.g., 4,286,501,930). Learners whisper it to their neighbour. The last person to hear it says it aloud. Class confirms if it matches the original. Repeat three times with different numbers.
Exercise
- 1Write the number 8,375,642,019 on the board. Ask learners to write this number in words in their exercise books. Learners must show all steps: identifying each digit and its place value, then writing the full word form. Acceptable response: Eight billion, three hundred and seventy-five million, six hundred and forty-two thousand, and nineteen.
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- 1Recall skip counting patterns and begin skip counting forwards and backwards in multiples of 10,000, 100,000, and 500,000
- 2Call out skip counting in 1,000s forwards: 1,000; 2,000; 3,000; 4,000. Learners repeat chorally. Then ask: If I continue, what is the next number? (5,000). Correct and continue to 10,000. Learners recognize the pattern increases by 1,000 each time.
- 3Draw a number line on the board showing: 0, 100,000, 200,000, 300,000. Ask learners: What is the difference between each number? (100,000). Learners hold up ten fingers to show the difference. Confirm: we are skip counting in 100,000s. What comes next? (400,000). Learners say aloud.
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- SKIP COUNTING FORWARDS IN 10,000S, 100,000S, AND 500,000S
- 1Display on the phone or laptop: 10,000; 20,000; 30,000; 40,000; 50,000; 60,000; 70,000; 80,000; 90,000; 100,000. Read aloud together: 'We are skip counting in 10,000s.' Learners identify the pattern: each number is 10,000 more than the last. Write on the board: '100,000 + 10,000 = 110,000. 110,000 + 10,000 = 120,000.' Continue to 200,000. Learners repeat the sequence.
- 2In groups of three, assign each group a starting number and direction: Group 1 (Kwesi, Efua, Sena): Start at 200,000 and skip count forwards in 100,000s for six numbers. Group 2 (Yaw, Akua, Kokou): Start at 300,000 and skip count forwards in 100,000s for six numbers. Each group writes their sequence on a mini whiteboard. Display all sequences. Verify they follow the pattern.
- 3Introduce skip counting in 500,000s. Write on the board: 500,000; 1,000,000; 1,500,000; 2,000,000; 2,500,000. Point: each number is 500,000 more. Learners copy the sequence into their books and identify the pattern aloud: 'Each number increases by 500,000.'
- 4Use the phone or laptop to display sequences visually so learners see the numbers clearly. This supports identification of the pattern.
- SKIP COUNTING BACKWARDS IN 10,000S, 100,000S, AND 500,000S
- 5Display backwards skip counting: 100,000; 90,000; 80,000; 70,000; 60,000; 50,000; 40,000; 30,000; 20,000; 10,000; 0. Read aloud: 'We are skip counting backwards in 10,000s. Each number is 10,000 less than the one before.' Learners repeat the sequence three times.
- 6Provide learners with a partially filled backwards skip counting sequence: 1,800,000; 1,700,000; 1,600,000; _____; 1,400,000; _____; 1,200,000. Ask: What is missing? (1,500,000 and 1,300,000). Learners work in pairs to complete the sequence. Check answers. Confirm the pattern: subtract 100,000 each time.
- 7Challenge activity: Learners start at 2,500,000 and skip count backwards in 500,000s for five numbers. They write: 2,500,000; 2,000,000; 1,500,000; 1,000,000; 500,000. Call on Ama and Kofi to read their sequences aloud. Verify correctness.
- 8Backwards skip counting is more challenging. Provide visual support (the phone or laptop) for struggling learners to reference the pattern.
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- 1laptop
- 2phone
- 3whiteboard and marker
- 4mini whiteboards and pens
- 5exercise books
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- 1Play Skip Counting Race: Call out a starting number and a direction (forward or backward) and the interval (10,000s, 100,000s, or 500,000s). Learners who volunteer stand and say the next three numbers in the sequence. If correct, they sit; if incorrect, another learner has a chance. Do this five times.
- 2Learners sit in pairs. One learner says a starting number; the partner skip counts forwards or backwards in a chosen interval for six numbers. Partners check each other's work. Switch roles. Do this twice per pair.
Exercise
- 1Provide learners with this task in their exercise books: Starting at 200,000, skip count forwards in 100,000s and write down six numbers in the sequence. Then, starting at 1,800,000, skip count backwards in 100,000s and write down five numbers. Acceptable responses: Forward: 200,000; 300,000; 400,000; 500,000; 600,000; 700,000. Backward: 1,800,000; 1,700,000; 1,600,000; 1,500,000; 1,400,000.
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- 1Recall the meaning of comparison symbols and identify which whole number is greater, less, or equal
- 2Write two numbers on the board: 45,678 and 45,687. Ask learners: Which number is bigger? Learners raise their hands. Confirm: 45,687 is bigger because 8 is greater than 7 in the tens place. Point to the symbol >. Say: This symbol means 'greater than.' Write: 45,687 > 45,678. Learners repeat: 'Forty-five thousand, six hundred and eighty-seven is greater than forty-five thousand, six hundred and seventy-eight.'
- 3Show three symbols on the board: >, <, =. Ask learners: What does each mean? Elicit responses. Confirm: > means 'greater than'; < means 'less than'; = means 'equal to.' Show the pair 523,401 and 523,401. Ask: Are they the same? Yes. Which symbol do we use? (=). Write: 523,401 = 523,401. Learners say aloud.
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- COMPARING TWO WHOLE NUMBERS USING PLACE VALUE AND SYMBOLS
- 1Display on the phone or laptop: 3,456,789 and 3,456,798. Ask learners: Are these numbers the same? No. Which is bigger? Guide learners step by step: Compare millions (both 3), compare hundred thousands (both 4), compare ten thousands (both 5), compare thousands (both 6), compare hundreds (both 7). Stop at tens: one has 8, one has 9. So 3,456,798 > 3,456,789. Write both forms on the board and circle the place where they differ. Learners copy into books.
- 2In groups of four, distribute these number pairs to compare: Kofi's group: 7,234,560 and 7,234,506; Ama's group: 5,678,901 and 5,768,901; Kwame's group: 2,345,600 and 2,345,600; Yaw's group: 8,901,234 and 8,109,234. Each group identifies which number is greater (or if equal) and writes the comparison using the correct symbol (>, <, or =). Circulate and check their logic. Ask each group to present one comparison and explain their thinking.
- 3Provide learners with a mixed list of eight numbers (ranging from 4-digit to 9-digit): 456,780; 465,780; 4,567,890; 4,576,890; 234,567; 234,576; 9,876,543; 9,786,543. Ask learners to circle the larger number in each pair. Check answers and ask Efua and Sena to explain how they found the largest digit difference.
- 4Use the phone or laptop to display number pairs visually so learners can clearly see the digits being compared. Emphasize comparing from left to right, stopping at the first place where digits differ.
- ORDERING MULTIPLE WHOLE NUMBERS FROM LEAST TO GREATEST OR GREATEST TO LEAST
- 5Write five numbers on the board (out of order): 3,456,789; 3,654,789; 3,456,987; 3,465,789; 3,456,879. Ask learners: Can we put these in order from smallest to largest? Guide them to compare the millions place (all are 3), then the hundred thousands place (identify 4 and 6). Numbers starting with 34 are smaller than 36. Order the 34 numbers by ten thousands. Result: 3,456,789 < 3,456,879 < 3,456,987 < 3,465,789 < 3,654,789. Learners write this chain in their books.
- 6Pair activity: Give each pair six numbers written on cards (mixed order): 2,345,678; 2,354,678; 2,345,876; 2,435,678; 2,345,687; 2,543,678. Learners arrange the cards from least to greatest and write the complete chain using < symbols. Example: 2,345,678 < 2,345,687 < 2,345,876 < 2,354,678 < 2,435,678 < 2,543,678. Call on Kwesi and Adwoa to read their chain aloud. Verify correctness.
- 7Challenge: Learners create their own set of four 8-digit numbers and order them from greatest to least. They write the chain using > symbols. Provide the template: __________ > __________ > __________ > __________. Select three learners to share their chains. Class verifies the order.
- 8Ordering multiple numbers builds on the comparison skill. Start with numbers that differ in different place values to challenge learners progressively.
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- 1laptop
- 2phone
- 3comparison symbol cards (>, <, =)
- 4mini whiteboards and pens
- 5number cards
- 6exercise books
- 7whiteboard and marker
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- 1Play Comparison Quick-Fire: Call out two numbers rapidly. Learners hold up a card or write the correct symbol (>, <, or =) on mini whiteboards. Show answers. Do this eight times with numbers of varying sizes (some same, some different by millions, some different by single digits).
- 2Learners work in pairs. One learner writes two numbers and asks: 'Which is greater?' The partner answers and explains which place value made the difference. Reverse roles. Do this three times per pair. Listen to explanations to assess understanding.
Exercise
- 1Provide learners with this task: Given the numbers 8,756,432; 8,657,432; 8,756,342; 8,756,423, arrange them from least to greatest and write the complete comparison chain using < symbols. Show all your working by circling or underlining the place value where each pair differs. Acceptable response: 8,657,432 < 8,756,342 < 8,756,423 < 8,756,432 (with annotations showing comparisons at hundred thousands, then tens, then ones).
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- 1Recall the relationship between powers of 10 and identify how to express whole numbers as powers of 10
- 2Write on the board: 1 = 10⁰, 10 = 10¹, 100 = 10². Ask learners: What pattern do you see? Elicit: each number has one more zero; the exponent increases by 1. Continue: 1,000 = 10³, 10,000 = 10⁴. Ask Kofi: If we follow the pattern, what is 10⁵? (100,000). Write it. Learners count the zeros aloud to verify.
- 3Show learners a phone displaying: 10² = 10 × 10. Say: This means we multiply 10 by itself 2 times. So 10² = 100. What about 10³? (10 × 10 × 10 = 1,000). Learners repeat the multiplication three times. Confirm the answer.
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- UNDERSTANDING AND APPLYING POWERS OF 10 TO EXPRESS WHOLE NUMBERS
- 1Display on the phone or laptop a table: Powers of 10 from 10⁰ to 10⁹. Write: 10⁰ = 1, 10¹ = 10, 10² = 100, 10³ = 1,000, 10⁴ = 10,000, 10⁵ = 100,000, 10⁶ = 1,000,000, 10⁷ = 10,000,000, 10⁸ = 100,000,000, 10⁹ = 1,000,000,000. Read each aloud. Learners copy the table into their notebooks and circle any patterns they notice.
- 2Teach learners to express numbers in expanded form using powers of 10. Write on the board: 3,456 = (3 × 10³) + (4 × 10²) + (5 × 10¹) + (6 × 10⁰). Say: This is the standard form expansion. The digit 3 is in the thousands place, so we write 3 × 10³. Calculate together: 3 × 1,000 = 3,000. Do the same for 4 × 100 = 400; 5 × 10 = 50; 6 × 1 = 6. Add: 3,000 + 400 + 50 + 6 = 3,456. Learners follow each step.
- 3Provide learners with the number 25,307. Ask them to express it in expanded form using powers of 10: (2 × 10⁴) + (5 × 10³) + (3 × 10²) + (0 × 10¹) + (7 × 10⁰). Learners work in pairs. Check answers. Call on Ama and Kwame to read their expansion aloud. Verify by calculating backwards.
- 4Expanded form with powers of 10 requires learners to match digits to place values. Use the phone or laptop to display the powers of 10 table as reference throughout.
- EXPRESSING LARGE INTEGERS IN STANDARD FORM (SCIENTIFIC NOTATION)
- 5Introduce scientific notation. Write on the board: 1,500,000 = 1.5 × 10⁶. Say: In scientific notation, we write one non-zero digit before the decimal, then multiply by the appropriate power of 10. The exponent tells us how many places to move the decimal point to the right to get the original number. Learners verify: 1.5 × 10⁶ means 1.5 × 1,000,000 = 1,500,000. Correct.
- 6Provide three numbers for learners to express in scientific notation: 4,200,000; 8,300,000,000; 5,670,000. Learners work in small groups (Yaw's group, Sena's group, Kokou's group). Each group takes one number and determines the power of 10. Guide: Count how many digits are after the first digit. That is the exponent. Results: 4.2 × 10⁶, 8.3 × 10⁹, 5.67 × 10⁶. Display results and verify together.
- 7Reverse activity: Give learners scientific notation and ask them to write the standard form. Examples: 2.35 × 10⁴ = 23,500; 7.1 × 10⁷ = 71,000,000. Learners work independently and then pair-check. Call on Efua to explain how she converted 7.1 × 10⁷.
- 8Scientific notation is an extension. Emphasize that the exponent equals the number of places the decimal moves. Use the phone or laptop to show both forms side by side for clarity.
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- 1laptop
- 2phone
- 3powers of 10 reference table
- 4exercise books
- 5whiteboard and marker
- 6poster materials (paper, markers)
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- 1Learners play Power of 10 Match: Display a number in standard form on one side (e.g., 50,000) and its expanded form using powers of 10 on the other side (e.g., 5 × 10⁴). Learners come to the board and match them. Do this five times with different numbers.
- 2Learners create a quick poster showing three numbers in all three forms: standard form, expanded form using powers of 10, and scientific notation. Examples: 2,000 = (2 × 10³) = 2 × 10³; 345,000 = (3 × 10⁵) + (4 × 10⁴) + (5 × 10³) = 3.45 × 10⁵. Display three learner posters (Kwesi's, Adwoa's, Kofi's) and verify correctness together.
Exercise
- 1Provide learners with this task in their exercise books: Express the number 7,240,000 in three forms: (1) expanded form using powers of 10, (2) standard form description, and (3) scientific notation. Show all your working. Acceptable response: (1) (7 × 10⁶) + (2 × 10⁵) + (4 × 10⁴); (2) Seven million, two hundred and forty thousand; (3) 7.24 × 10⁶.
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