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> < =

Item 1. Write down your prediction. Then vote. Fill in the blank with either >, <, or = . > < =. Item 1. Discuss and write down your group's explanation. Fill in the blank with either >, <, or = . > < =. Item 1. Many children will choose “ < ”. Why? . < .

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> < =

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  1. Item 1 Write down your prediction. Then vote. Fill in the blank with either >, <, or = • > • < • =

  2. Item 1 Discuss and write down your group's explanation. Fill in the blank with either >, <, or = • > • < • =

  3. Item 1 Many children will choose “<”. Why? < Because they think “division makes smaller”. For example, 20 ÷ 4 < 20. 20 candies to be shared equally among 4 children will result in 5 candies per child, and 5 candies is less than 20 candies.

  4. Item 1 The correct answer is “>”. Why? > Because the divisor in this case is less than 1. For example, 20 ÷ ¼ > 20. Suppose you have 20 chocolate bars. If each child gets ¼ of a bar, then one bar can be shared by 4 children. So 20 bars can be shared by 80 children. 80 > 20.

  5. Item 2 Write down your prediction. Then vote. If N is a natural number, then N can take any of these values: 1, 2, 3, 4, 5, …. Is the following inequality always true, sometimes true, or never true? 67 89 N is a natural number:  N <N • Always True (AT) • Sometimes True (ST) • Never True (NT)

  6. Item 2 Discuss and write down your group's explanation. If N is a natural number, then N can take any of these values: 1, 2, 3, 4, 5, …. Is the following inequality always true, sometimes true, or never true? 67 89 N is a natural number:  N <N • Always True (AT) • Sometimes True (ST) • Never True (NT)

  7. Item 2 Many children will choose “NT”. Why? 67 89 N is a natural number:  N <N Because they think “multiplication makes bigger”. For example, 6  10 < 10 is false (In this case, N = 10). 6  10 = 10 + 10 + 10 + 10 + 10 + 10 = 60. So “6 times 10 makes 10 bigger”.

  8. Item 2 67 89 Note: is a proper fraction. i.e, < 1. The correct answer is “AT”. Why? 67 89 67 89 67 89 N is a natural number:  N <N Suppose N = 10.  10 ? 10

  9. Item 2 67 89 Note: is a proper fraction. i.e, < 1. 1  = 10 10 = The correct answer is “AT”. Why? 67 89 67 89 N is a natural number:  N <N Suppose N = 10.

  10. Item 2 67 89 Note: is a proper fraction. i.e, < 1. The correct answer is “AT”. Why? 67 89 67 89 67 89 N is a natural number:  N <N < Suppose N = 10.  10 10 <

  11. Item 2 67 89 Note: is a proper fraction. i.e, < 1. The correct answer is “AT”. Why? 67 89 67 89 67 89 67 89 N is a natural number:  N <N < In general,  N N . . . < . . . A portion of N units N units  N is actually a fractional part of the quantity N. smaller A proper fraction times a number makes the number ______.

  12. Item 3 Write down your prediction. Then vote. Note: If N is a natural number, then N can take any of these values: 1, 2, 3, 4, …. Is the following inequality always true, sometimes true, or never true? 2 35 2 35 N is a natural number: N > • Always True (AT) • Sometimes True (ST) • Never True (NT)

  13. Item 3 Discuss and write down your group's explanation. Note: If N is a natural number, then N can take any of these values: 1, 2, 3, 4, …. Is the following inequality always true, sometimes true, or never true? 2 35 2 35 N is a natural number: N > • Always True (AT) • Sometimes True (ST) • Never True (NT)

  14. Item 3 Note: If N is a natural number, then N can take any of these values: 1, 2, 3, 4, …. Many children will choose “AT”. Why? 2 35 2 35 N is a natural number: N > If N = 10, then 10  = If N = 3, then 3  = If N = 2, then 2  = + = . 2 35 4 35 2 35 2 35 6 35 2 35 2 35 2 35 4 35 2 35 6 35 2 35 2 35 20 35 2 35 20 35 2 35 2 35 2 35 + + = . + + = . … 10 times And > . And > . And > .

  15. Item 3 Note: If N is a natural number, then N can take any of these values: 1, 2, 3, 4, …. The correct answer is “ST”. Why? 2 35 2 35 2 35 2 35 N is a natural number: N > If N = 1, then 1  = . 2 35 2 35 2 35 2 35 N  . The correct inequality is And = .

  16. Item 4 Write down your prediction. Then vote. Is the following inequality always true, sometimes true, or never true? 11 25 N is a natural number: N÷ <N • Always True (AT) • Sometimes True (ST) • Never True (NT)

  17. Item 4 Discuss and write down your group's explanation. Is the following inequality always true, sometimes true, or never true? 11 25 N is a natural number: N÷ <N • Always True (AT) • Sometimes True (ST) • Never True (NT)

  18. Item 4 Many children will choose “AT”. Why? 11 25 N is a natural number: N÷ <N Because they think “division makes smaller”.

  19. Item 4 + + + + = = The correct answer is “NT”. Why? 11 25 N is a natural number: N÷ <N 11 25 11 25 3 25 25 25 11 25 11 25 11 25 11 25 Because N÷ means “How many ’s are in N?” Suppose N = 1. Then 1 ÷ means “How many ’s are in 1?”

  20. Item 4 + + + + = 1 = 3 11 unit of 1 unit of 1 unit of The correct answer is “NT”. Why? 11 25 N is a natural number: N÷ <N 3 11 11 25 11 25 11 25 11 25 11 25 11 25 11 25 Because N÷ means “How many ’s are in N?” Suppose N = 1. Then 1 ÷ means “How many ’s are in 1?” 2 or 25 11 Answer:

  21. Item 4 25 11 25 11 The correct answer is “NT”. Why? 11 25 N is a natural number: N÷ <N 11 25 11 25 > 1 > N 1 ÷ = 1  N÷ = N

  22. Item 4 25 11 25 11 The correct inequality is N÷ >N The correct answer is “NT”. Why? 11 25 11 25 N is a natural number: N÷ <N 11 25 11 25 > 1 > N N÷ = N 1 ÷ = 1  larger Dividing a number by a proper fraction makes the number ______.

  23. Item 5 Write down your prediction. Then vote. Is the following inequality always true, sometimes true, or never true? 32 23 N is a natural number:  N <N • Always True (AT) • Sometimes True (ST) • Never True (NT)

  24. Item 5 Discuss and write down your group's explanation. Is the following inequality always true, sometimes true, or never true? 32 23 N is a natural number:  N <N • Always True (AT) • Sometimes True (ST) • Never True (NT)

  25. Item 5 Some children will choose “NT”. Why? Because is an improper fraction. Because they think “multiplication makes bigger”. Other children will choose “AT”. Why? Because they think “a fraction times a number makes it smaller”. 32 23 32 23 N is a natural number:  N <N 32 23 32 23 32 23 “NT” . Why? The correct answer is _____ i.e., > 1  N > N  1 > 1

  26. Learning Points:

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