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

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

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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. Item 1

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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. Item 1

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

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

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N is a natural number: N < N 67 89 Many children will choose “NT”. Why? 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. Item 2 So “6 times 10 makes 10 bigger”.

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

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

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

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

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

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

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N is a natural number: 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? N > 2 35 2 35 If N = 2, then 2 = 2 35 + =. 2 35 2 35 4 35 2 35 4 35 And >. If N = 3, then 3 = 2 35 2 35 6 35 And >. + + =. 2 35 2 35 6 35 2 35 If N = 10, then 10 = 2 35 2 35 20 35 And >. + + =. … 2 35 20 35 2 35 10 times Item 3

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

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

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

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

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

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

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

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

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

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

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

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