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

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

3. 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

4. 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

5. 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.

6. 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, ….

7. 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”.

8.  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

9. 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

10. 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

11. 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

12. 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.

13. 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, ….

14. 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

15. 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, ….

16. 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.

17. 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)

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

19. 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 ++=

20. 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

21. 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

22. 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?

23. 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.

24. 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)

25. 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

26. Learning Points: