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A. >
B. <
C. =
Fill in the blank with either >, <, or =
Item 1 Write down your prediction. Then vote.
A. >
B. <
C. =
Fill in the blank with either >, <, or =
Item 1 Discuss and write down your group's explanation.
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
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
Is the following inequality always true, sometimes true, or never true?
N is a natural number: N < N 6789
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.
Item 2 Discuss 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 6789
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, ….
N is a natural number: N < N 6789
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”.
6789
10
10 ?
N is a natural number: N < N 6789
The correct answer is “AT”. Why?
Item 2
Suppose N = 10.
Note: is a proper fraction. 6789 i.e, < 1. 67
89
N is a natural number: N < N 6789
The correct answer is “AT”. Why?
Item 2
Suppose N = 10.
=
10
10 =1
Note: is a proper fraction. 6789 i.e, < 1. 67
89
N is a natural number: N < N 6789
The correct answer is “AT”. Why?
Item 2
Suppose N = 10.
6789
10
10 <
<
Note: is a proper fraction. 6789 i.e, < 1. 67
89
N is a natural number: N < N 6789
The correct answer is “AT”. Why?
Item 2
In general,
6789
N
N
<
<
. . .
A portion of N units
. . .
N units
N is actually a fractional part of the quantity N. 6789
A proper fraction times a number makes the number ______.smaller
Note: is a proper fraction. 6789 i.e, < 1. 67
89
Is the following inequality always true, sometimes true, or never true?
N is a natural number: N > 235
235
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.
Item 3 Discuss and write down your group's explanation.
Is the following inequality always true, sometimes true, or never true?
N is a natural number: N > 235
235
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, ….
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 > 235
235
If N = 2, then 2 =235 + = .
235
235
435
235
435And > .
If N = 3, then 3 =235
235
635And > . + + = . 2
352
356
352
35
If N = 10, then 10 =235
235
2035And > . + + = . …
235
2035
235
10 times
Item 3
N is a natural number:
The correct answer is “ST”. Why?
N > 235
235
If N = 1, then 1 = .
235
235
235
235And = .
The correct inequality is N .
235
235
Item 3
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?
N is a natural number: 1125
Item 4
N ÷ < N
A. Always True (AT)
B. Sometimes True (ST)
C. Never True (NT)
Write down your prediction. Then vote.
Item 4 Discuss and write down your group's explanation.
Is the following inequality always true, sometimes true, or never true?
N is a natural number: 1125N ÷ < N
A. Always True (AT)
B. Sometimes True (ST)
C. Never True (NT)
N is a natural number:
Many children will choose “AT”. Why?
Because they think “division makes smaller”.
Item 4
1125N ÷ < N
N is a natural number:
Item 4
1125N ÷ < N
The correct answer is “NT”. Why?
Because N ÷ means “How many ’s are in N?” 1125
11 25
Suppose N = 1.
Then 1 ÷ means “How many ’s are in 1?” 1125
1125
++ =
1125
1125
325
2525
++ =
N is a natural number:
Item 4
1125N ÷ < N
The correct answer is “NT”. Why?
Because N ÷ means “How many ’s are in N?” 1125
1125
Suppose N = 1.
++ =
++ = 1
Then 1 ÷ means “How many ’s are in 1?” 1125
1125
1125
1 unit of 1125
1 unit of 1125
unit of311
Answer: 2511 2 or3
11
N is a natural number:
Item 4
1125N ÷ < N
The correct answer is “NT”. Why?
1 ÷ = 1 1125
2511
N ÷ = N 1125
2511 > N
> 1
N is a natural number:
Item 4
1125N ÷ < N
Dividing a number by a proper fraction makes the number ______.
The correct inequality is
larger
1 ÷ = 1 1125
2511
N ÷ = N 1125
2511 > N
> 1
N ÷ > N 1125
The correct answer is “NT”. Why?
Is the following inequality always true, sometimes true, or never true?
N is a natural number:
Item 5
N < N 3223
A. Always True (AT)
B. Sometimes True (ST)
C. Never True (NT)
Write down your prediction. Then vote.
Item 5 Discuss 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 3223
A. Always True (AT)
B. Sometimes True (ST)
C. Never True (NT)
N is a natural number:
Some children will choose “NT”. Why?Because they think “multiplication makes bigger”.
Item 5
N < N 3223
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. 3223
1 > 13223
N > N3223
“NT” . Why?
i.e., > 13223
Learning Points:
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