a.> b.< c.= fill in the blank with either >,

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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