fourth grade - njctlcontent.njctl.org › courses › math › 4th-grade-math › ... · fourth...

/ 162 Slide 2 / 162

Fourth Grade

Fraction Decimal Concepts

2015-11-23

www.njctl.org

Slide 3 / 162

Table of Contents

- Number Line Location

- Convert Decimals to Fractions- Convert Fractions to Decimals

Click on the topic to go to that section

- Understanding Fractions- Mixed Numbers- Compare and Order Fractions- Equivalent Fractions

Slide 4 / 162

Understanding Fractions

click to return to table of contents

Slide 5 / 162

1 02345678910 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10

##

Mr. Number Line is taking a short nap. He's a little tired from a long day of problem solving!

What type of numbers is he using to count sheep?

12 3

4 5

Positive WHOLE NumbersClick for Answer

Slide 6 / 162

1 02345678910 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10

##

While napping, Mr. Number Line is dreaming of pepperoni pizza! What type of numbers would you

use to help Mr. Number Line count the total number of pizzas in his dream?

Fractions and/or Mixed NumbersClick for Answer

Talk to an elbow partner and share how you would count the pizzas.

How are fractions different from whole numbers?

http://www.njctl.org

http://www.njctl.org

page61svg

page129svg

page105svg

page2svg

page21svg

page34svg

page59svg

page1svg

(Answer) / 162

1 02345678910 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10

##

While napping, Mr. Number Line is dreaming of pepperoni pizza! What type of numbers would you

use to help Mr. Number Line count the total number of pizzas in his dream?

Fractions and/or Mixed NumbersClick for Answer

Talk to an elbow partner and share how you would count the pizzas.

How are fractions different from whole numbers?

[This object is a pull tab]

Teac

her N

otes

Students could use one of the following strategies to count the halves.

Using only fractions: 1/2 2/2 3/2 4/2 5/2 6/2 7/2one half...two halves...three halves...

Using fractions and whole numbers: 1/2 1 3/2 2 5/2 3 7/2one half.... one....three halves....two....

Using fractions, whole numbers and mixed numbers:

1 1 2 2 3 3

one half....one....one and one half....two.....

Great way to go over difference between whole numbers, fractions and mixed numbers.

12

12

12

12

Slide 7 / 162

Fractions represent what is BETWEEN whole numbers. A fraction is a PART of a WHOLE.

The first fractions we will learn about are PROPER FRACTIONS. Examples of proper fractions are shown below in word form:

one

half

one

quarter

two

thirds

three

fourths

four

fifths

three

eighths

five

tenths

one

sixths

Proper Fractions in Standard Form: 38

23

510

14

45

12

34

16

Slide to the right to reveal fractions in standard form.

Slide 7 (Answer) / 162

Fractions represent what is BETWEEN whole numbers. A fraction is a PART of a WHOLE.

The first fractions we will learn about are PROPER FRACTIONS. Examples of proper fractions are shown below in word form:

one

half

one

quarter

two

thirds

three

fourths

four

fifths

three

eighths

five

tenths

one

sixths

Proper Fractions in Standard Form: 38

23

510

14

45

12

34

16

Slide to the right to reveal fractions in standard form.


Teac

her N

otes

Students may need to review standard form. Practice with the 8 fractions on this slide. Have students explain how a fraction is written in standard form. If important

vocabulary (numerator and denominator) does not come easily, the slides that follow will go over these terms. The most important thing is that students know that standard

form is the typical way we see fractions. A number on top and a number on the bottom and a line segment in

between. By the way this line segment is called the vinculum or fraction bar.

IMPORTANT: The word document "Proper Fraction - Flash Cards" contains the 8 fractions on this slide plus eight additional proper fractions. Students can work in groups to write the standard form on each flash card.

Once students cut out these flash cards, they can write "Proper Fraction" on the blank side.

Slide 8 / 162

38

23

510

14

45

12

34

16

Let's look at the 8 proper fractions we discussed on the previous slide.

Talk to an elbow partner and share what you know about these proper fractions. Write down any important ideas you discuss with

your partner so that you can share these ideas with the whole class.

We will organize our ideas on the next slide.

Slide 9 / 162

38

23

510

14

45

12

34

16

Slide 10 / 162

Let's review what we know so far about fractions.

0 1 2

{1. All Proper Fractions can be found between 0 and 1 on a number line.

Proper Fractions

2. Whole numbers are the first types of numbers we learn about. Whole numbers are found in the real world, but fractions are used much more frequently.

Brainstorm with a partner where we can find fractions in the real world.

/ 162 Slide 12 / 162

123

4567

8910

1211

1/4c

1/2c

3/4c

1c

Slide 13 / 162

Let's review some important vocabulary to help us better understand fractions. Noomy the Numerator and Deeno the

Denominator are here to help us.

Noomy the numerator represents the top part of a fraction.

He shows the PART of the fraction that we are looking at.

PART and Purple both start with P.

Deeno the denominator represents the bottom of a fraction.

He shows the WHOLE (or ONE) that we are looking at.

ONE and Orange both start with O.

Slide 14 / 162

Every fraction is division and every division problem can be shown as a fraction. Even the division sign looks like a fraction.

Click on the top part of the division sign.

Click on the bottom part of the division sign.

NUMERATOR

DENOMINATOR

Slide 15 / 162

Fractions can be used to name a part of a whole object.

You ate of the pie.

Slide 16 / 162

Fractions can also be used to name a part of a collection of objects.

of the balls are

needed for practice.

/ 162

Naming Fractions

23

top number = numeratorbottom number = denominator

Slide 18 / 162

1 Which number is the numerator in the fraction?


1 Which number is the numerator in the fraction?


Ans

wer

2

Slide 19 / 162

2 Which number is the denominator in the fraction?


2 Which number is the denominator in the fraction?


Ans

wer

7

Slide 20 / 162

3 Which fraction has a 5 in the denominator?

A

B

C

(Answer) / 162

3 Which fraction has a 5 in the denominator?

A

B

C


Ans

wer

C

Slide 21 / 162

4 Which fraction has a 3 in the numerator?

A

B

C


4 Which fraction has a 3 in the numerator?

A

B

C


Ans

wer

A

Slide 22 / 162

5 What fraction of this set is blue?


5 What fraction of this set is blue?


Ans

wer

37

Slide 23 / 162

6 What fraction of this set is purple?

(Answer) / 162

6 What fraction of this set is purple?


Ans

wer

25

Slide 24 / 162

7 What fraction of this set is red?


7 What fraction of this set is red?


Ans

wer

36

Slide 25 / 162

Mixed Numbers


Slide 26 / 162

Take out the following number of pattern blocks

hexagon1

trapezoid9

rhombus

8

triangle11

Slide 27 / 162

If a hexagon is worth 1, what are 3 trapezoids worth?

click for answer

page1svg

/ 162

If a hexagon is worth 1, what are 4 rhombi worth?click for answer

Slide 29 / 162

8 If a hexagon is worth 1, what are 5 triangles worth?

click for answer



click for answer


Ans

wer

Slide 30 / 162

9 If a hexagon is worth 1, what are 5 trapezoids worth?




Ans

wer

Slide 31 / 162

10 If a hexagon is worth 1, what are 8 rhombi worth?

(Answer) / 162

10 If a hexagon is worth 1, what are 8 rhombi worth?


Ans

wer

Slide 32 / 162





Ans

wer

Slide 33 / 162





Ans

wer

Slide 34 / 162

Sometimes the hexagon is not worth one.

What do we do if a unit other than one is given?

First figure out what one is worth, then solve the problem.click

/ 162

13 If the triangle is , what shape is ONE?

A hexagon B rhombus C trapezoid


13 If the triangle is , what shape is ONE?

A hexagon B rhombus C trapezoid


Ans

wer

B

Slide 36 / 162

14 If the triangle is , what is a trapezoid worth?


14 If the triangle is , what is a trapezoid worth?


Ans

wer

34

Slide 37 / 162

15 If the triangle is , what is the hexagon worth?


15 If the triangle is , what is the hexagon worth?


Ans

wer

64

/ 162

Fractions that are greater than one are often called improper fractions, even

though there is nothing improper about them.

Improper Fraction Mixed Number

Slide 39 / 162

A mixed number is a number that has a whole part and a fractional part.

For example: 6 is the whole part is the fractional part

Slide 40 / 162

To convert an improper fraction to a mixed number.

First divide 31 by 6

56 31 -30 1

QuotientDivisor

Remainder

Then write in the form:

quotient remainderdivisor

click for mixed number

Slide 41 / 162

To convert an improper fraction to a mixed number.

First divide 30 by 4

74 30 -28 2

QuotientDivisor

Remainder

Then write in the form:

quotientremainder

divisor

Slide 42 / 162

Match the Mixed Numbers and Improper Fractions.

Slide 43 / 162

(Answer) / 162 Slide 44 / 162

Slide 44 (Answer) / 162 Slide 45 / 162


(Answer) / 162 Slide 47 / 162



Compare and Order Fractions


page1svg

/ 162

The first step when comparing fractions is to look at the numerators and denominators.

numeratorsdenominators

Slide 51 / 162

When the denominators are the same:

- the unit fractions are the same size- only need to compare the number of pieces ###

(numerators) need to be compared

Slide 52 / 162

Reorder the following fractions from least to greatest.

Slide 53 / 162

22 Which of the following is ordered least to greatest?

A B C



A B C


Ans

wer

B

Slide 54 / 162

23 Which of the following is ordered greatest to least?

A B C

(Answer) / 162


A B C


Ans

wer

A

Slide 55 / 162

When the numerators are the same:

- there are the same number of pieces- compare the size of the denominator

The smaller the denominator, the larger the size of

each piece.

The larger the denominator, the smaller the size of each piece.

Slide 56 / 162

Reorder the following fractions from least to greatest.

Slide 57 / 162


A B C



A B C


Ans

wer

B

Slide 58 / 162


A B C

(Answer) / 162


A B C


Ans

wer

C

Slide 59 / 162

If numerators and denominators are not the same, we need to use other methods to compare fractions.

Use benchmarks to see if the fraction is close to 0, 1/2, or 1 and then order them.

012 1

Slide 60 / 162

26 Which fraction is closest to zero?

A

B

C

D



A

B

C

D


Ans

wer

B

Slide 61 / 162

27 Which fraction is closest to one?

A

B

C

D



A

B

C

D


Ans

wer

A

/ 162

28 Which fraction is closest to a half?

A

B

C

D



A

B

C

D


Ans

wer

C

Slide 63 / 162


A

B

C

D



A

B

C

D


Ans

wer

D

Slide 64 / 162


A

B

C

D



A

B

C

D


Ans

wer

A

/ 162


A

B

C

D



A

B

C

D


Ans

wer

C

Slide 66 / 162

Use benchmarks of 0, 1/2 and 1 to order the fractions least to greatest.

Slide 67 / 162

Use benchmarks of 0, 1/2 and 1 to order the fractions least to greatest.

Slide 68 / 162


A B C



A B C


Ans

wer

A

/ 162


A B C



A B C


Ans

wer

B

Slide 70 / 162

If the previous strategies don't work to compare fractions, we need to find

equivalent fractions in order to compare them.

Equivalent Fractions


Slide 71 / 162

Click below to use this interactive number line.

Slide 72 / 162

A fraction stick is a model for the whole, or ONE.

Use it to find equivalent fractions.

Find equivalent fractions for

Slide 73 / 162

Fraction Stick Chart

page1svg

http://www.cut-the-knot.org/Curriculum/Arithmetic/EquivalentFractions.shtml

(Answer) / 162

Fraction Stick Chart


Teac

her N

otes Use a print out of a

fraction stick chart or use manipulatives as shown here to aide students in their understanding of equivalent fractions.

Slide 74 / 162

34 Find an equivalent fraction for




Ans

wer

6/8, 9/12, etc.

Slide 75 / 162





Ans

wer

16/32, 24/48, etc.

Slide 76 / 162


(Answer) / 162



Ans

wer

1 2/6, 1 3/9, etc.

Slide 77 / 162





Ans

wer

14/12, 21/18, etc.

Slide 78 / 162

A fraction stick is a model for the whole, or ONE.

Use it to compare fractions.

Which number is larger? or

Slide 79 / 162

38 Which number is larger?

A B



A B


Ans

wer

B

/ 162


A B



A B


Ans

wer

B

Slide 81 / 162


A B



A B

[This object is a pull tab]A

nsw

er

A

Slide 82 / 162

Splitting Fractions Sticks to Make Equivalent Fractions

What fraction of the whole is shaded?

Slide 83 / 162

If a horizontal line is drawn to divide each part of the rectangle into 2 parts, what fraction of the whole is shaded?

Has the shaded amount of the rectangle changed?

/ 162

41 What fraction of the whole is shaded now?


41 What fraction of the whole is shaded now?


Ans

wer

412

Slide 85 / 162

42 What fraction of the whole is shaded?


42 What fraction of the whole is shaded?


nsw

er

14

Slide 86 / 162

43 Use these two horizontal lines to divide the whole.

What fraction of the whole is shaded now?


43 Use these two horizontal lines to divide the whole.

What fraction of the whole is shaded now?


Ans

wer

312

/ 162

44 Is the shaded region the same in each of these?

Yes No


44 Is the shaded region the same in each of these?

Yes No


Ans

wer

Yes

Slide 88 / 162

19

19

19

What do you notice about the denominators in each set of equivalent fractions?

Slide 89 / 162

What patterns have you noticed in the previous examples about making equivalent fractions?

What important idea do we know about multiplying by 1?

Slide 90 / 162

Multiplication RuleTo find an equivalent fraction, multiply both the

numerator and the denominator of the fraction by the same number.

Slide 91 / 162

25

= ??

Use the multiplication table to make equivalent fractions.Pu

ll

(Answer) / 162

25

= ??

Use the multiplication table to make equivalent fractions.

Pull


Teac

her N

otes To see fractions

equivalent to 2/5, move the fraction

circle along the strips between 2 and 5.

Slide 92 / 162

Find three equivalent fractions.

Slide 93 / 162

45 Which two fractions are equivalent to ?

A B C D


45 Which two fractions are equivalent to ?

A B C D


nsw

er

B & D

Slide 94 / 162

46 What fractions are equivalent to ?

A B C D


46 What fractions are equivalent to ?

A B C D


Ans

wer

D

/ 162 Slide 96 / 162

48 What is a fraction equivalent to ?

Slide 97 / 162

49 What is a fraction equivalent to ?

Slide 98 / 162

What important idea to we know about dividing by 1?

How can we use division to find equivalent fractions?

Slide 99 / 162

Steps to Simplifying Fractions

1. Find the GCF of both numbers.2. Divide the numerator and denominator by that number.

3. Answer will be the fraction in simplified form.

GCF = 2

Slide 100 / 162

/ 162

50 What is in simplified form?




Ans

wer

1/3

Slide 102 / 162





Ans

wer

1/2

Slide 103 / 162





Ans

wer

1/2

/ 162





Ans

wer

1/5

Slide 105 / 162





Ans

wer

1/8

Slide 106 / 162 Slide 106 (Answer) / 162

/ 162 Slide 107 (Answer) / 162



/ 162 Slide 110 (Answer) / 162


Slide 112 / 162

Converting Decimals to Fractions


Slide 113 / 162

Converting a Decimal to a Fraction1. Put the digits in the numerator.

2. The denominator represents the place value.3. Simplify fraction if you can.

Example:

0.9 =

0.25 =

page1svg

/ 162

Match the following decimals with their fraction equivalents.

0.6 =

0.3 =

0.06 =

0.03 =

Slide 115 / 162

61 What fraction is equivalent to the decimal below? (Be sure answer is in simplified form.)

0.7 =

Slide 116 / 162


0.44 =

Slide 117 / 162


0.2 =

Slide 118 / 162


0.05 =

Slide 119 / 162


0.33 =

/ 162

Converting Fractions to Decimals


Slide 121 / 162

Converting fractions to decimal form by changing the denominator.

Steps:1. Use mental math, the multiplication rule or the division rule to

change each fraction to an equivalent fraction having a denominator of 10 or 100.

2. Write the new fraction as a decimal.

Slide 122 / 162

Examples:

x 4

x 4

x 5

x 5

6

6_

_

Slide 123 / 162

Slide 124 / 162 Slide 125 / 162

page1svg

(Answer) / 162 Slide 126 / 162


68 What is the fraction in decimal form?




Ans

wer

0.2

Slide 128 / 162

(Answer) / 162 Slide 129 / 162



(Answer) / 162 Slide 132 / 162


Convert the following fractions to decimals.

When you can not make an equivalent fraction with a denominator of 10 or 100, then you must divide to find the decimal equivalent.

Slide 134 / 162 Slide 135 / 162

/ 162





Ans

wer

0.625

Slide 137 / 162





Ans

wer

0.125

Slide 138 / 162

3 1

Notice what happens with this division.This is called a repeating decimal and it is written as

0.3 and is read as point three repeating.

Slide 139 / 162

Use a calculator to convert these fractions to decimals to see the repeating pattern.

fraction calculator display decimal

23

49

5 12

4 11

/ 162 Slide 140 (Answer) / 162



/ 162

Number Line Location


Slide 144 / 162

0.4 0.5

On the following number line, draw a line and move the decimals to their correct location.

0.420.45

0.48


0.4 0.5


0.420.45

0.48


Teac

her N

otes

Steps:1. Divide the number line into smaller parts using tick marks.2. Compare the decimals and place them correctly.

Slide 145 / 162

6.45 6.46


6.4526.458


6.45 6.46


6.4526.458


Teac

her N

otes

Steps:1. Divide the number line

into smaller parts using tick marks.

2. Compare the decimals and place them correctly.

Slide 146 / 162

Label the numbers on the number line.

2 3

page1svg

(Answer) / 162


2 3


Teac

her N

otes

Steps:1. Convert numbers to same form. 2. Divide the number line into smaller parts using tick marks.2. Compare the numbers and place them correctly.

Slide 147 / 162





Teac

her N

otes

Steps:1. Convert numbers to same

form. 2. Divide the number line into smaller parts using tick marks.2. Compare the numbers and

place them correctly.

Slide 148 / 162

79 Where would the following number be correctly placed on the number line?

A B C D

9 109.5



A B C D

9 109.5[This object is a pull tab]

Ans

wer

C

Slide 149 / 162


A B C D

5 65.5

(Answer) / 162


A B C D

5 65.5


Ans

wer

A

Slide 150 / 162


A B C D

2 32.5



A B C D

2 32.5


Ans

wer

C

Slide 151 / 162


A B C D

0 10.5



A B C D

0 10.5


Ans

wer

B

Slide 152 / 162


A B C D

0 10.5

(Answer) / 162


A B C D

0 10.5


Ans

wer

C

Slide 153 / 162


A B C D

0 10.5



A B C D

0 10.5


Ans

wer

C

Slide 154 / 162


A B C D

0 21

Be careful of the scale of the number line!



A B C D

0 21

Be careful of the scale of the number line!


Ans

wer

C

Slide 155 / 162


A B C D

0 21

(Answer) / 162


A B C D

0 21


Ans

wer

A

Slide 156 / 162


A B C D

0 21 3



A B C D

0 21 3


Ans

wer

C

Slide 157 / 162

Steps to Create Your Own Number Line1. Convert numbers all to the same form.

2. Order the numbers to determine the range of numbers you need to include.

3. Draw a number line and divide it into equal size pieces.

4. Put a dot and label each number.

Slide 158 / 162

Example:Plot and label the numbers in the box on a number line.

1. Convert numbers all to the same form. In this case, all to decimal will be the easiest.

1.5, 0.75, 0.2, 1.2, 0.45

2. Order the numbers to determine the range of numbers you need to include. 0.2, 0.45, 0.75, 1.2, 1.5

We need a number line from 0 to 2

Slide 159 / 162

3. Draw a number line and divide it into equal size pieces. Label 0, 1 and 2 Divide in between the whole numbers into tenths.


.2 .45 .75 1.2 1.5

0 1 2

0 1 2

/ 162

Example:Plot and label the numbers in the box on a number line.

1. Convert numbers all to the same form. In this case, all to decimal will be the easiest.

1.2, 0.6, 0.4, 1.8, 1

2. Order the numbers to determine the range of numbers you need to include.

0.4, 0.6, 1, 1.2, 1.8 We need a number line from 0 to 2

Slide 161 / 162

3. Draw a number line and divide it into equal size pieces. Label 0, 1 and 2 Divide in between the whole numbers into two-tenths.


0 1 2

0 1 2.4 .6 1.2 1.8

Slide 162 / 162

Plot and label the following sets of numbers on a number line. Make a separate number line for each set.

Set 1 Set 2 Set 3

fourth grade - njctlcontent.njctl.org › courses › math › 4th-grade-math › ... · fourth...

Documents