fractiondecimalconcepts20130122.notebook March 06,...

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fractiondecimalconcepts20130122.notebook

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March 06, 2015

www.njctl.org

This material is made freely available at www.njctl.org and is intended for the noncommercial use of students and teachers. These materials may not be used for any commercial purpose without the written permission of the owners. NJCTL maintains its website for the convenience of teachers who wish to make their work available to other teachers, participate in a virtual professional learning community, and/or provide access to course materials to parents, students and others.

Click to go to website:www.njctl.org

New Jersey Center for Teaching and Learning

Progressive Mathematics Initiative

www.njctl.org

4th Grade

FractionDecimal Concepts

www.njctl.org

20130122

Table of Contents

Table of Contents

Number Line Location

Convert Decimals to FractionsConvert Fractions to Decimals

Click on the topic to go to that section

Fraction ReviewMixed Numbers

Compare and Order FractionsEquivalent Fractions

Fraction Review

Fraction Review

click to return to table of contents

part to whole relationship

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

You ate of the pie.

part of a group

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

of the balls are needed for practice.


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naming fractions

Naming fractions

23

top number = numeratorbottom number = denominator

question

1 Which number is the numerator in the fraction?

question

2 Which number is the denominator in the fraction?

question

3 Which fraction has a 5 in the denominator?

A

B

C

question

4 Which fraction has a 3 in the numerator?

A

B

C

question

5 What fraction of this set is blue?


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question

6 What fraction of this set is purple?

Jan 1810:47 PM

7 What fraction of this set is red?

Mixed Numbers

Mixed Numbers


pattern blocks

Take out the following number of pattern blocks

hexagon1

trapezoid9

rhomb

us

8triangle11

pattern blocks example

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

click for answer

pattern block example

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


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question

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

click for answer

question

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

click for answer

question

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

click for answer

question

11 If a hexagon is worth 1, what are 11 triangles worth?

click for answer

question

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

click for answer

hexagon not worth one

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


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question

13 If the triangle is , what shape is ONE?

A hexagon

B rhombusC trapezoid

question

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

question

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

Improper fractions

Fractions that are greater than one are often called improper fractions, even though there is nothing improper about them.

Improper Fraction Mixed Number

Mixed Number

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

Mixed Number Example

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


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Mixed Number Example

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:

quotient remainderdivisor

click for mixed number

Matching

Match the Mixed Numbers and Improper Fractions.

question

16 Write the fraction as a whole number or a mixed number.

question


question


question



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question


question


Compare and Order Fractions

Compare and Order Fractions


comparing

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

numeratorsdenominators

denominators the same

When the denominators are the same:

the unit fractions are the same sizeonly need to compare the number of pieces (numerators) need to be compared

ordering

Order the following fractions least to greatest.


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question

22 Which of the following is ordered least to greatest?

A B C

question

23 Which of the following is ordered greatest to least?

A B C

numerators the same

When the numerators are the same:

there are the same number of piecescompare 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.

ordering

Order the following fractions least to greatest.

question


A B C

question

25 Which of the following is ordered greatest to least?

A B C


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benchmarks

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.

0 12 1

question

26 Which fraction is closest to zero?

A

B

C

D

question

27 Which fraction is closest to one?

A

B

C

D

question

28 Which fraction is closest to a half?

A

B

C

D

question

29 Which fraction is closest to one?

A

B

C

D

question

30 Which fraction is closest to a half?

A

B

C

D


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question

31 Which fraction is closest to zero?

A

B

C

D

ordering

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

ordering

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

question


A B C

question


A B C

Equivalent Fractions

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

equivalent fractions in order to compare them.

Equivalent Fractions



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interactive number line

Click below to use this interactive number line.

fraction stick

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

Use it to find equivalent fractions.

Find equivalent fractions for

dgr

FRACTION STICK CHART

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

Pull

Pull

for teacher directions

question

34 Find an equivalent fraction for

question


question



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question


fractio stick model

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

Use it to compare fractions.

Which number is larger? or

question

38 Which number is larger?

A B

question


A B

question


A B

Fraction Stick Splitting

Splitting Fractions Sticks to Make Equivalent Fractions

What fraction of the whole is shaded?


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Fraction Stick Splitting

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?

question

41 What fraction of the whole is shaded now?

question

42 What fraction of the whole is shaded?

question

43 Use these two horizontal lines to divide the whole.

What fraction of the whole is shaded now?

question

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

Yes No

denominators

110

110

15

110

112

112

112

112

112

112

110

110

110

110

18

18

18

18

16

16

16

14

14

12

112

112

112

112

16

16

13

19

19

19

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


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patterns

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

What important idea do we know about multiplying by 1?

Multiplication Rule

Multiplication Rule

To find an equivalent fraction, multiply both the numerator and the denominator of the fraction by the same number.

multiplication table

25

= ??

Use the multiplication table to make equivalent fractions.

Pull To see fractions

equivalent to 2/5, move the fraction circle along the strips between 2 and 5.

example

Find three equivalent fractions.

question

45 What fractions are equivalent to ?

A B C D

question

46 What fractions are equivalent to ?

A B C D


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question

47 What is a fraction equivalent to ?

question


question


division

What important idea to we know about dividing by 1?

How can we use division to find equivalent fractions?

Division Rule

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

examples

Try these.

GCF = 8

GCF = 12


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question

50 What is in simplified form?

question


question


question


question


question

55 Which fractions are equivalent?

A B C


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question


A B C

question


A B C

question

58 What number can go in the box to make the numbers equivalent?

question


question


Decimals to Fractions

Converting Decimals to Fractions



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steps

To convert a decimal to a fraction:

1. Put the digits in the numerator.2. The denominator represents the place value.3. Simplify fraction if you can.

Example:

0.9 =

0.25 =

practice

Match the following decimals with their fraction equivalents.

0.6 =

0.3 =

0.06 =

0.03 =

question

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

0.7 =

question


0.44 =

question


0.2 =

question


0.05 =


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question


0.7 =0.33 =

Fractions to Decimals

Converting Fractions to Decimals


steps

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.

Way 1

examples

Examples:

x 4

x 4

x 5

x 5

6

6_

_

matching

Match each decimal to its equivalent fraction.

0.7

0.280.35

0.14

matching

Match each decimal to its equivalent fraction.

3.12

3.853.823.8


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question

66 What is the fraction in decimal form?

question


question


question


question


question



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question


question


convert

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.

Way 2

example solved

.3758 3.000 24 60 56 40 40 0

Steps:1. The numerator is the dividend and the denominator is the divisor.2. Put a decimal point in the dividend and add zeros as needed.3. Divide.

example

16 3

Steps:1. The numerator is the dividend and the denominator is the divisor.2. Put a decimal point in the dividend and add zeros as needed.3. Divide.

question



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question


repeating decimal

3 1

Notice what happens with this division.This is called a repeating decimal andit is written as 0.3 and is read as point three repeating.

_

repeating examples

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

fraction calculator display decimal

23

49

5 12

4 11

question

76 Which of the following repeating decimals is equivalent to

A 1.3

B 1.3

C 0.3

D 1.3333333333333333333

question


A 0.8B 1.2C 0.81D 0.818181818

question


A 4.83B 1.2C 4.83D 4.83333333333


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number line example

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

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

PullPull

for steps

number line example

6.45 6.46

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

6.4526.458

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

PullPull

for steps

number line example

Label the numbers on the number line.

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.

PullPull

for steps

2 3

number line example

Label the numbers on the number line.

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.

PullPull

for steps

question

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

A B C D

9 109.5


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question


A B C D

5 65.5

question


A B C D

2 32.5

question


A B C D

0 10.5

question


A B C D

0 10.5

question


A B C D

0 10.5

question


A B C D

0 21

Be careful of the scale of the number line!


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question


A B C D

0 21

question


A B C D

0 21 3

number line steps

Steps to create your own number line.

1. 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.

Example 1

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


0.2, 0.45, 0.75, 1.2, 1.5We need a number line from 0 to 2

Example 1

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


.2 .45 .75 1.2 1.5

0 1 2

0 1 2

Example 2

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


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


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Example 2

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


0 1 2

0 1 2.4 .6 1.2 1.8

Practice

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

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