Upload
others
View
1
Download
0
Embed Size (px)
Citation preview
fractiondecimalconcepts20130122.notebook
1
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.
fractiondecimalconcepts20130122.notebook
2
March 06, 2015
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?
fractiondecimalconcepts20130122.notebook
3
March 06, 2015
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
click to return to table of contents
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
fractiondecimalconcepts20130122.notebook
4
March 06, 2015
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
fractiondecimalconcepts20130122.notebook
5
March 06, 2015
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
fractiondecimalconcepts20130122.notebook
6
March 06, 2015
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
17 Write the fraction as a whole number or a mixed number.
question
18 Write the fraction as a whole number or a mixed number.
question
19 Write the fraction as a whole number or a mixed number.
fractiondecimalconcepts20130122.notebook
7
March 06, 2015
question
20 Write the fraction as a whole number or a mixed number.
question
21 Write the fraction as a whole number or a mixed number.
Compare and Order Fractions
Compare and Order Fractions
click to return to table of contents
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.
fractiondecimalconcepts20130122.notebook
8
March 06, 2015
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
24 Which of the following is ordered least to greatest?
A B C
question
25 Which of the following is ordered greatest to least?
A B C
fractiondecimalconcepts20130122.notebook
9
March 06, 2015
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
fractiondecimalconcepts20130122.notebook
10
March 06, 2015
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
32 Which of the following is ordered least to greatest?
A B C
question
33 Which of the following is ordered least to greatest?
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
click to return to table of contents
fractiondecimalconcepts20130122.notebook
11
March 06, 2015
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
35 Find an equivalent fraction for
question
36 Find an equivalent fraction for
fractiondecimalconcepts20130122.notebook
12
March 06, 2015
question
37 Find an equivalent fraction for
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
39 Which number is larger?
A B
question
40 Which number is larger?
A B
Fraction Stick Splitting
Splitting Fractions Sticks to Make Equivalent Fractions
What fraction of the whole is shaded?
fractiondecimalconcepts20130122.notebook
13
March 06, 2015
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?
fractiondecimalconcepts20130122.notebook
14
March 06, 2015
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
fractiondecimalconcepts20130122.notebook
15
March 06, 2015
question
47 What is a fraction equivalent to ?
question
48 What is a fraction equivalent to ?
question
49 What is a fraction equivalent to ?
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
fractiondecimalconcepts20130122.notebook
16
March 06, 2015
question
50 What is in simplified form?
question
51 What is in simplified form?
question
52 What is in simplified form?
question
53 What is in simplified form?
question
54 What is in simplified form?
question
55 Which fractions are equivalent?
A B C
fractiondecimalconcepts20130122.notebook
17
March 06, 2015
question
56 Which fractions are equivalent?
A B C
question
57 Which fractions are equivalent?
A B C
question
58 What number can go in the box to make the numbers equivalent?
question
59 What number can go in the box to make the numbers equivalent?
question
60 What number can go in the box to make the numbers equivalent?
Decimals to Fractions
Converting Decimals to Fractions
click to return to table of contents
fractiondecimalconcepts20130122.notebook
18
March 06, 2015
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
62 What fraction is equivalent to the decimal below? (Be sure answer is in simplified form.)
0.44 =
question
63 What fraction is equivalent to the decimal below? (Be sure answer is in simplified form.)
0.2 =
question
64 What fraction is equivalent to the decimal below? (Be sure answer is in simplified form.)
0.05 =
fractiondecimalconcepts20130122.notebook
19
March 06, 2015
question
65 What fraction is equivalent to the decimal below? (Be sure answer is in simplified form.)
0.7 =0.33 =
Fractions to Decimals
Converting Fractions to Decimals
click to return to table of contents
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
fractiondecimalconcepts20130122.notebook
20
March 06, 2015
question
66 What is the fraction in decimal form?
question
67 What is the fraction in decimal form?
question
68 What is the fraction in decimal form?
question
69 What is the fraction in decimal form?
question
70 What is the fraction in decimal form?
question
71 What is the fraction in decimal form?
fractiondecimalconcepts20130122.notebook
21
March 06, 2015
question
72 What is the fraction in decimal form?
question
73 What is the fraction in decimal form?
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
74 What is the fraction in decimal form?
fractiondecimalconcepts20130122.notebook
22
March 06, 2015
question
75 What is the fraction in decimal form?
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
77 Which of the following repeating decimals is equivalent to
A 0.8B 1.2C 0.81D 0.818181818
question
78 Which of the following repeating decimals is equivalent to
A 4.83B 1.2C 4.83D 4.83333333333
fractiondecimalconcepts20130122.notebook
23
March 06, 2015
Number Line Location
Number Line Location
click to return to table of contents
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
fractiondecimalconcepts20130122.notebook
24
March 06, 2015
question
80 Where would the following number be correctly placed on the number line?
A B C D
5 65.5
question
81 Where would the following number be correctly placed on the number line?
A B C D
2 32.5
question
82 Where would the following number be correctly placed on the number line?
A B C D
0 10.5
question
83 Where would the following number be correctly placed on the number line?
A B C D
0 10.5
question
84 Where would the following number be correctly placed on the number line?
A B C D
0 10.5
question
85 Where would the following number be correctly placed on the number line?
A B C D
0 21
Be careful of the scale of the number line!
fractiondecimalconcepts20130122.notebook
25
March 06, 2015
question
86 Where would the following number be correctly placed on the number line?
A B C D
0 21
question
87 Where would the following number be correctly placed on the number line?
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
2. Order the numbers to determine the range of numbers you need to include.
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.
4. Put a dot and label each number.
.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
2. Order the numbers to determine the range of numbers you need to include.
0.4, 0.6, 1, 1.2, 1.8We need a number line from 0 to 2
fractiondecimalconcepts20130122.notebook
26
March 06, 2015
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.
4. Put a dot and label each number.
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