1. Number and Operations - Fractions Operations and Algebraic Thinking
MATH UNIT 3
Number and Operations - Fractions
Operations and Algebraic Thinking

2. DECIMAL FRACTIONS

3. A fraction where the denominator (the bottom number) is a power of ten
A fraction where the denominator (the bottom number) is a power of ten. You can write decimal fractions with a decimal point and no denominator.

4. 7/10 is a decimal fraction and it can be shown as 0
7/10 is a decimal fraction and it can be shown as /100 is a decimal fraction and it can be shown as 0.43

5. EQUIVALENT FRACTIONS

6. DENOMINATOR

7. NUMERATOR

8. TENTHS

9. HUNDREDTHS

10. ONE WHOLE

11. EXPANDED FORM

12. Students will read decimal fractions with denominators of 10 and 100.
Students will write decimal fractions with denominators of 10 and 100.
Students will identify decimal fractions with denominators of 10 and 100.
MAFS.4.NF.3.5

13. Each of these fractions is special
Each of these fractions is special. What is special about each of these fractions?

14. When you read fractions with a denominator of 10 or 100 you say: TENTHS or HUNDREDTHS. This fraction is read as : three tenths This fractions is read as : eight hundredths

15. READ EACH FRACTION
3/10
60/100
8/10
45/100
12/100
7/10
29/100
2/10
5/10
99/100
9/10
78/100

16. fifty-eight hundredths seven tenths thirty-four hundredths four tenths
WRITE EACH FRACTION
fifty-eight hundredths
seven tenths
thirty-four hundredths
four tenths
three tenths
five hundredths
sixty-seven hundredths
twenty-one hundredths
eight hundredths
one tenth
forty-two hundredths
nine tenths

17. Students will represent fractions with a denominator of 10 and fractions with a denominator of 100 using models. grids - base ten blocks - number lines

18. One unit is 1/100 or 0. 01 One rod or long is 1/10 or 10/100 or 0
One unit is 1/100 or 0.01 One rod or long is 1/10 or 10/100 or 0.1 or 0.10 One flat is one whole or 10/10 or 100/100 or 1

19. WRITE THE FRACTION

20. Write as a fraction and a decimal. Remember: equals 1/100

21. Write as a fraction and a decimal. Remember: equals 1/100

22. Write as a fraction and a decimal. Remember: equals 1/100

23. Write as a fraction and a decimal. Remember: equals 1/100

24. Write as a fraction and a decimal. Remember: equals 1/100

25. Write as a fraction and a decimal. Remember: equals 1/100

26. You can use a number line to show decimal fractions
You can use a number line to show decimal fractions. The top number line has a denominator of 10. The lower number line has a denominator of 100.

27. Use the number line to locate the decimal fraction.
0.7 or 7/10

28. Use the number line to locate the decimal fraction.
0.1 or 1/10

29. Use the number line to locate the decimal fraction.
0.4 or 4/10

30. Use the number line to locate the decimal fraction.
0.9 or 9/10

31. Use the number line to locate the decimal fraction.
0.3 or 3/10

32. Use the number line to locate these decimal fractions.
30/100 or 0.30

33. Use the number line to locate these decimal fractions.
62/100 or 0.62

34. Use the number line to locate these decimal fractions.
9/100 or 0.09

35. Use the number line to locate these decimal fractions.
75/100 or 0.75

36. Use the number line to locate these decimal fractions.
26/100 or 0.26

37. Use the number line to locate these decimal fractions.
100/100 or 1.00

38. Look at the base ten blocks. The ONE is cut into 10 pieces which are
Rewrite a fraction with a denominator of 10 as an equivalent fraction with a denominator of 100.
Look at the base ten
blocks. The ONE is cut
into 10 pieces which are
each cut into 10 pieces.
That means there are 100
cubes in the WHOLE ONE
flat X 10 = 100
ONE FLAT TEN RODS CUBES
WHOLE TENTHS HUNDREDTHS

39. X 10 = 100
X 10
HINT:
There are 10 rods in a flat. There are 10 unit cubes in each rod.
10 X 10 = 100

40. Write the equivalent fractions.
3/10 =
7/10 =
1/10 =
5/10 =
9/10 =
2/10 =
8/10 =
4/10 =
6/10 =
80/100 =
40/100 =
10/100 =
70/100 =
50/100 =
30/100 =
90/100 =

41. Equivalent fractions please… 6 / 10 = 60 / 100 or 6 / 10 = 60 / 100

42. Equivalent fraction please… ___ / 100 = ___ / ___

43. Equivalent fraction please… ___ / 100 = ___ / ___

44. Equivalent fraction please… ___ / 100 = ___ / ___ = _____

45. Write both the fraction and the words

46. Write in word form and fractions and decimals
Write in word form and fractions and decimals. ____ / ____ = ____ / ____ _____ hundredths = 0.___ = ____ tenths = 0.___

47. Write in word form and fractions and decimals
Write in word form and fractions and decimals. ____ / ____ = ____ / ____ _____ hundredths = 0.___ = ____ tenths = 0.___

48. Write in word form and fractions and decimals
Write in word form and fractions and decimals. ____ / ____ = ____ / ____ _____ hundredths = 0.___ = ____ tenths = 0.___

49. Write in word form and fractions and decimals
Write in word form and fractions and decimals. ____ / ____ = ____ / ____ _____ hundredths = 0.___ = ____ tenths = 0.___

50. Write in word form and fractions and decimals
Write in word form and fractions and decimals. ____ / ____ _____ hundredths = 0.___

51. Write in word form and fractions and decimals
Write in word form and fractions and decimals. ____ / ____ _____ hundredths = 0.___

52. Write in word form and fractions and decimals
Write in word form and fractions and decimals. ____ / ____ _____ hundredths = 0.___

53. Write in word form and fractions and decimals
Write in word form and fractions and decimals. _____ / _____ = ____ / ____ _____ tenths = 0.___ = _____ hundredths = 0.___

54. Write in word form and fractions and decimals
Write in word form and fractions and decimals. ____ / ____ = ____ / ____ ____ tenths = 0.___ = ____ hundredths = 0.___

55. Write in word form and fractions and decimals
Write in word form and fractions and decimals. ____ / ____ _____ hundredths = 0.___

56. Write in word form and fractions and decimals
Write in word form and fractions and decimals. ____ / ____ = ____ / ____ ____ tenths = 0.___ = ____ hundredths = 0.___

57. Write in word form and fractions and decimals
Write in word form and fractions and decimals. ____ / ____ = ____ / ____ ____ tenths = 0.___ = ____ hundredths = 0.___

58. Write in word form and fractions and decimals
Write in word form and fractions and decimals. ____ / ____ ____ hundredths = 0._____

59. Show 0.2 or 2/10 and 20/100 in the models below.

60. Show 0.5 or 5/10 and 50/100 in the models below.

61. Show 0.46 and 46/100 in the model below.

62. Show 0.11 and 11/100 in the model below.

63. ___/___ = 0.___ ___/___ = 0.___
Compare the base ten blocks to compare fractions and decimals.
< = >
___/___ = 0.___ ___/___ = 0.___

64. ___/___ = 0.___ ___/___ = 0.___
Compare the base ten blocks to compare fractions and decimals.
< = >
___/___ = 0.___ ___/___ = 0.___

65. ___/___ = 0.___ ___/___ = 0.___
Compare the base ten blocks to compare fractions and decimals.
< = >
___/___ = 0.___ ___/___ = 0.___

66. ___/___ = 0.___ ___/___ = 0.___
Compare the base ten blocks to compare fractions and decimals.
< = >
___/___ = 0.___ ___/___ = 0.___

67. ___/___ = 0.___ ___/___ = 0.___
Compare the base ten blocks to compare fractions and decimals.
< = >
___/___ = 0.___ ___/___ = 0.___

68. ___/___ = 0.___ ___/___ = 0.___
Compare the base ten blocks to compare fractions and decimals.
< = >
___/___ = 0.___ ___/___ = 0.___

69. ___/___ = ___ ___/___ = 0.___
Compare the base ten blocks to compare fractions and decimals.
< = >
___/___ = ___ ___/___ = 0.___

70. ___/___ = ___ ___/___ = 0.___
Compare the base ten blocks to compare fractions and decimals.
< = >
___/___ = ___ ___/___ = 0.___

71. ___/___ = ___ ___/___ = 0.___
Compare the base ten blocks to compare fractions and decimals.
< = >
___/___ = ___ ___/___ = 0.___

72. Compare the base ten blocks to compare fractions and decimals.
< = >
___ / ___ = 0.___ ___ / ___ = 0.___
Write the fraction and the decimal.

73. Compare the base ten blocks to compare fractions and decimals.
< = >
___ / ___ = 0.___ ___ / ___ = 0.___
Write the fraction and the decimal.

74. Compare the base ten blocks to compare fractions and decimals.
< = >
___ / ___ = __.___ ___ / ___ = __.___
Write the fraction and the decimal.

75. Compare the base ten blocks to compare fractions and decimals.
< = >
___ / ___ = __.___ ___ / ___ = __.___
Write the fraction and the decimal.

76. Students will identify the place value of digits to the right of
the decimal point.
Students will demonstrate place value of decimals through the
hundredths using concrete materials.
Students will use different-sized grids to represent equivalency of
decimals to fractions with denominators of 10 or 100.
Students will explain the relationship between fractions and decimals
in graphic models.
MAFS.4.NF.3.6

77. This is a PLACE VALUE chart. Learn to draw a place value chart.

78. Identify and label each part of the PLACE VALUE chart.

79. Write the number 589 and 4/10 in the PLACE VALUE chart.

80. Write 703 and 54/100 in the Place Value chart.

81. Write an eight in the tens place. Write a three in the ones place
Write an eight in the tens place. Write a three in the ones place. Write a five in the hundreds place. Write a one in the tenths place.
READ YOUR NUMBER

82. Write an nine in the tenths place. Write a four in the hundredths place. Write a seven in the ones place. Write a two in the tens place.
READ YOUR NUMBER

83. Write an six in the hundredths place. Write a five in the tens place
Write an six in the hundredths place. Write a five in the tens place. Write a zero in the ones place. Write a two in the tenths place.
READ YOUR NUMBER

84. Write an zero in the tenths place. Write a five in the tens place
Write an zero in the tenths place. Write a five in the tens place. Write an eight in the hundredths place. Write a nine in the ones place.
READ YOUR NUMBER

85. Write a seven in the tens place. Write a nine in the hundredths place
Write a seven in the tens place. Write a nine in the hundredths place. Write a four in the ones place. Write a three in the hundreds place. Write a five in the tenths place. READ YOUR NUMBER!

86. Write a zero in the hundredths place. Write an eight in the tens place
Write a zero in the hundredths place. Write an eight in the tens place. Write a six in the ones place. Write a two in the hundreds place. Write a one in the tenths place. READ YOUR NUMBER.

87. Write a four in the tenths place. Write a three in the ones place
Write a four in the tenths place. Write a three in the ones place. Write a two in the hundredths place. Write a nine in the hundreds place. Write a six in the tens place. READ YOUR NUMBER.

88. Circle the value of this number in base ten blocks. 4.91

89. Circle the value of this number in base ten blocks. 3.02

90. Circle the value of this number in base ten blocks. 5.38

91. Circle the value of this number in base ten blocks. 8.26

92. Circle the value of this number in base ten blocks. 2.75

93. thirty-nine hundredths and can be written as 39/100
Students will translate the word form of a decimal into its equivalent fraction.
0.39 reads
thirty-nine hundredths and can be written as 39/100
0.71 reads
0.28 reads
0.46 reads
0.05 reads
0.99 reads

94. 0.17 reads
0.68 reads
0.06 reads
0.24 reads
0.03 reads
0.77 reads

95. 0.94 reads
0.26 reads
0.82 reads
1.05 reads
0.60 reads
0.45 reads

96. you have an IMPROPER FRACTION
Students will translate fractions greater than ONE with denominators of 10 and into equivalent decimal form.
When the NUMERATOR
is larger than the
DENOMINATOR
you have an IMPROPER FRACTION
resulting in a whole number on the LEFT and a decimal fraction on the RIGHT.

97. Let’s translate some improper fractions into decimals. 13/10 = 1.3
13/10 = 1.3
Because the numerator: 13 is larger than the denominator: 10, we have an improper fraction - meaning that we have a WHOLE number and a part.
11/10
26/10
32/10
18/10

98. 29/10
45/10
10/10
100/10
82/10
55/10
90/10
64/10
71/10
33/10
15/10
84/10

99. 429/100
945/100
101/100
728/100
186/100
505/100
790/100
645/100
281/100
397/100
564/100
840/100

100. Students will represent a decimal value on a number line.
What decimal does each dot represent?
0.2

101. What decimal and fraction does each dot represent?

102. Complete each fraction on the number line. Several are done for you.

103. P = _____ Q = _____ R = _____
Label the value of each dot on the number line.
P = _____ Q = _____ R = _____

104. Label each decimal value on the number line. 0.32 0.59 0.11 0.75

105. Label each decimal value on the number line. 0.02 0.93 0.67 0.24

106. Label each decimal value on the number line. 0.46 0.88 0.23 0.67

107. Label each fractional value on the number line

108. Label each fractional value on the number line

109. Label each fractional value on the number line

110. Students will explain their thinking when labeling a decimal fraction on a number line. “I think that 32/100 is more than 30/100 (3/10) and that it is less than 40/100 (4/10). So I think it will be closer to 30/100. I would place it on the number line near that value.”

111. 19/100 Explain your thinking . . .
_________________________________________________________________________________ _________________________________________________________________________________ _________________________________________________________________________________

112. 63/100 Explain your thinking . . .
_________________________________________________________________________________ _________________________________________________________________________________ _________________________________________________________________________________

113. 41/100 Explain your thinking . . .
_________________________________________________________________________________ _________________________________________________________________________________ _________________________________________________________________________________

114. Students will explain that decimals can only be compared when they refer to the same whole.
Students will compare decimals with and without models and record the comparison numerically using symbols
< = >
Students will justify the comparison by reasoning about the size of the decimal or by using a visual model.
MAFS.4.NF.3.7

115. This is a candy bar. It is divided into 10 equal pieces
This is a candy bar. It is divided into 10 equal pieces. This is a candy bar. It is divided into 10 equal pieces, too. We CAN NOT compare them because they are NOT THE SAME! Each model shows 10/10 but the whole Hershey’s is much bigger than the other candy bar so these decimals can not be compared.

116. Can these decimal fractions be compared?
Remember that comparisons are only valid when the two decimals refer to the same whole.
0.1
1/10
0.1
1/10

117. Can these decimal fractions be compared?
Remember that comparisons are only valid when the two decimals refer to the same whole.
0.1
1/10
0.1
1/10

118. Can these decimal fractions be compared?
Remember that comparisons are only valid when the two decimals refer to the same whole.
0.1
1/10
0.1
1/10

119. Can these decimal fractions be compared?
Remember that comparisons are only valid when the two decimals refer to the same whole.
0.1
1/10
0.1
1/10

120. Can these decimal fractions be compared?
Remember that comparisons are only valid when the two decimals refer to the same whole.
0.1
1/10
0.1
1/10

121. Can these decimal fractions be compared? Why not?
Remember that comparisons are only valid when the two decimals refer to the same whole.
0.45
45/100
0.01
1/100

122. Can these decimal fractions be compared?
Remember that comparisons are only valid when the two decimals refer to the same whole.
0.01
1/100
0.01
1/100

123. Compare these decimal fractions.
< = >
____

124. Compare these decimal fractions.
< = >
____

125. Compare these decimal fractions.
< = >
____

126. Compare these decimal fractions.
< = >
____

127. Compare these decimal fractions.
< = >
____

128. Compare these decimal fractions.
< = >
____

129. Compare these decimal fractions.
< = >
2.1 ____

130. Compare these decimal fractions.
< = >
____

131. Students will identify and demonstrate
numeric and growing shape patterns.
Students will generate a number or shape pattern that
follows a given one-step rule.
follows a given two-step rule.
Students will identify features in patterns following a given rule.
MAFS.4.OA.3.5

132. This is a numeric pattern. Numeric means number
This is a numeric pattern. Numeric means number. You have been doing numeric patterns since Kindergarten.

133. These are also numeric patterns. Can you find the rule
These are also numeric patterns. Can you find the rule? ____ ____ ____ Rule: ___________ ____ ____ ____

134. These are also numeric patterns. Can you find the rule?

135. Let’s play a game. Follow the Rules and see the pattern you create.
Start at the number 7
Multiply by 2

136. Let’s play a game. Follow the Rules and see the pattern you create.
Start at the number 100
Divide by 2

137. Let’s play a game. Follow the Rules and see the pattern you create.
Start at the number 15
Add 7

138. Let’s play a game. Follow the Rules and see the pattern you create.
Start at the number 19
Subtract 3

139. Let’s play a game. Follow the Rules and see the pattern you create.
Start at the number 4
Multiply by 5

140. As you create numeric patterns look for features of that pattern.
RULE
PATTERN
FEATURES
START WITH 4 ADD 5
4, 9, 14, 19, 24, 29, …
The numbers all end with a or a 9
START WITH 1 MULTIPLY BY 5
1, 5, 25, 125, 625, …
After the starting number all numbers end in a 5
All numbers are ODD
Start with and subtract 3
100, 97, 94, 91, 88, 85 …
The numbers alternate from EVEN to ODD

141. Look for features of each pattern.
RULE
PATTERN
FEATURES
START WITH 12 ADD 3
START WITH 2 MULTIPLY BY 10
START WITH DIVIDE BY 4

142. Look for features of each pattern.
RULE
PATTERN
FEATURES
START WITH 45 ADD 6
START WITH 88 SUBRACT 4
START WITH 8 MULTIPLY BY 3

143. Look for features of each pattern.
RULE
PATTERN
FEATURES
ADD 4 AND
THEN MULTIPLY BY 2
START AT THE NUMBER 10
SUBTRACT 6 AND
THEN MULTIPLY BY 3
START AT THE NUMBER 18
ADD 5 AND
THEN DIVIDE BY 2

144. Look for features of each pattern.
RULE
PATTERN
FEATURES
MULTIPLY BY 3 AND
THEN SUBTRACT 2
START AT THE NUMBER 11
MULTIPLY BY 6 AND
THEN ADD 2
START AT THE NUMBER 1
MULTIPLY BY 5 AND
THEN ADD 7
START AT THE NUMBER 10

145. Look for features of each pattern.
RULE
PATTERN
FEATURES
MULTIPLY BY 2 AND
THEN SUBTRACT 4
START AT THE NUMBER 6
MULTIPLY BY 5 AND
THEN ADD 3
START AT THE NUMBER 9
MULTIPLY BY 4 AND
THEN DIVIDE BY 2
START AT THE NUMBER 15

146. Given the pattern – what is the RULE?
8, 15, 22, 29, ____
3, 9, 27, 81, ____
320, 160, 80, 40, ____

147. Given the pattern – what is the RULE? CHALLENGE
1, 3, 5, 7, 11, ___
1, 1, 4, 4, 7, 7, 10, 10, ___
1. emirp etanretla

148. This is a growing pattern
This is a growing pattern. What does the figure look like that comes next? What does the 8th figure look like?

149. WHAT COMES NEXT? These are growing patterns. See how the shape grows?
WHAT IS THE RULE?

150. This is a growing pattern
This is a growing pattern. What does the figure look like that comes next? What does the 7th figure look like?

151. This is a growing pattern
This is a growing pattern. What does the figure look like that comes 10th?

152. This is a growing pattern
This is a growing pattern. What does the figure look like that comes next?

153. This is a growing pattern
This is a growing pattern. What does the figure look like that comes 6th?

154. This is a growing pattern
This is a growing pattern. What does the figure look like that comes next?

155. This is a growing pattern
This is a growing pattern. What does the figure look like that comes next?

156. What is the RULE for this growing pattern
What is the RULE for this growing pattern? Can you predict what will be the 5th figure?