Name _________________________________________________ Extend Your Thinking
9-1
Patterns in Numbers 1.
2.
3.
8
1 � 2
1 � 4
24
1 �� 10
20
18
16
1 � 2
8
1 � 3
27
9
2
1 � 9
18
2
1 � 6
3
15
1 � 5
1 � 5
100
20
1 � 5
1 � 7
56
8
1 � 2
6
3
4.
5.
6.
7.
4
1 � 2
16
30
15
1 � 8
16
2
3
12
1 � 4
3
200
40
1 � 5
300
60
2 � 7
28
8
3 � 7
14
6
1 � 3
9
3
1 � 4
12
3
32
Use with pages 404–405.
© Scott Foresman Addison Wesley 5
Find each pattern. Fill in the missing numbers.
113
Name _________________________________________________ Extend Your Thinking
9-2
Critical Thinking Which is greatest? Circle one. 1 �� 4
2.
1 �� 10
3.
2 �� 9
4.
3 �� 10
5.
1 �� 2
6.
1 �� 8
7.
1 �� 10
8.
1 �� 100
114
of 1 yard
of 1 mile
of 1 yard
of 1 mile
2 �� 3
of 1 foot
10 inches
200 yards
500 feet
3 �� 4
7 inches
of 1 foot
400 yards
1,400 feet
of 1 gallon
1 quart
3 pints
of 1 gallon
1 �� 2
2 pints
of 2,000 pounds
of 2,000 pounds
Use with pages 406–407.
of 1 quart
100 pounds
2,000 ounces
50 pounds
320 ounces
© Scott Foresman Addison Wesley 5
1.
Name _________________________________________________ Extend Your Thinking
9-3
Decision Making Lisa and her mother are making pizza for a pizza party. She compared prices at three stores for the things they will need. The following chart shows what she found. Use the chart to help you answer the questions below. Tomato Sauce
Dough Packages
Cheese
Mushrooms
Store 1
$2.50 3 cans
$0.98 each
$1.79 10 oz
$0.75 1 � lb 2
Store 2
$3.20 4 cans
$1.79 2 packages
$2.40 1 lb
1.60 1 lb
Store 3
$4.20 6 cans
$2.71 3 packages
$1.92 12 oz
$5.00 5 lb
1. Estimate the cost per can of tomato sauce. store 1
store 2
store 3
___________________
___________________
___________________
2. Estimate the cost per package of dough. store 1
store 2
store 3
___________________
___________________
___________________
store 1
store 2
store 3
___________________
___________________
___________________
4. Estimate the cost per pound of mushrooms. store 1
store 2
store 3
___________________
___________________
___________________
5. Where should Lisa shop? Explain. __________________________________________________________________________
Use with pages 408–409.
115
© Scott Foresman Addison Wesley 5
3. Estimate the cost per ounce of cheese.
Name _________________________________________________ Extend Your Thinking
9-4
Critical Thinking You can use drawings to find �14� � �12�. First find the common denominator and draw that many counters. 1 �� 2
1 �� 4
Draw a ring around �12� of them. Draw a box around �14� of the ringed squares. Write a fraction that shows what part of the set the boxed square is: �18� 1. Use this picture to find �15� � �14�. Common denominator: ________ 1 �� 5
Common denominator: ________ 1 �� 3
� �34� � __________
3. Use this picture to find �14� � �67�. Common denominator: ________ 1 �� 4
� �67� � __________
4. How was the number of counters for each of 1–3 chosen? __________________________________________________________________________ 116
Use with pages 410–411.
© Scott Foresman Addison Wesley 5
2. Use this picture to find �13� � �34�. 3 �� 4
� �14� � __________
Name _________________________________________________ Extend Your Thinking
9-5
Patterns in Numbers Fill in the missing fractions to complete the pattern. Then write the rule with a variable. 1. 1, �12�, �14�, _________, _________, _________ Rule: _________________ 2. �23�, �29�, �22�7 , _________, _________, _________ Rule: _________________ 16 � 3. �12�, �13�, _________, �24�7 , �88�1 , � 243 , _________, _________
Rule: _________________ 27 81 729 � �� �� 4. �38�, _________, � 128 , 512 , _________, 8,192 , _________
Rule: _________________ 81 � 5. �56�, �12�, _________, �59�0 , _________, � 1,250 , _________
Rule: _________________ 1 � 6. 2, �13�, _________, _________, � 648 , _________
© Scott Foresman Addison Wesley 5
Rule: _________________ 68 � 7. 4�14�, 1�13�4 , _________, _________, � 2,401
Rule: _________________ 8. Write your own fraction pattern. Write your rule using a variable. __________________________________________________________________________
Rule: __________________________________________________________ Use with pages 412–413.
117
Name _________________________________________________ Extend Your Thinking
9-6
Visual Thinking
1.
a.
b.
c.
2.
a.
b.
c.
3.
a.
b.
c.
4.
a.
b.
c.
118
Use with pages 416–417.
© Scott Foresman Addison Wesley 5
The figures on the right can be folded along their dotted lines to form a cube. Circle the figure on the right that forms the cube on the left.
Name _________________________________________________ Extend Your Thinking
9-7
Decision Making Jacob’s Pie Shop offers a range of pies at reasonable prices. He looks at the cost of making each pie and how much he should charge. Use the table to answer the questions. Pie
Cost of Ingredients
Apple
$6
Cherry
$8
Blueberry Peach
Size of Slice (as a fraction of pie)
Price of Each Slice
1 �� 12 1 � 8 1 �� 10 1 � 6
$0.75
$11 $5.40
$0.90 $1.10 $1.25
1. What is the cost of the ingredients for each slice of pie? Apple ____________
Cherry ____________
Blueberry ____________
Peach ____________
2. All the slices are the same size. Explain why the fractional amounts are different. _______________________________________
3. What is the price for each pie as it is sold in pieces? Apple ____________
Cherry ____________
Blueberry ____________
Peach ____________
Apple ____________
Cherry ____________
Blueberry ____________
Peach ____________
5. Do you think Jacob should increase any of his pie prices? Why? __________________________________________________________________________ __________________________________________________________________________
6. Jacob decides to charge an additional $3 per pie. How much will each slice of pie be now? Apple ____________
Cherry ____________
Blueberry ____________
Peach ____________ Use with pages 420–421.
119
© Scott Foresman Addison Wesley 5
4. What is the cost of ingredients for each whole pie?
Name _________________________________________________ Extend Your Thinking
9-8
Patterns in Numbers Tell what rule was used to make the pattern. What are the next two numbers? 1. �12�, �14�, �18�, �11�6 , _________, _________ Rule: _____________________ 2.
1 2 4 8 16 ��, ��, ��, ��, ��, _________, _________ 100 100 100 100 100
Rule: _____________________ 3. 1�12�, 2�14�, 3�38�, 5�11�6 , _________, _________ Rule: _____________________ 4. 10�11�0 , 8�35�, 7�11�0 , 5�35�, _________, _________ Rule: _____________________ 5. 5�13�, 7, 8�23�, 10�13�, _________, _________ Rule: _____________________
Rule: _____________________ Make up your own number patterns. Leave some blank spaces. Give them to a classmate to solve. 7. _________, _________, _________, _________, _________, _________ 8. _________, _________, _________, _________, _________, _________
120
Use with pages 422–423.
© Scott Foresman Addison Wesley 5
6. �23�, �29�, �22�7 , �82�1 , _________, _________
Name _________________________________________________ Extend Your Thinking
9-9
Visual Thinking Each figure on the left is a fractional part of a circle. Circle the figure on the right that makes up the rest of that figure. 1.
2.
3.
© Scott Foresman Addison Wesley 5
4.
5.
Use with pages 426–427.
121
Name _________________________________________________ Extend Your Thinking
9-10
Critical Thinking
Divide the rectangle into thirds. 1. How many thirds are there? ____________ Divide one third into thirds again. 2. How many sections are there now? ____________ 3. Continue the pattern three more times. Each time you divide a section, tell how many sections you have in total. __________________ 4. What pattern do you see? ____________ Divide the square into quarters. 5. How many quarters are there? ____________ Divide one fourth into fourths again. 6. How many sections are there now? 7. Continue the pattern 3 more times. Each time you divide a section, tell how many sections you have in total. ________________ 8. What pattern do you see? ____________
122
Use with pages 428–429.
© Scott Foresman Addison Wesley 5
____________
