Chapter 1 Student Assignments - Northwest ISD Moodle
Lesson 1.1 Assignment Name_________________________________________________________ Date__________________________
So Many Numbers, So Little Time Number Sort Ling’s teacher gives her students the following numbers to sort. ___
_____ __ ___ 16 , p, ___ 1 12 , 15, √4 , 2 ___ 4 , 8003.876, 0.2%, 2√ 25 , 3 __ 5%, 233 , √0.36 , 2.14, |26|, ___ 18 3 10 3
√
1. Ling groups the following numbers together with the rationale that they are all repeating decimals. ___
√10
16 , ___ 1 ___ 12 , 2 ___ 4 , 3 __ 18
3
3
Do you agree with Ling’s grouping? Explain your reasoning.
2. Ling groups the following numbers together with the rationale that they are all positive numbers. ___
_____ __ 1 , 2.14, |26|, ___ 12 , 15, √ 4 , 8003.876, 0.2%, 3 __ 4 , p, ___ 5%, √0.36 18 10 3
√
Do you agree with Ling’s grouping? Explain your reasoning.
3. Ling and a classmate, Maddison, both created groups of irrational numbers. Analyze their groupings. Maddison’s Grouping
© Carnegie Learning
Ling’s Grouping ___
√10
___
___
p, ___ 4 , 2√ 25
√
p, ___ 4 10
Which student correctly grouped the irrational numbers? Explain your reasoning.
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Lesson 1.2 Assignment Name_________________________________________________________ Date__________________________
Is It a Bird or a Plane? Rational Numbers 1. The Harrison family owns a local bakery that specializes in cupcakes. They make over 25 different flavors of cupcakes ranging from plain vanilla or chocolate to key lime flavored cupcakes. a. The family arrives early each day to make their cupcakes. The most popular cupcake is peanut butter cup, so they decide to make 10 dozen, or 120 of them. Identify the set(s) of numbers to which 120 belongs. Explain your answer.
3 cups of flour. Identify the set(s) of numbers to which this b. The recipe for 24 cupcakes calls for 1 __ 4 amount belongs.
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2. A family shops at local grocery stores for sugar. They spend a lot of time in the first part of the 7 -pound bag of week comparing prices of different items. One grocery store is advertising a 4 __ 8 sugar for $3.50. Another grocery store is advertising a 4.9-pound bag of sugar for $3.50, while a 11 -pound bag of sugar for the same price. third store is advertising a 4 ___ 12 a. Write the two fractional weights as decimals.
b. Graph all the weights in decimal form on the number line shown.
4.86
4.87
4.88
4.89
4.90
4.91
4.92
4.93
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Lesson 1.2 Assignment
page 2
c. Use the number line to determine which bag of sugar is the best buy. Write your answer using complete sentences.
3. A recipe that a local bakery uses for bread calls for wheat flour. The recipe for 18 loaves calls 1 cups of wheat flour. Because of the uncertainty of how the loaves will sell, the bakery only for 1 __ 4 makes 54 for the day. How many cups of wheat flour will the bakery need?
4. The local farmer’s market is doing fairly well. But like any other business, it has good days and bad days. Because vegetables do not stay fresh for long, any that they do not sell go to waste and the business loses money on those vegetables. On Monday of one week they made $225.45 profit, but
© Carnegie Learning
the following day they had a loss of $285.85. What was the net money profit for the two days?
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Lesson 1.3 Assignment Name_________________________________________________________ Date__________________________
Sew What? Irrational Numbers 1. Marcy Green is the manager for her high school softball team. She is in charge of equipment as well as recording statistics for each player on the team. The table shows some batting statistics for the four infielders on the team during the first 8 games of the season.
At Bats
Hits
Brynn Thomas
36
16
Hailey Smith
32
12
Serena Rodrigez
33
11
Kata Lee
35
14
© Carnegie Learning
Player
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Lesson 1.3 Assignment
page 2
In order to compare the batting averages of the players, Marcy must convert all of the ratios of hits to at-bats to decimal form. Complete the table to determine the batting averages for each player. When finding the decimal form, continue to divide until you see a pattern. Write your answer using both dots and bar notation for repeating decimals.
Player
Fraction of Hits to At-Bats
Reduced Fraction
Calculation
Batting Average
Brynn Thomas
Hailey Smith
Serena Rodriguez
a. Write the batting averages of the players in order from lowest to highest. Who has the best batting average so far?
© Carnegie Learning
Kata Lee
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Lesson 1.3 Assignment
page 3
Name_________________________________________________________ Date__________________________ b. Marcy keeps track of how many home runs each infielder hits on the high school softball team. For each player, the fraction of home runs per at-bats is given in decimal form. Determine how many home runs each player has had so far. __
Brynn: 0.05
© Carnegie Learning
Hailey: 0.15625
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Lesson 1.3 Assignment
page 4
___
Serena: 0.12
© Carnegie Learning
Kata: 0.2
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Lesson 1.3 Assignment
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Name_________________________________________________________ Date__________________________ 2. The distances from each base to the next is 60 feet on the field. The softball “diamond” is a square shape. A diagram of the field is shown. 2nd Base 60 ft
60 ft 1st Base
3rd Base
60 ft
60 ft Home
a. Is it possible to exactly measure the distance from home plate to second base? Use the Pythagorean Theorem by filling in the blanks below. Explain your answer.
a2 1 b2 5 c2
602 1 602 5 c2 3600 1 3600 5 c2 _______
5 c
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√
5 c2
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Lesson 1.3 Assignment
page 6
b. Marcy uses an estimate of 84 feet for the distance between home plate and second base. One of the coaches argues that she should be using 85 feet for the distance. Use a calculator to square all the numbers shown. Who is correct? Explain your answer. 84.12 5
84.22 5
84.42 5
84.52 5
84.62 5
84.72 5
84.82 5
84.92 5
85.02 5
84.02 5
84.32 5
© Carnegie Learning
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Lesson 1.4 Assignment Name_________________________________________________________ Date__________________________
Worth 1000 Words Real Numbers and Their Properties 1. Nolan is saving money to buy a new snowboard. So far he has $245 saved. a. List the set(s) of numbers to which the real number 245 belongs.
b. Nolan spends $86.49 on a new ski jacket. Does this belong to the same set of numbers as 245? Why or why not?
c. The company that sold the ski jacket that Nolan bought claims it is warm enough for a temperature of 25°C. To which number sets does 25 belong?
d. A week after Nolan buys his jacket, the store has a sale and offers one-third off all of its ski
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jackets. The value of one-third as a decimal is 0.333333…. Is this an irrational number?
e. After a couple of weeks of spending more money on accessories, Nolan finds that he only has $45.50 left. What is the additive inverse of this number? What does it mean to Nolan and his bank account?
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Lesson 1.4 Assignment
page 2
f. Nolan does not spend any more money so he still has $45.50 in his account. He saves another $35.50, goes to the bank and puts that in the account for a total of $81. He then saves another $19 and goes to the bank and puts that in the account for a total of $100. In order to save trips to the bank, he could have added together the $35.50 and $19 for a total of $54.50, then gone to the bank and added that to the $45.50 for a total of $100. What property of addition is being represented by this situation? Explain.
g. Nolan needed to repair his car and had to borrow money from his parents to pay for it. He owes his parents $335. So his net worth currently is 2335. If he pays his parents $300 after his next paycheck, his net worth will be 2$35 (he owes them $35). Conversely, if Nolan has $300 in the bank and then must pay $335 for repairs his net worth will also be 2$35. What property of
© Carnegie Learning
addition is being represented by this situation? Explain.
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Lesson 1.4 Assignment
page 3
Name_________________________________________________________ Date__________________________ h. Nolan and his five friends are planning a 3-day ski trip. The cost of a one-day lift ticket is $52 per person. Use the Associative Property of Multiplication to show different ways in which they could determine the total cost of the tickets. Explain each way.
i. Nolan finally saves up enough money for his snowboard. It costs $1235. If he is only going © Carnegie Learning
to buy one snowboard, then it will cost him $1235. What identity is being used in this situation? Explain.
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© Carnegie Learning
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So Many Numbers, So Little Time Number Sort Ling’s teacher gives her students the following numbers to sort. ___
_____ __ ___ 16 , p, ___ 1 12 , 15, √4 , 2 ___ 4 , 8003.876, 0.2%, 2√ 25 , 3 __ 5%, 233 , √0.36 , 2.14, |26|, ___ 18 3 10 3
√
1. Ling groups the following numbers together with the rationale that they are all repeating decimals. ___
√10
16 , ___ 1 ___ 12 , 2 ___ 4 , 3 __ 18
3
3
Do you agree with Ling’s grouping? Explain your reasoning.
2. Ling groups the following numbers together with the rationale that they are all positive numbers. ___
_____ __ 1 , 2.14, |26|, ___ 12 , 15, √ 4 , 8003.876, 0.2%, 3 __ 4 , p, ___ 5%, √0.36 18 10 3
√
Do you agree with Ling’s grouping? Explain your reasoning.
3. Ling and a classmate, Maddison, both created groups of irrational numbers. Analyze their groupings. Maddison’s Grouping
© Carnegie Learning
Ling’s Grouping ___
√10
___
___
p, ___ 4 , 2√ 25
√
p, ___ 4 10
Which student correctly grouped the irrational numbers? Explain your reasoning.
Chapter 1 Assignments • 1
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© Carnegie Learning
2 • Chapter 1 Assignments
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Lesson 1.2 Assignment Name_________________________________________________________ Date__________________________
Is It a Bird or a Plane? Rational Numbers 1. The Harrison family owns a local bakery that specializes in cupcakes. They make over 25 different flavors of cupcakes ranging from plain vanilla or chocolate to key lime flavored cupcakes. a. The family arrives early each day to make their cupcakes. The most popular cupcake is peanut butter cup, so they decide to make 10 dozen, or 120 of them. Identify the set(s) of numbers to which 120 belongs. Explain your answer.
3 cups of flour. Identify the set(s) of numbers to which this b. The recipe for 24 cupcakes calls for 1 __ 4 amount belongs.
© Carnegie Learning
2. A family shops at local grocery stores for sugar. They spend a lot of time in the first part of the 7 -pound bag of week comparing prices of different items. One grocery store is advertising a 4 __ 8 sugar for $3.50. Another grocery store is advertising a 4.9-pound bag of sugar for $3.50, while a 11 -pound bag of sugar for the same price. third store is advertising a 4 ___ 12 a. Write the two fractional weights as decimals.
b. Graph all the weights in decimal form on the number line shown.
4.86
4.87
4.88
4.89
4.90
4.91
4.92
4.93
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Lesson 1.2 Assignment
page 2
c. Use the number line to determine which bag of sugar is the best buy. Write your answer using complete sentences.
3. A recipe that a local bakery uses for bread calls for wheat flour. The recipe for 18 loaves calls 1 cups of wheat flour. Because of the uncertainty of how the loaves will sell, the bakery only for 1 __ 4 makes 54 for the day. How many cups of wheat flour will the bakery need?
4. The local farmer’s market is doing fairly well. But like any other business, it has good days and bad days. Because vegetables do not stay fresh for long, any that they do not sell go to waste and the business loses money on those vegetables. On Monday of one week they made $225.45 profit, but
© Carnegie Learning
the following day they had a loss of $285.85. What was the net money profit for the two days?
4 • Chapter 1 Assignments
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Lesson 1.3 Assignment Name_________________________________________________________ Date__________________________
Sew What? Irrational Numbers 1. Marcy Green is the manager for her high school softball team. She is in charge of equipment as well as recording statistics for each player on the team. The table shows some batting statistics for the four infielders on the team during the first 8 games of the season.
At Bats
Hits
Brynn Thomas
36
16
Hailey Smith
32
12
Serena Rodrigez
33
11
Kata Lee
35
14
© Carnegie Learning
Player
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Lesson 1.3 Assignment
page 2
In order to compare the batting averages of the players, Marcy must convert all of the ratios of hits to at-bats to decimal form. Complete the table to determine the batting averages for each player. When finding the decimal form, continue to divide until you see a pattern. Write your answer using both dots and bar notation for repeating decimals.
Player
Fraction of Hits to At-Bats
Reduced Fraction
Calculation
Batting Average
Brynn Thomas
Hailey Smith
Serena Rodriguez
a. Write the batting averages of the players in order from lowest to highest. Who has the best batting average so far?
© Carnegie Learning
Kata Lee
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Lesson 1.3 Assignment
page 3
Name_________________________________________________________ Date__________________________ b. Marcy keeps track of how many home runs each infielder hits on the high school softball team. For each player, the fraction of home runs per at-bats is given in decimal form. Determine how many home runs each player has had so far. __
Brynn: 0.05
© Carnegie Learning
Hailey: 0.15625
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Lesson 1.3 Assignment
page 4
___
Serena: 0.12
© Carnegie Learning
Kata: 0.2
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Lesson 1.3 Assignment
page 5
Name_________________________________________________________ Date__________________________ 2. The distances from each base to the next is 60 feet on the field. The softball “diamond” is a square shape. A diagram of the field is shown. 2nd Base 60 ft
60 ft 1st Base
3rd Base
60 ft
60 ft Home
a. Is it possible to exactly measure the distance from home plate to second base? Use the Pythagorean Theorem by filling in the blanks below. Explain your answer.
a2 1 b2 5 c2
602 1 602 5 c2 3600 1 3600 5 c2 _______
5 c
© Carnegie Learning
√
5 c2
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Lesson 1.3 Assignment
page 6
b. Marcy uses an estimate of 84 feet for the distance between home plate and second base. One of the coaches argues that she should be using 85 feet for the distance. Use a calculator to square all the numbers shown. Who is correct? Explain your answer. 84.12 5
84.22 5
84.42 5
84.52 5
84.62 5
84.72 5
84.82 5
84.92 5
85.02 5
84.02 5
84.32 5
© Carnegie Learning
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Lesson 1.4 Assignment Name_________________________________________________________ Date__________________________
Worth 1000 Words Real Numbers and Their Properties 1. Nolan is saving money to buy a new snowboard. So far he has $245 saved. a. List the set(s) of numbers to which the real number 245 belongs.
b. Nolan spends $86.49 on a new ski jacket. Does this belong to the same set of numbers as 245? Why or why not?
c. The company that sold the ski jacket that Nolan bought claims it is warm enough for a temperature of 25°C. To which number sets does 25 belong?
d. A week after Nolan buys his jacket, the store has a sale and offers one-third off all of its ski
© Carnegie Learning
jackets. The value of one-third as a decimal is 0.333333…. Is this an irrational number?
e. After a couple of weeks of spending more money on accessories, Nolan finds that he only has $45.50 left. What is the additive inverse of this number? What does it mean to Nolan and his bank account?
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Lesson 1.4 Assignment
page 2
f. Nolan does not spend any more money so he still has $45.50 in his account. He saves another $35.50, goes to the bank and puts that in the account for a total of $81. He then saves another $19 and goes to the bank and puts that in the account for a total of $100. In order to save trips to the bank, he could have added together the $35.50 and $19 for a total of $54.50, then gone to the bank and added that to the $45.50 for a total of $100. What property of addition is being represented by this situation? Explain.
g. Nolan needed to repair his car and had to borrow money from his parents to pay for it. He owes his parents $335. So his net worth currently is 2335. If he pays his parents $300 after his next paycheck, his net worth will be 2$35 (he owes them $35). Conversely, if Nolan has $300 in the bank and then must pay $335 for repairs his net worth will also be 2$35. What property of
© Carnegie Learning
addition is being represented by this situation? Explain.
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Lesson 1.4 Assignment
page 3
Name_________________________________________________________ Date__________________________ h. Nolan and his five friends are planning a 3-day ski trip. The cost of a one-day lift ticket is $52 per person. Use the Associative Property of Multiplication to show different ways in which they could determine the total cost of the tickets. Explain each way.
i. Nolan finally saves up enough money for his snowboard. It costs $1235. If he is only going © Carnegie Learning
to buy one snowboard, then it will cost him $1235. What identity is being used in this situation? Explain.
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© Carnegie Learning
14 • Chapter 1 Assignments
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