G8 U2 Constructed Response
Name: ________________________________________ Date:_______________
Grade 8 Unit 2 Constructed Response Radicals and Integers TASK 1: Combining Exponents (CCSS: 8.EE.1 [m]; SMP: 1, 3, 4, 6)
1. Deana encounters the following problem on a test: 75 × 76 She does the following work to get her solution: 75 × 76 495×6 4930 a. After analyzing her answer, write a critique in which you identify and explain any errors in her work. Correct any errors in her reasoning.
b. What is the correct answer to the problem Deana encountered on her test? Show your work in detailed and organized steps.
Answer: __________________
Copyright © Swun Math Grade 8 Unit 2 Constructed Response, Page 1
Grade 8 Unit 2 Constructed Response Radicals and Integers 2. Examine the expression below. 65 × 64 ×
1 62
a. Demonstrate how to simplify the expression using two different methods you have learned. Method 1
Method 2
Answer:
Answer:
b. After simplifying the expression, write an explanation in which you compare the two methods you showed above. Which of the two was the most efficient in solving the problem? Support your discussion with evidence from your work.
Copyright © Swun Math Grade 8 Unit 2 Constructed Response, Page 2
Grade 8 Unit 2 Constructed Response Radicals and Integers 3. a. Simplify the following expression. Show your work in detailed and organized steps. 𝑠 3 𝑡 5 𝑢2 𝑠 6 𝑡 4 (𝑢2 )2
Answer: ___________________ b. How would your solution be different if you were simplifying the reciprocal of the expression above?
Copyright © Swun Math Grade 8 Unit 2 Constructed Response, Page 3
Grade 8 Unit 2 Constructed Response Radicals and Integers TASK 2: Solving Square and Cubic Equations (CCSS: 8.EE.2 [m]; SMP: 1, 2, 4, 6, 8 )
4. a. Solve the equation below. Show your work in detailed and organized steps −14𝑥 2 − 3 = −31
Answer: __________________ b. After solving the equation, classify your answer as rational or irrational number. Justify your answer using your knowledge of rational and irrational numbers.
c. In the table below, show and explain the process necessary to prove that your answer is correct. Process
Explanation of Steps
Copyright © Swun Math Grade 8 Unit 2 Constructed Response, Page 4
Grade 8 Unit 2 Constructed Response Radicals and Integers 5. Cameron is helping his dad place tiles in the living room of their new home. The tiles they have selected for their square living room each measure 1 square foot. If there will be a total of 225 tiles covering the entire floor, calculate the length of each side of their living room. a. Before you begin solving the problem, write an explanation of the meaning of the problem, and describe a strategy for finding the solution. (What does the information given in the problem represent and how does this help you develop a strategy for solving it?)
b. Solve the problem using the strategy you described and create an illustration to demonstrate your understanding of the problem.
Answer: ____________________ Copyright © Swun Math Grade 8 Unit 2 Constructed Response, Page 5
Grade 8 Unit 2 Constructed Response Radicals and Integers 6. Stan is buying a storage container to store food for the dogs he cares for at his pet daycare and grooming business. When he orders the container he is told that it is in the shape of a cube and that it has a volume of 64ft3. Stan wants to know what the dimensions of the storage container are going to be so he knows where to place it, but he does not know how to find these values. a. Write an explanation in which you describe a strategy that can be used to find the dimensions of the storage container.
b. Find the dimension of the storage container using the strategy you described above. Show your work in detailed and organized steps.
Answer: __________________ c. After clearing out a storage room at his pet daycare, Stan decides that he would like to purchase more containers for supplies. The area of this square closet is 100 ft2. What are the measurements of the length and width of this room? Show your work in detailed and organized steps.
Answer: __________________ Copyright © Swun Math Grade 8 Unit 2 Constructed Response, Page 6
Grade 8 Unit 2 Constructed Response Radicals and Integers d. Using your answer from parts b and c determine how many containers he can buy and place on the floor of the room without needing to stack them. Support your discussion with evidence from your work.
Copyright © Swun Math Grade 8 Unit 2 Constructed Response, Page 7
Grade 8 Unit 2 Constructed Response Radicals and Integers TASK 3: Scientific Notation (CCSS: 8.EE.3 [m], 8.EE.4 [m]; SMP: 1, 4, 6, 8)
7. The table below shows seven measurements written in decimal form and scientific notation. Complete the table by finding the missing decimal or scientific notation for a-f, and give an example of real-life quantities that could have these measurements. Decimal
Scientific Notation
a. 40 m b.
3.5 × 10−2
c. 60, 000,000 m d.
9 × 10−4
e. 3 m f.
9 × 103
Copyright © Swun Math Grade 8 Unit 2 Constructed Response, Page 8
Example
Grade 8 Unit 2 Constructed Response Radicals and Integers 8. Craig and Suzanne are monitoring a large honey bee colony. During the spring months they estimate that the colony has a population of 6.53 × 104 . In the winter months they observe that the colony’s population drops by 7.89 × 103 . What is the total population of the honey bee colony in the winter months? a. Set up an expression that can be used to find this difference in the colony’s population. Answer: __________________________ b. Using the expression you wrote above, find the population of the honey bees in the winter.
Answer: __________________________ c. Explain the process you used to find your answer. Were there any steps or symbols in this process that were important in solving this problem?
Copyright © Swun Math Grade 8 Unit 2 Constructed Response, Page 9
Grade 8 Unit 2 Constructed Response Radicals and Integers 9. The table below shows the different sizes of the five oceans on Earth. Use this information to answer the following questions. Ocean Name Arctic Ocean Atlantic Ocean Indian Ocean Pacific Ocean Southern Ocean
Size 1.4 × 107 𝑘𝑚2 1.06 × 108 𝑘𝑚2 7.36 × 107 𝑘𝑚2 ? 2.03 × 107 𝑘𝑚2
a. How many times larger is the Indian Ocean than the Southern Ocean? Show your work in detailed and organized steps, and give your answer in scientific notation.
Answer: ____________________ b. In the table below show and explain the process necessary to prove that your answer is correct. Process
Explanation of Steps
Copyright © Swun Math Grade 8 Unit 2 Constructed Response, Page 10
Grade 8 Unit 2 Constructed Response Radicals and Integers c. The size of the Pacific Ocean is 1.18 × 101 times larger than the size of the Arctic Ocean. What is the size of the Pacific Ocean? Show your work in detailed and organized steps. Give your answer in scientific notation.
Answer: _________________________ d. After finding your solutions in part A and C, write an explanation in which you compare the process you used to find each solution. What mathematical notations were important in the process for finding each solution?
Copyright © Swun Math Grade 8 Unit 2 Constructed Response, Page 11
Grade 8 Unit 2 Constructed Response Radicals and Integers TASK 1: Combining Exponents (CCSS: 8.EE.1 [m]; SMP: 1, 3, 4, 6)
1. Deana encounters the following problem on a test: 75 × 76 She does the following work to get her solution: 75 × 76 495×6 4930 a. After analyzing her answer, write a critique in which you identify and explain any errors in her work. Correct any errors in her reasoning.
b. What is the correct answer to the problem Deana encountered on her test? Show your work in detailed and organized steps.
Answer: __________________
Copyright © Swun Math Grade 8 Unit 2 Constructed Response, Page 1
Grade 8 Unit 2 Constructed Response Radicals and Integers 2. Examine the expression below. 65 × 64 ×
1 62
a. Demonstrate how to simplify the expression using two different methods you have learned. Method 1
Method 2
Answer:
Answer:
b. After simplifying the expression, write an explanation in which you compare the two methods you showed above. Which of the two was the most efficient in solving the problem? Support your discussion with evidence from your work.
Copyright © Swun Math Grade 8 Unit 2 Constructed Response, Page 2
Grade 8 Unit 2 Constructed Response Radicals and Integers 3. a. Simplify the following expression. Show your work in detailed and organized steps. 𝑠 3 𝑡 5 𝑢2 𝑠 6 𝑡 4 (𝑢2 )2
Answer: ___________________ b. How would your solution be different if you were simplifying the reciprocal of the expression above?
Copyright © Swun Math Grade 8 Unit 2 Constructed Response, Page 3
Grade 8 Unit 2 Constructed Response Radicals and Integers TASK 2: Solving Square and Cubic Equations (CCSS: 8.EE.2 [m]; SMP: 1, 2, 4, 6, 8 )
4. a. Solve the equation below. Show your work in detailed and organized steps −14𝑥 2 − 3 = −31
Answer: __________________ b. After solving the equation, classify your answer as rational or irrational number. Justify your answer using your knowledge of rational and irrational numbers.
c. In the table below, show and explain the process necessary to prove that your answer is correct. Process
Explanation of Steps
Copyright © Swun Math Grade 8 Unit 2 Constructed Response, Page 4
Grade 8 Unit 2 Constructed Response Radicals and Integers 5. Cameron is helping his dad place tiles in the living room of their new home. The tiles they have selected for their square living room each measure 1 square foot. If there will be a total of 225 tiles covering the entire floor, calculate the length of each side of their living room. a. Before you begin solving the problem, write an explanation of the meaning of the problem, and describe a strategy for finding the solution. (What does the information given in the problem represent and how does this help you develop a strategy for solving it?)
b. Solve the problem using the strategy you described and create an illustration to demonstrate your understanding of the problem.
Answer: ____________________ Copyright © Swun Math Grade 8 Unit 2 Constructed Response, Page 5
Grade 8 Unit 2 Constructed Response Radicals and Integers 6. Stan is buying a storage container to store food for the dogs he cares for at his pet daycare and grooming business. When he orders the container he is told that it is in the shape of a cube and that it has a volume of 64ft3. Stan wants to know what the dimensions of the storage container are going to be so he knows where to place it, but he does not know how to find these values. a. Write an explanation in which you describe a strategy that can be used to find the dimensions of the storage container.
b. Find the dimension of the storage container using the strategy you described above. Show your work in detailed and organized steps.
Answer: __________________ c. After clearing out a storage room at his pet daycare, Stan decides that he would like to purchase more containers for supplies. The area of this square closet is 100 ft2. What are the measurements of the length and width of this room? Show your work in detailed and organized steps.
Answer: __________________ Copyright © Swun Math Grade 8 Unit 2 Constructed Response, Page 6
Grade 8 Unit 2 Constructed Response Radicals and Integers d. Using your answer from parts b and c determine how many containers he can buy and place on the floor of the room without needing to stack them. Support your discussion with evidence from your work.
Copyright © Swun Math Grade 8 Unit 2 Constructed Response, Page 7
Grade 8 Unit 2 Constructed Response Radicals and Integers TASK 3: Scientific Notation (CCSS: 8.EE.3 [m], 8.EE.4 [m]; SMP: 1, 4, 6, 8)
7. The table below shows seven measurements written in decimal form and scientific notation. Complete the table by finding the missing decimal or scientific notation for a-f, and give an example of real-life quantities that could have these measurements. Decimal
Scientific Notation
a. 40 m b.
3.5 × 10−2
c. 60, 000,000 m d.
9 × 10−4
e. 3 m f.
9 × 103
Copyright © Swun Math Grade 8 Unit 2 Constructed Response, Page 8
Example
Grade 8 Unit 2 Constructed Response Radicals and Integers 8. Craig and Suzanne are monitoring a large honey bee colony. During the spring months they estimate that the colony has a population of 6.53 × 104 . In the winter months they observe that the colony’s population drops by 7.89 × 103 . What is the total population of the honey bee colony in the winter months? a. Set up an expression that can be used to find this difference in the colony’s population. Answer: __________________________ b. Using the expression you wrote above, find the population of the honey bees in the winter.
Answer: __________________________ c. Explain the process you used to find your answer. Were there any steps or symbols in this process that were important in solving this problem?
Copyright © Swun Math Grade 8 Unit 2 Constructed Response, Page 9
Grade 8 Unit 2 Constructed Response Radicals and Integers 9. The table below shows the different sizes of the five oceans on Earth. Use this information to answer the following questions. Ocean Name Arctic Ocean Atlantic Ocean Indian Ocean Pacific Ocean Southern Ocean
Size 1.4 × 107 𝑘𝑚2 1.06 × 108 𝑘𝑚2 7.36 × 107 𝑘𝑚2 ? 2.03 × 107 𝑘𝑚2
a. How many times larger is the Indian Ocean than the Southern Ocean? Show your work in detailed and organized steps, and give your answer in scientific notation.
Answer: ____________________ b. In the table below show and explain the process necessary to prove that your answer is correct. Process
Explanation of Steps
Copyright © Swun Math Grade 8 Unit 2 Constructed Response, Page 10
Grade 8 Unit 2 Constructed Response Radicals and Integers c. The size of the Pacific Ocean is 1.18 × 101 times larger than the size of the Arctic Ocean. What is the size of the Pacific Ocean? Show your work in detailed and organized steps. Give your answer in scientific notation.
Answer: _________________________ d. After finding your solutions in part A and C, write an explanation in which you compare the process you used to find each solution. What mathematical notations were important in the process for finding each solution?
Copyright © Swun Math Grade 8 Unit 2 Constructed Response, Page 11
