Unit 2 Plan - Grade 6

Title	Assessment
Unit 2 Assessment 2024 Released Items	Problem 1 Which expression represents 5 more than the product of 2 and y? A. $2+y+5$ B. $2y+5$ C. $5+\frac{2}{y}$ D. $5+\frac{y}{2}$ Show Solution B Problem 2 Which value of b makes the inequality $3b > 12$ true? A. 2 B. 3 C. 4 D. 5 Show Solution D Problem 3 A coordinate plane can be used to show the distance, in units, between two locations. The location of Jack's house and a store are listed below. Jack's house is located at $(-7, -8)$ . The store is located at $(-7, 4)$ . What is the distance, in units, between Jack's house and the store? A. 4 B. 8 C. 12 D. 14 Show Solution C Problem 4 Which number line represents $x \ge -3$ ? A [Number line with a closed circle at -3 and an arrow pointing to the left] B [Number line with a closed circle at -3 and an arrow pointing to the right] C [Number line with an open circle at -3 and an arrow pointing to the right] D [Number line with an open circle at -3 and an arrow pointing to the left] Image Description: Four number lines are presented, each ranging from -6 to 6. Option A: A solid (closed) circle is plotted at -3. A bold line extends to the left, indicating all numbers less than or equal to -3. Option B: A solid (closed) circle is plotted at -3. A bold line extends to the right, indicating all numbers greater than or equal to -3. Option C: An open circle is plotted at -3. A bold line extends to the right, indicating all numbers greater than -3. Option D: An open circle is plotted at -3. A bold line extends to the left, indicating all numbers less than -3. Show Solution B Problem 5 What is the value of the expression $8^2 \div 4 \times 2^3$ ? A. 16 B. 24 C. 96 D. 128 Show Solution D Problem 6 Ben purchases $1\frac{1}{4}$ pounds of nuts and puts them into bags. Each bag holds $\frac{1}{8}$ pound of nuts. He uses all the nuts to fill each bag completely. How many bags does Ben fill with nuts? A. $\frac{5}{32}$ B. $1\frac{1}{8}$ C. 2 D. 10 Show Solution D Problem 7 Which expression represents the opposite of the number $-2\frac{1}{2}$ ? A. $-(2\frac{1}{2})$ B. $-(-2\frac{1}{2})$ C. $-2(\frac{1}{2})$ D. $2(-\frac{1}{2})$ Show Solution B Problem 8 A diagram of a cube is shown below. What is the volume, in cubic inches, of the cube? A. $1\frac{7}{8}$ B. $7\frac{1}{2}$ C. $15\frac{5}{8}$ D. $20\frac{5}{6}$ Image Description: A line drawing of a 3D cube. The length of one side is labeled as $2\frac{1}{2}$ inches. Show Solution C Problem 9 Tammy and Jacob collect stamps. Tammy has s stamps. Jacob has 4 fewer than 3 times the number of stamps Tammy has. Which expression can be used to represent the number of stamps Jacob has? A. $3 - 4s$ B. $3s - 4$ C. $4 - 3s$ D. $4s - 3$ Show Solution B Problem 10 A container holds 6 gallons of liquid. How many pints of liquid does the container hold? A. 6 B. 8 C. 24 D. 48 Show Solution D Problem 11 What ordered pair represents the location of a point that is the reflection of the point $(-4, 6)$ over the x-axis? A. $(4, 6)$ B. $(-4, -6)$ C. $(6, -4)$ D. $(-6, 4)$ Show Solution B Problem 12 An isosceles trapezoid is shown below. What is the area, in square centimeters, of the isosceles trapezoid? A. 120 B. 150 C. 195 D. 240 Image Description: An isosceles trapezoid with a horizontal top base labeled 10 cm and a horizontal bottom base labeled 16 cm. The height of the trapezoid is indicated by a dashed vertical line labeled 15 cm, connecting the top base to the bottom base at a right angle. Show Solution C Problem 13 An inequality is shown below. $-\frac{9}{20} > -\frac{21}{24}$ Which statement about the locations of the numbers on a number line is true? A. $-\frac{9}{20}$ is to the left of $-\frac{21}{24}$ and to the right of 0 on a number line. B. $-\frac{9}{20}$ is to the right of $-\frac{21}{24}$ and to the left of 0 on a number line. C. $-\frac{9}{20}$ is to the left of $-\frac{21}{24}$ and to the left of 0 on a number line. D. $-\frac{9}{20}$ is to the right of $-\frac{21}{24}$ and to the right of 0 on a number line. Show Solution B Problem 14 There are 104 calories in an 8-ounce serving of soda. How many calories are in 1 ounce of soda? A. 13 B. 26 C. 52 D. 96 Show Solution A Problem 15 Jose builds a skateboard ramp in the shape of a right triangular prism. The net below shows the dimensions of each part of the ramp. What is the surface area, in square feet, of the ramp? A. 90 B. 75 C. 51 D. 44 Image Description: A net of a right triangular prism. The net consists of three rectangles arranged in a row with two right triangles attached to the top and bottom of the middle rectangle. The middle rectangle measures 6 ft wide by 4 ft high. The left rectangle measures 2.5 ft wide by 4 ft high. The right rectangle measures 6.5 ft wide by 4 ft high. Attached to the top and bottom of the middle (6 ft wide) rectangle are two identical right triangles. For each triangle, the leg attached to the rectangle is 6 ft. The vertical leg is labeled 2.5 ft, and the hypotenuse is labeled 6.5 ft. Show Solution A Problem 16 The number 4 is 16% of what number? A. 12 B. 20 C. 25 D. 64 Show Solution C Problem 17 A machine produces chocolates at a constant rate. In 42 minutes, the machine produces 7 pounds of chocolates. How long, in minutes, will it take the machine to produce 9 pounds of chocolates? A. 6 B. 15 C. 54 D. 63 Show Solution C Problem 18 The dimensions of a cereal box in the shape of a right rectangular prism are shown below. $8\frac{1}{10} \text{ inches by } 4\frac{4}{5} \text{ inches by } 12\frac{1}{2} \text{ inches}$ What is the volume, in cubic inches, of the cereal box? A. 24 B. $25\frac{2}{5}$ C. $384\frac{1}{25}$ D. 486 Show Solution D Problem 19 A tutoring company charges $25.00 per hour to tutor a student. How many hours of tutoring would cost$ 62.50? A. $2\frac{1}{2}$ B. $3\frac{1}{2}$ C. $37\frac{1}{2}$ D. $87\frac{1}{2}$ Show Solution A Problem 20 The four vertices of a parallelogram are plotted on the coordinate plane shown below. What is the distance, in units, between vertices A and D? Answer: ______ units Image Description: A coordinate plane showing four plotted points forming a parallelogram. Point A is located at $(-6, 6)$ . Point D is located at $(4, 6)$ . Point B is located at $(2, -4)$ . Point C is located at $(12, -4)$ . Problem 21 What value of n makes the equation $\frac{n}{8} = 17$ true? Answer: ______ Problem 22 An artist uses a ratio of 6 gallons of orange paint to 8 gallons of blue paint. If the artist uses 1 gallon of blue paint, how many gallons of orange paint will they use? Answer: ______ gallon(s) Problem 23 A diagram of a rectangular flag, with a shaded section, is shown below. What is the area, in square centimeters, of the shaded section of the flag? Show your work. Answer: ______ square centimeters Problem 24 A student claims that the expression $6 + 8x$ is equivalent to the expression $3(3 + 5x)$ . What is incorrect about the student's claim? Be sure to include an equivalent expression to $3(3 + 5x)$ in your response. Explain your answer. Problem 25 Mike needs a ticket every time he rides the bus. Given the equation $c = 2.75t$ , what is the relationship between t, the number of tickets that Mike buys, and c, the total cost? Be sure to identify which variable is independent and which variable is dependent in your answer. Explain your answer. Problem 26 A student claims that 4 is the greatest common factor of 24 and 40, because the two numbers are both multiples of 4. Is the student's claim correct? Explain how you determined your answer. Problem 27 A prism made of unit cubes is shown below. What perfect cube is represented by the volume of the prism? Be sure to include what you know about volume and exponents in your answer. Explain your answer. Image Description: A large cube constructed from smaller unit cubes. The cube is 4 units wide, 4 units high, and 4 units deep. The front face shows a 4x4 grid of squares. Problem 28 The location of Jake's school and house are represented on the coordinate plane shown below. What is the distance, in units, from Jake's school to his house? Be sure to include the coordinates for both locations and how those coordinates can be used to determine your answer. Explain how you determined your answer. Image Description: A coordinate plane showing two points. A point labeled "House" is plotted at $(3, 6)$ . A point labeled "School" is plotted at $(3, 2)$ . Problem 29 Rex and Nero are saving money for new bikes. They both start with $0.00 and save at a constant rate for 16 months. The tables below show Rex's and Nero's total savings, in dollars, at the end of different numbers of months.</p> <p><strong>REX'S SAVINGS</strong></p> <table> <thead> <tr> <th align="left">Number of Months</th> <th align="left">Savings (dollars)</th> </tr> </thead> <tbody><tr> <td align="left">2</td> <td align="left">18</td> </tr> <tr> <td align="left">4</td> <td align="left">36</td> </tr> <tr> <td align="left">6</td> <td align="left">54</td> </tr> <tr> <td align="left">8</td> <td align="left">72</td> </tr> </tbody></table> <p><strong>NERO'S SAVINGS</strong></p> <table> <thead> <tr> <th align="left">Number of Months</th> <th align="left">Savings (dollars)</th> </tr> </thead> <tbody><tr> <td align="left">3</td> <td align="left">36</td> </tr> <tr> <td align="left">6</td> <td align="left">72</td> </tr> <tr> <td align="left">9</td> <td align="left">108</td> </tr> <tr> <td align="left">12</td> <td align="left">144</td> </tr> </tbody></table> <p>At the end of 16 months, what is the difference between the amount of money Rex saved and the amount of money Nero saved?</p> <p>Show your work.</p> <p>Answer:$ ______

Problem 1

Which expression represents 5 more than the product of 2 and y?

A. $2+y+5$
B. $2y+5$
C. $5+\frac{2}{y}$
D. $5+\frac{y}{2}$

Show Solution

B

Problem 2

Which value of b makes the inequality $3b > 12$ true?

A. 2
B. 3
C. 4
D. 5

Show Solution

D

Problem 3

A coordinate plane can be used to show the distance, in units, between two locations. The location of Jack's house and a store are listed below.

Jack's house is located at $(-7, -8)$ .
The store is located at $(-7, 4)$ .

What is the distance, in units, between Jack's house and the store?

A. 4
B. 8
C. 12
D. 14

Show Solution

C

Problem 4

Which number line represents $x \ge -3$ ?

A [Number line with a closed circle at -3 and an arrow pointing to the left]
B [Number line with a closed circle at -3 and an arrow pointing to the right]
C [Number line with an open circle at -3 and an arrow pointing to the right]
D [Number line with an open circle at -3 and an arrow pointing to the left]

Image Description: Four number lines are presented, each ranging from -6 to 6.

Option A: A solid (closed) circle is plotted at -3. A bold line extends to the left, indicating all numbers less than or equal to -3.
Option B: A solid (closed) circle is plotted at -3. A bold line extends to the right, indicating all numbers greater than or equal to -3.
Option C: An open circle is plotted at -3. A bold line extends to the right, indicating all numbers greater than -3.
Option D: An open circle is plotted at -3. A bold line extends to the left, indicating all numbers less than -3.

Show Solution

B

Problem 5

What is the value of the expression $8^2 \div 4 \times 2^3$ ?

A. 16
B. 24
C. 96
D. 128

Show Solution

D

Problem 6

Ben purchases $1\frac{1}{4}$ pounds of nuts and puts them into bags. Each bag holds $\frac{1}{8}$ pound of nuts. He uses all the nuts to fill each bag completely. How many bags does Ben fill with nuts?

A. $\frac{5}{32}$
B. $1\frac{1}{8}$
C. 2
D. 10

Show Solution

D

Problem 7

Which expression represents the opposite of the number $-2\frac{1}{2}$ ?

A. $-(2\frac{1}{2})$
B. $-(-2\frac{1}{2})$
C. $-2(\frac{1}{2})$
D. $2(-\frac{1}{2})$

Show Solution

B

Problem 8

A diagram of a cube is shown below.

What is the volume, in cubic inches, of the cube?

A. $1\frac{7}{8}$
B. $7\frac{1}{2}$
C. $15\frac{5}{8}$
D. $20\frac{5}{6}$

Image Description: A line drawing of a 3D cube. The length of one side is labeled as $2\frac{1}{2}$ inches.

Show Solution

C

Problem 9

Tammy and Jacob collect stamps. Tammy has s stamps. Jacob has 4 fewer than 3 times the number of stamps Tammy has. Which expression can be used to represent the number of stamps Jacob has?

A. $3 - 4s$
B. $3s - 4$
C. $4 - 3s$
D. $4s - 3$

Show Solution

B

Problem 10

A container holds 6 gallons of liquid. How many pints of liquid does the container hold?

A. 6
B. 8
C. 24
D. 48

Show Solution

D

Problem 11

What ordered pair represents the location of a point that is the reflection of the point $(-4, 6)$ over the x-axis?

A. $(4, 6)$
B. $(-4, -6)$
C. $(6, -4)$
D. $(-6, 4)$

Show Solution

B

Problem 12

An isosceles trapezoid is shown below.

What is the area, in square centimeters, of the isosceles trapezoid?

A. 120
B. 150
C. 195
D. 240

Image Description: An isosceles trapezoid with a horizontal top base labeled 10 cm and a horizontal bottom base labeled 16 cm. The height of the trapezoid is indicated by a dashed vertical line labeled 15 cm, connecting the top base to the bottom base at a right angle.

Show Solution

C

Problem 13

An inequality is shown below.

$-\frac{9}{20} > -\frac{21}{24}$

Which statement about the locations of the numbers on a number line is true?

A. $-\frac{9}{20}$ is to the left of $-\frac{21}{24}$ and to the right of 0 on a number line.
B. $-\frac{9}{20}$ is to the right of $-\frac{21}{24}$ and to the left of 0 on a number line.
C. $-\frac{9}{20}$ is to the left of $-\frac{21}{24}$ and to the left of 0 on a number line.
D. $-\frac{9}{20}$ is to the right of $-\frac{21}{24}$ and to the right of 0 on a number line.

Show Solution

B

Problem 14

There are 104 calories in an 8-ounce serving of soda. How many calories are in 1 ounce of soda?

A. 13
B. 26
C. 52
D. 96

Show Solution

A

Problem 15

Jose builds a skateboard ramp in the shape of a right triangular prism. The net below shows the dimensions of each part of the ramp.

What is the surface area, in square feet, of the ramp?

A. 90
B. 75
C. 51
D. 44

Image Description: A net of a right triangular prism. The net consists of three rectangles arranged in a row with two right triangles attached to the top and bottom of the middle rectangle.

The middle rectangle measures 6 ft wide by 4 ft high.
The left rectangle measures 2.5 ft wide by 4 ft high.
The right rectangle measures 6.5 ft wide by 4 ft high.
Attached to the top and bottom of the middle (6 ft wide) rectangle are two identical right triangles. For each triangle, the leg attached to the rectangle is 6 ft. The vertical leg is labeled 2.5 ft, and the hypotenuse is labeled 6.5 ft.

Show Solution

A

Problem 16

The number 4 is 16% of what number?

A. 12
B. 20
C. 25
D. 64

Show Solution

C

Problem 17

A machine produces chocolates at a constant rate. In 42 minutes, the machine produces 7 pounds of chocolates. How long, in minutes, will it take the machine to produce 9 pounds of chocolates?

A. 6
B. 15
C. 54
D. 63

Show Solution

C

Problem 18

The dimensions of a cereal box in the shape of a right rectangular prism are shown below.

$8\frac{1}{10} \text{ inches by } 4\frac{4}{5} \text{ inches by } 12\frac{1}{2} \text{ inches}$

What is the volume, in cubic inches, of the cereal box?

A. 24
B. $25\frac{2}{5}$
C. $384\frac{1}{25}$
D. 486

Show Solution

D

Problem 19

A tutoring company charges $25.00 per hour to tutor a student. How many hours of tutoring would cost$ 62.50?

A. $2\frac{1}{2}$
B. $3\frac{1}{2}$
C. $37\frac{1}{2}$
D. $87\frac{1}{2}$

Show Solution

A

Problem 20

The four vertices of a parallelogram are plotted on the coordinate plane shown below.

What is the distance, in units, between vertices A and D?

Answer: ______ units

Image Description: A coordinate plane showing four plotted points forming a parallelogram.

Point A is located at $(-6, 6)$ .
Point D is located at $(4, 6)$ .
Point B is located at $(2, -4)$ .
Point C is located at $(12, -4)$ .

Problem 21

What value of n makes the equation $\frac{n}{8} = 17$ true?

Answer: ______

Problem 22

An artist uses a ratio of 6 gallons of orange paint to 8 gallons of blue paint. If the artist uses 1 gallon of blue paint, how many gallons of orange paint will they use?

Answer: ______ gallon(s)

Problem 23

A diagram of a rectangular flag, with a shaded section, is shown below.

What is the area, in square centimeters, of the shaded section of the flag?

Show your work.

Answer: ______ square centimeters

Problem 24

A student claims that the expression $6 + 8x$ is equivalent to the expression $3(3 + 5x)$ . What is incorrect about the student's claim?

Be sure to include an equivalent expression to $3(3 + 5x)$ in your response.

Explain your answer.

Problem 25

Mike needs a ticket every time he rides the bus. Given the equation $c = 2.75t$ , what is the relationship between t, the number of tickets that Mike buys, and c, the total cost?

Be sure to identify which variable is independent and which variable is dependent in your answer.

Explain your answer.

Problem 26

A student claims that 4 is the greatest common factor of 24 and 40, because the two numbers are both multiples of 4. Is the student's claim correct?

Explain how you determined your answer.

Problem 27

A prism made of unit cubes is shown below.

What perfect cube is represented by the volume of the prism?

Be sure to include what you know about volume and exponents in your answer.

Explain your answer.

Image Description: A large cube constructed from smaller unit cubes. The cube is 4 units wide, 4 units high, and 4 units deep. The front face shows a 4x4 grid of squares.

Problem 28

The location of Jake's school and house are represented on the coordinate plane shown below.

What is the distance, in units, from Jake's school to his house?

Be sure to include the coordinates for both locations and how those coordinates can be used to determine your answer.

Explain how you determined your answer.

Image Description: A coordinate plane showing two points.

A point labeled "House" is plotted at $(3, 6)$ .
A point labeled "School" is plotted at $(3, 2)$ .

Problem 29

Rex and Nero are saving money for new bikes. They both start with $0.00 and save at a constant rate for 16 months. The tables below show Rex's and Nero's total savings, in dollars, at the end of different numbers of months.</p> <p><strong>REX'S SAVINGS</strong></p> <table> <thead> <tr> <th align="left">Number of Months</th> <th align="left">Savings (dollars)</th> </tr> </thead> <tbody><tr> <td align="left">2</td> <td align="left">18</td> </tr> <tr> <td align="left">4</td> <td align="left">36</td> </tr> <tr> <td align="left">6</td> <td align="left">54</td> </tr> <tr> <td align="left">8</td> <td align="left">72</td> </tr> </tbody></table> <p><strong>NERO'S SAVINGS</strong></p> <table> <thead> <tr> <th align="left">Number of Months</th> <th align="left">Savings (dollars)</th> </tr> </thead> <tbody><tr> <td align="left">3</td> <td align="left">36</td> </tr> <tr> <td align="left">6</td> <td align="left">72</td> </tr> <tr> <td align="left">9</td> <td align="left">108</td> </tr> <tr> <td align="left">12</td> <td align="left">144</td> </tr> </tbody></table> <p>At the end of 16 months, what is the difference between the amount of money Rex saved and the amount of money Nero saved?</p> <p>Show your work.</p> <p>Answer:$ ______

Unit 2 2024 — Unit Plan