7th Grade Math: Unit 4

Unit 4 – Item 1
Sandy and Marshall are both looking at the angle relationships below to determine the m ∠ 2. They were given the following information:

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Whose statement do you agree with and why?

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Unit 4 – Item 2
How many of these wedges would you need to create a right angle?

Unit 4 – Item 3
Jamarcus and Moises are using the diagram below to discuss the relationship between ∠AEX and ∠BEY.

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Who do you agree with? Explain your answer.

Unit 4 – Item 4
Use the diagram to answer the questions.

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Part A
What is the angle relationship between ∠STM and ∠ETM?

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Part B
Write an equation that could represent the relationship between ∠STM and ∠ETM.

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Part C
What is the angle measurement of ∠STM?

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Unit 4 – Item 5
The gym teacher at Maple Avenue Elementary School, Mrs. Johnson, is setting up a game for field day. Part of the game is shooting a beach ball through a basketball hoop. The
circumference of a basketball hoop in the gym is 57 inches. The diameter of a beach ball is 16 inches. Will the beach ball fit through the basketball hoop? Explain your answer.

(Use 3.14 for 𝜋 )

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Unit 4 – Item 6
Cake Boss, Buddy Valastro, baked a cake in the shape of a cone. When serving the cake, he first cut it vertically down the middle of the cake. What two-dimensional shape was formed by the cut?

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Unit 4 – Item 7
Complementary angles add up to 90°. If angle ABC is 42°, what is the measurement of angle DBC?

Unit 4 – Item 8
Use the diagram to answer the questions below.

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Part A
What is the relationship between ∠ACE and ∠BCD?

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Part B
Write an equation to represent the diagram

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Part C
Determine the measurement of ∠ACE.

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Unit 4 – Item 9
A monster truck’s tires typically have a diameter of 66 inches. How far does a wheel travel in one rotation? Explain your reasoning.

(Use 3.14 for 𝜋).

Unit 4 – Item 10
The Rock Soda Company wants to design a new soda can that uses less aluminum. This would save money and be better for the environment. As a member of the Rock Soda Company design team, it is your responsibility to design a new can that reduces the amount of material needed for each can. The dimensions of the current can are shown below.

(Round your answers to the nearest hundredth. Use 3.14 for 𝜋).


Can Dimensions:
Diameter = 6.6 cm
Height = 12.27 cm

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Your task includes:
Determine the volume and surface area of the current soda can.
Draw a net of the current can including dimensions.
Design a new can that has the same volume but uses less materials (lower surface area).

Whose statement do you agree with and why?

Unit 4 – Item 2How many of these wedges would you need to create a right angle?

Who do you agree with? Explain your answer.

Part AWhat is the angle relationship between ∠STM and ∠ETM?

Part BWrite an equation that could represent the relationship between ∠STM and ∠ETM.

Part CWhat is the angle measurement of ∠STM?

Unit 4 – Item 6Cake Boss, Buddy Valastro, baked a cake in the shape of a cone. When serving the cake, he first cut it vertically down the middle of the cake. What two-dimensional shape was formed by the cut?

Unit 4 – Item 7Complementary angles add up to 90°. If angle ABC is 42°, what is the measurement of angle DBC?

Part AWhat is the relationship between ∠ACE and ∠BCD?

Part BWrite an equation to represent the diagram

Part CDetermine the measurement of ∠ACE.

Unit 4 – Item 9A monster truck’s tires typically have a diameter of 66 inches. How far does a wheel travel in one rotation? Explain your reasoning.(Use 3.14 for 𝜋).

Your task includes:Determine the volume and surface area of the current soda can.Draw a net of the current can including dimensions.Design a new can that has the same volume but uses less materials (lower surface area).

Unit 4 – Item 2
How many of these wedges would you need to create a right angle?

Part A
What is the angle relationship between ∠STM and ∠ETM?

Part B
Write an equation that could represent the relationship between ∠STM and ∠ETM.

Part C
What is the angle measurement of ∠STM?

Unit 4 – Item 6
Cake Boss, Buddy Valastro, baked a cake in the shape of a cone. When serving the cake, he first cut it vertically down the middle of the cake. What two-dimensional shape was formed by the cut?

Unit 4 – Item 7
Complementary angles add up to 90°. If angle ABC is 42°, what is the measurement of angle DBC?

Part A
What is the relationship between ∠ACE and ∠BCD?

Part B
Write an equation to represent the diagram

Part C
Determine the measurement of ∠ACE.

Unit 4 – Item 9
A monster truck’s tires typically have a diameter of 66 inches. How far does a wheel travel in one rotation? Explain your reasoning.

(Use 3.14 for 𝜋).

Your task includes:
Determine the volume and surface area of the current soda can.
Draw a net of the current can including dimensions.
Design a new can that has the same volume but uses less materials (lower surface area).