8th Grade Math: Unit 5

Unit 5 – Item 1
A construction project requires a diagonal beam in a rectangular structure

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The length of the diagonal (d) is given by the Pythagorean Theorem: d = √𝑎2 + 𝑏2, where a and b are the lengths of the two legs of the right triangle. If a = 5 meters and b = 7 meters,
find the exact length of the diagonal and then provide a rational approximation.

Unit 5 – Item 2
Tanya and Michelle are comparing √36 and ^3√36 

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Who is correct? Explain your reasoning.

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Unit 5 - Item 3

Select the three correct statements

Unit 5 – Item 4
Allison has a square garden with an area of 140 square feet. What is the approximate length
of one side of the garden? Round to the nearest hundredth place.

The table below shows the number of students in Mr. William’s studying 8th-grade math compared to those taking his Algebra: Concepts & Connections class. 

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How many times more students are studying 8th-grade math compared to those taking Algebra: Concepts & Connections class?

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Unit 5 – Item 6
Jacob says the area of the TV is 3^20. Malachi says the area of the TV is 3^9. Explain who is correct.

Unit 5 Item 7

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Express the distance from the Earth to the Sun in scientific notation.

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One mile is approximately equal to 1.60934 kilometers. Evaluate the distance in kilometers. Write your answer in scientific notation.

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Unit 5 – Item 8
The Mercedes Benz Stadium can hold up to 7.1 x 104 people. The State Farm Arena can hold
about 1.7 x 104. How many more people can the Mercedes Benz Stadium hold than the State
Farm Arena? Write your answer in standard form and scientific notation form.

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Unit 5 - Item 9

Who is correct?

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Unit 5 – Item 10
A space exploration agency is planning a mission to take a photograph of a distant nebula, a
cloud of gas and dust in outer space. The distance from Earth to the nebula is approximately
3.8 𝑥 10^8 kilometers. The agency’s unmanned spaceship travels at a speed of 5.3 𝑥 10^3 kilometers per hour. Calculate the time in hours it takes for the spaceship to travel
distance to the nebula. Display your answer in scientific notation.

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Unit 5 – Item 11
A factory produces boxes of staples that each contain 5x10^3 staples. Every hour the factory produces 6,000 boxes. If the factory operates 24 hours per day, how many staples are produced each week. Express your answer in scientific notation.

The length of the diagonal (d) is given by the Pythagorean Theorem: d = √𝑎2 + 𝑏2, where a and b are the lengths of the two legs of the right triangle. If a = 5 meters and b = 7 meters,find the exact length of the diagonal and then provide a rational approximation.

Who is correct? Explain your reasoning.

Unit 5 - Item 3Select the three correct statements

How many times more students are studying 8th-grade math compared to those taking Algebra: Concepts & Connections class?

Unit 5 – Item 6Jacob says the area of the TV is 3^20. Malachi says the area of the TV is 3^9. Explain who is correct.

Express the distance from the Earth to the Sun in scientific notation.

One mile is approximately equal to 1.60934 kilometers. Evaluate the distance in kilometers. Write your answer in scientific notation.

Unit 5 – Item 8The Mercedes Benz Stadium can hold up to 7.1 x 104 people. The State Farm Arena can holdabout 1.7 x 104. How many more people can the Mercedes Benz Stadium hold than the StateFarm Arena? Write your answer in standard form and scientific notation form.

Unit 5 - Item 9Who is correct?

Unit 5 – Item 11A factory produces boxes of staples that each contain 5x10^3 staples. Every hour the factory produces 6,000 boxes. If the factory operates 24 hours per day, how many staples are produced each week. Express your answer in scientific notation.

The length of the diagonal (d) is given by the Pythagorean Theorem: d = √𝑎2 + 𝑏2, where a and b are the lengths of the two legs of the right triangle. If a = 5 meters and b = 7 meters,
find the exact length of the diagonal and then provide a rational approximation.

Unit 5 - Item 3

Select the three correct statements

Unit 5 – Item 6
Jacob says the area of the TV is 3^20. Malachi says the area of the TV is 3^9. Explain who is correct.

Unit 5 – Item 8
The Mercedes Benz Stadium can hold up to 7.1 x 104 people. The State Farm Arena can hold
about 1.7 x 104. How many more people can the Mercedes Benz Stadium hold than the State
Farm Arena? Write your answer in standard form and scientific notation form.

Unit 5 - Item 9

Who is correct?

Unit 5 – Item 11
A factory produces boxes of staples that each contain 5x10^3 staples. Every hour the factory produces 6,000 boxes. If the factory operates 24 hours per day, how many staples are produced each week. Express your answer in scientific notation.