Algebra 2 8-1 Complete Lesson: Inverse Variation

Posljednje ažuriranje over 4 years ago

Napomena autora:

A complete formative lesson with embedded slideshow, mini lecture screencasts, checks for understanding, practice items, mixed review, and reflection. I create these assignments to supplement each lesson of Pearson's Common Core Edition Algebra 1, Algebra 2, and Geometry courses. See also mathquest.net and twitter.com/mathquestEDU.

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Algebra 2 8-1 Complete Lesson: Inverse Variation

Posljednje ažuriranje over 4 years ago

Napomena autora:

Solve It! You have 20 bags of mulch. You plan to spread the mulch from all the bags to make a rectangular layer that is 3-in. thick.
How many square feet can you cover?
If l and w represent the length and width of the rectangle in feet, what equation relates l and w?
Justify your reasoning.

You can cover a square foot with a 3-in. layer 6 times with each bag. So with each bag, you can cover 6 ft² with a 3-in. layer, and with 20 bags, you can cover 120 ft² with a 3-in. layer.

You can cover a square foot with a 3-in. layer 8 times with each bag. So with each bag, you can cover 8 ft² with a 3-in. layer, and with 20 bags, you can cover 160 ft² with a 3-in. layer.

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Problem 1 Got It? Classify each table as representing a direct variation, an inverse variation, or neither. Identify the function model for the direct and inverse variations.
NOTE: Any model that is neither direct variation nor direct variation will not have a function model.

Direct variation
Inverse variation
Neither

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Problem 2 Got It? Suppose x and y vary inversely, and x = 8 when y = -7.
Drag the appropriate item from the left to respond to each question on the right.

What is the function that models the inverse variation?
What does the graph of this function look like?
What is y when x = 2?

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Problem 3 Got It? After a major storm, your math calss volunteers to remove debris from yards. The table shows the time t in minutes that it takes a group of n students to remove the debris from an average-sized yard.
What function models the time needed to clear the debris from an average-sized yard relative to the number of students who do the work?

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Problem 3 Got It? After a major storm, your math calss volunteers to remove debris from yards. The table shows the time t in minutes that it takes a group of n students to remove the debris from an average-sized yard?
How many students should there be to clear debris from an average-sized yard in at most 25 minutes?

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Problem 4 Got It? The number of bags of mulch you need to cover a planting area varies jointly with the area to be mulched a in square feet and the depth of the mulch d in feet. If you need 10 bags to mulch 120 ft² to a depth of 3 in., how many bags do you need to mulch 200 ft² to a depth of 4 in.?

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Problem 5 Got It? How much potential energy would a 41-kg diver have standing on a 10-m diving platform?

410 joules

4010 joules

4018 joules

418 joules

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Problem 5 Got It? An 80-kg diver stands on a 6-m diving platform. At what height should a 40-kg diver stand to have equal potential energy? Do you need to find the potential energy of either diver to solve this? Explain.

6 m
9 m
10 m
12 m
Yes. You must calculate the potential energy of both divers in order to determine at what height of the second diver their PE will be equivalent.
No. You don't need to calculate the potential energy of either diver in order to determine at what height of the second diver the PE will be equivalent.

At what height should a 40-kg diver stand to have equal potential energy?
Do you need to find the potential energy of either diver to solve this?

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Is the relationship between the variables in the table a direct variation, an inverse variation, or neither? What equation models the direct or inverse variation?

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Is the relationship between the variables in the table a direct variation, an inverse variation, or neither? What equation models the direct or inverse variation?

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Writing: Describe how the pairs in the left column are related based on the equation below.

p and s
p and qrt

Vary jointly
Vary inversely

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Error Analysis: A student described the relationship between the variables in the equation below as d varies directly with r and inversely with t. Correct the error in relating the variables.

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Review Lesson 7-6: Solve each equation. Match a solution from the left with each equation on the right.

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Review Lesson 6-2: Multiply and simplify. Match a simplified expression from the left with each expression on the right.

Review Lesson 2-7: Match a description from the left with each equation on the right to describe how the equation is a transformation of the parent function y = |x|.

Translate left 2 units.
Translate right 2 units.
Translate up 2 units.
Translate down 2 units.
Stretch horizontally by a factor of 2.
Stretch vertically by a factor of 2.

y = |x| + 2
y = |x + 2|
y = 2|x|

Vocabulary Review: Which expression(s) do NOT contain a constant term?

Use Your Vocabulary: Use the true and false boxes on the left to tag each statement on the right.

true
false

As the radius of a pizza increases, the circumference of the pizza also increases. This relationship represents a direct variation.
As the number of miles a car is driven increases, the number of gallons of gas in the car's tank decreases. This relationship represents an inverse variation.
As the number of pages in a book increases, the weight of the book increases. This relationship represents an inverse variation.

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Notes: Take a clear picture or screenshot of your Cornell notes for this lesson. Upload it to the canvas. Zoom and pan as needed.
For a refresher on the Cornell note-taking system, click here.

Reflection: Math Success

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Algebra 2 8-1 Complete Lesson: Inverse Variation

Algebra 2 8-1 Complete Lesson: Inverse Variation

Solve It! You have 20 bags of mulch. You plan to spread the mulch from all the bags to make a rectangular layer that is 3-in. thick. How many square feet can you cover? If l and w represent the length and width of the rectangle in feet, what equation relates l and w? Justify your reasoning.

Problem 1 Got It? Classify each table as representing a direct variation, an inverse variation, or neither. Identify the function model for the direct and inverse variations. NOTE: Any model that is neither direct variation nor direct variation will not have a function model.

Problem 2 Got It? Suppose x and y vary inversely, and x = 8 when y = -7. Drag the appropriate item from the left to respond to each question on the right.

Problem 4 Got It? The number of bags of mulch you need to cover a planting area varies jointly with the area to be mulched a in square feet and the depth of the mulch d in feet. If you need 10 bags to mulch 120 ft2 to a depth of 3 in., how many bags do you need to mulch 200 ft2 to a depth of 4 in.?

Problem 5 Got It? How much potential energy would a 41-kg diver have standing on a 10-m diving platform?

Problem 5 Got It? An 80-kg diver stands on a 6-m diving platform. At what height should a 40-kg diver stand to have equal potential energy? Do you need to find the potential energy of either diver to solve this? Explain.

Is the relationship between the variables in the table a direct variation, an inverse variation, or neither? What equation models the direct or inverse variation?

Is the relationship between the variables in the table a direct variation, an inverse variation, or neither? What equation models the direct or inverse variation?

Writing: Describe how the pairs in the left column are related based on the equation below.

Error Analysis: A student described the relationship between the variables in the equation below as d varies directly with r and inversely with t. Correct the error in relating the variables.

Review Lesson 7-6: Solve each equation. Match a solution from the left with each equation on the right.

Review Lesson 6-2: Multiply and simplify. Match a simplified expression from the left with each expression on the right.

Review Lesson 2-7: Match a description from the left with each equation on the right to describe how the equation is a transformation of the parent function y = |x|.

Vocabulary Review: Which expression(s) do NOT contain a constant term?

Use Your Vocabulary: Use the true and false boxes on the left to tag each statement on the right.

Notes: Take a clear picture or screenshot of your Cornell notes for this lesson. Upload it to the canvas. Zoom and pan as needed.For a refresher on the Cornell note-taking system, click here.

Reflection: Math Success

Solve It! You have 20 bags of mulch. You plan to spread the mulch from all the bags to make a rectangular layer that is 3-in. thick. How many square feet can you cover? If l and w represent the length and width of the rectangle in feet, what equation relates l and w? Justify your reasoning.

Problem 1 Got It? Classify each table as representing a direct variation, an inverse variation, or neither. Identify the function model for the direct and inverse variations. NOTE: Any model that is neither direct variation nor direct variation will not have a function model.

Problem 2 Got It? Suppose x and y vary inversely, and x = 8 when y = -7. Drag the appropriate item from the left to respond to each question on the right.

Problem 4 Got It? The number of bags of mulch you need to cover a planting area varies jointly with the area to be mulched a in square feet and the depth of the mulch d in feet. If you need 10 bags to mulch 120 ft2 to a depth of 3 in., how many bags do you need to mulch 200 ft2 to a depth of 4 in.?

Problem 5 Got It? How much potential energy would a 41-kg diver have standing on a 10-m diving platform?

Problem 5 Got It? An 80-kg diver stands on a 6-m diving platform. At what height should a 40-kg diver stand to have equal potential energy? Do you need to find the potential energy of either diver to solve this? Explain.

Is the relationship between the variables in the table a direct variation, an inverse variation, or neither? What equation models the direct or inverse variation?

Is the relationship between the variables in the table a direct variation, an inverse variation, or neither? What equation models the direct or inverse variation?

Writing: Describe how the pairs in the left column are related based on the equation below.

Error Analysis: A student described the relationship between the variables in the equation below as d varies directly with r and inversely with t. Correct the error in relating the variables.

Review Lesson 7-6: Solve each equation. Match a solution from the left with each equation on the right.

Review Lesson 6-2: Multiply and simplify. Match a simplified expression from the left with each expression on the right.

Review Lesson 2-7: Match a description from the left with each equation on the right to describe how the equation is a transformation of the parent function y = |x|.

Vocabulary Review: Which expression(s) do NOT contain a constant term?

Use Your Vocabulary: Use the true and false boxes on the left to tag each statement on the right.

Notes: Take a clear picture or screenshot of your Cornell notes for this lesson. Upload it to the canvas. Zoom and pan as needed.For a refresher on the Cornell note-taking system, click here.

Reflection: Math Success

Solve It! You have 20 bags of mulch. You plan to spread the mulch from all the bags to make a rectangular layer that is 3-in. thick.
How many square feet can you cover?
If l and w represent the length and width of the rectangle in feet, what equation relates l and w?
Justify your reasoning.

Problem 1 Got It? Classify each table as representing a direct variation, an inverse variation, or neither. Identify the function model for the direct and inverse variations.
NOTE: Any model that is neither direct variation nor direct variation will not have a function model.

Problem 2 Got It? Suppose x and y vary inversely, and x = 8 when y = -7.
Drag the appropriate item from the left to respond to each question on the right.

Notes: Take a clear picture or screenshot of your Cornell notes for this lesson. Upload it to the canvas. Zoom and pan as needed.
For a refresher on the Cornell note-taking system, click here.

Solve It! You have 20 bags of mulch. You plan to spread the mulch from all the bags to make a rectangular layer that is 3-in. thick.
How many square feet can you cover?
If l and w represent the length and width of the rectangle in feet, what equation relates l and w?
Justify your reasoning.

Problem 1 Got It? Classify each table as representing a direct variation, an inverse variation, or neither. Identify the function model for the direct and inverse variations.
NOTE: Any model that is neither direct variation nor direct variation will not have a function model.

Problem 2 Got It? Suppose x and y vary inversely, and x = 8 when y = -7.
Drag the appropriate item from the left to respond to each question on the right.

Notes: Take a clear picture or screenshot of your Cornell notes for this lesson. Upload it to the canvas. Zoom and pan as needed.
For a refresher on the Cornell note-taking system, click here.