Lesson 16 Slides | Fishtank Learning

Anchor Problems - Problem 1

Look at the four figures shown below.

a. What do you notice about each figure? What do you wonder about each figure?

b. What measurements would you need in each figure to determine its volume?

Guiding Questions

How is each figure created? Is it composed of multiple shapes? Is it only a part of a shape?
How are shapes in each figure related to one another? What measurements do they share?
What if you were given the slant height and the radius of the cone in Figure A, could you determine the volume of the cone?
How would you go about finding the volume of Figure D?
How would you go about finding the volume of the shaded space in Figure C?

Notes

This Anchor Problem should be used on Day 1. The purpose of this Anchor Problem is to encourage students to take multiple looks at a complex shape to better understand how it was created and how the measurements of the various shapes within the figure are related to one another (MP.7). This kind of thinking, powered by the whole class, will prime students for the challenging tasks they will encounter in the class activity.

Anchor Problems - Problem 2

Option #1: Glasses

The diagram shows three glasses (not drawn to scale). The measurements are all in centimeters.

The bowl of glass 1 is cylindrical. The inside is 5 cm and the inside height is 6 cm.
The bowl of glass 2 is composed of a hemisphere attached to a cylinder. The inside diameter of both the hemisphere and the cylinder is 6 cm. The height of the cylinder is 3 cm.
The bowl of glass 3 is an inverted cone. The inside diameter is 6 cm and the inside slant height is 6 cm.

Calculate the volume of the bowl of each of these glasses.
Glass 2 is filled with water and then half the water is poured out. Find the height of the water.

Guiding Questions

What do you notice about the diagram? What do you wonder?
Describe the shapes and measurements that are involved in this problem.
What is your strategy or approach to solve this problem? What are your peers’ approaches?
Do you have all of the information you need to solve the problem? Specifically looking at Glass 3, what is the difference between slant height and vertical height?
How will you organize your work space?

Notes

Students choose or are assigned one of the five Anchor Problems (#2 - #6) to work on with a small group of peers. After collaboratively developing a strategy and preparing a solution, students should create a poster of their response.
Day 1: Students in small groups should develop their approach or strategy to solve the problem and begin solving.
Day 2: Students in small groups finalize their solution and prepare a poster to represent their response. Students do a gallery walk around the room and complete Anchor Problem #7.

Anchor Problems - Problem 3

Option #2: Shipping Rolled Oats

Rolled oats (dry oatmeal) come in cylindrical containers with a diameter of $$5$$ inches and a height of $${9 {1\over2}}$$ inches. These containers are shipped to grocery stores in boxes. Each shipping box contains six rolled oats containers. The shipping company is trying to figure out the dimensions of the box for shipping the rolled oats containers that will use the least amount of cardboard. They are only considering boxes that are rectangular prisms so that they are easy to stack.

a. What is the surface area of the box needed to ship these containers to the grocery store that uses the least amount of cardboard?

b. What is the volume of this box?

Guiding Questions

Describe the situation in your own words.
Describe the shapes and measurements that are involved in this problem.
What is your strategy or approach to solve this problem? What are your peers’ approaches?
Do you have all of the information you need to solve the problem?
How will you organize your work space?

Notes

Students choose or are assigned one of the five Anchor Problems (#2 - #6) to work on with a small group of peers. After collaboratively developing a strategy and preparing a solution, students should create a poster of their response.
Day 1: Students in small groups should develop their approach or strategy to solve the problem and begin solving.
Day 2: Students in small groups finalize their solution and prepare a poster to represent their response. Students do a gallery walk around the room and complete Anchor Problem #7.

Anchor Problems - Problem 4

Option #3: Comparing Snow Cones

Pablo's Icy Treat Stand sells homemade frozen juice treats as well as snow cones. Originally, Pablo used paper cone cups with a diameter of 3.5 inches and a height of 4 inches.

His supply store stopped carrying these paper cones, so he had to start using more standard paper cups. These are truncated cones (cones with the "pointy end" sliced off) with a top diameter of 3.5 inches, a bottom diameter of 2.5 inches, and a height of 4 inches.

Because some customers said they missed the old cones, Pablo put a sign up saying, "The new cups hold 50% more!" His daughter Letitia wonders if her father's sign is correct. Help her find out.

How much juice can cup A hold? (While cups for juice are not usually filled to the top, we can assume frozen juice treats would be filled to the top of the cup.)
How much juice can cup B hold?
By what percentage is cup B larger in volume than cup A?
Snow cones have ice filling the cup as well as a hemisphere of ice sticking out of the top of each cup. How much ice is in a snow cone for each cup?
By what percentage is the snow cone in cup B larger than the snow cone in conical cup A?
Is Pablo’s sign accurate?

Guiding Questions

What do you notice about the diagrams? What do you wonder?
Describe the shapes and measurements that are involved in this problem.
What is your strategy or approach to solve this problem? What are your peers’ approaches?
Do you have all of the information you need to solve the problem?
How will you organize your work space?

Notes

Students choose or are assigned one of the five Anchor Problems (#2 - #6) to work on with a small group of peers. After collaboratively developing a strategy and preparing a solution, students should create a poster of their response.
Day 1: Students in small groups should develop their approach or strategy to solve the problem and begin solving.
Day 2: Students in small groups finalize their solution and prepare a poster to represent their response. Students do a gallery walk around the room and complete Anchor Problem #7.

Anchor Problems - Problem 5

Option #4: Flower Vases

My sister’s birthday is in a few weeks and I would like to buy her a new vase to keep fresh flowers in her house. She often forgets to water her flowers and needs a vase that holds a lot of water. In a catalog, there are three vases available and I want to purchase the one that holds the most water. The first vase is a cylinder with diameter 10cm and height 40cm. The second vase is a cone with base diameter 16cm and height 45cm. The third vase is a sphere with diameter 18cm.

Which vase should I purchase?
How much more water does the largest vase hold than the smallest vase?
Suppose the diameter of each vase decreases by 2cm. Which vase would hold the most water?
The vase company designs a new vase that is shaped like a cylinder on the bottom and a cone on top. The catalog states that the width is 12cm and the total height is 42cm. What would the height of the cylinder part have to be in order for the total volume to be 1,224 π cm³?
Design your own vase with composite shapes, determine the volume, and write an ad for the catalog.

Guiding Questions

What do you notice about the diagrams? What do you wonder?
Describe the shapes and measurements that are involved in this problem.
What is your strategy or approach to solve this problem? What are your peers’ approaches?
Do you have all of the information you need to solve the problem?
How will you organize your work space?

Notes

Students choose or are assigned one of the five Anchor Problems (#2 - #6) to work on with a small group of peers. After collaboratively developing a strategy and preparing a solution, students should create a poster of their response.
Day 1: Students in small groups should develop their approach or strategy to solve the problem and begin solving.
Day 2: Students in small groups finalize their solution and prepare a poster to represent their response. Students do a gallery walk around the room and complete Anchor Problem #7.

Anchor Problems - Problem 6

Option #5: Tennis & Golf Balls

Tennis balls are packaged into cylindrical cans to ship and sell. Three tennis balls fit into one cylinder so that the height of the three balls is equal to the height of the cylinder, and the diameter of one ball is equal to the diameter of the cylinder.

The radius of one tennis ball is $${1.3}$$ inches. How much air space is in the cylinder around the tennis balls?

Golf balls are sometimes packaged into square prisms to ship and sell. Three golf balls fit into one square prism, similar to how the tennis balls fit into the cylinder.

What is the formula for the volume of the square prism? Give your answer in terms of $$d$$, the diameter of the golf ball.
The volume of the square prism is $${192 \space \mathrm{cm}^3}$$. What is the diameter of one golf ball?
How much air space is in the square prism around the golf balls?

Guiding Questions

What do you notice about the diagram? What do you wonder?
Describe the shapes and measurements that are involved in this problem.
What is your strategy or approach to solve this problem? What are your peers’ approaches?
Do you have all of the information you need to solve the problem?
How will you organize your work space?

Notes

Students choose or are assigned one of the five Anchor Problems (#2 - #6) to work on with a small group of peers. After collaboratively developing a strategy and preparing a solution, students should create a poster of their response.
Day 1: Students in small groups should develop their approach or strategy to solve the problem and begin solving.
Day 2: Students in small groups finalize their solution and prepare a poster to represent their response. Students do a gallery walk around the room and complete Anchor Problem #7.

Anchor Problems - Problem 7

Choose a problem that you did not solve already and review the work of your peers on their poster.

a. Briefly describe their approach to the problem.

b. Would you have taken a similar approach? Why or why not?

c. Do you agree with their solution?

Guiding Questions

How is this new problem similar to the one your group solved? How is it different?
Did your peers use any of the same approaches that you did in solving your problem?
What questions do you have for your peers who solved this problem?

Notes

This Anchor Problem should be completed on Day 2 after doing a gallery walk of completed posters.
If time allows, match up students from different groups to engage in this Anchor Problem in person.

Fishtank Learning

8th Grade Math
Unit 7: Pythagorean Theorem and Volume
Lesson 16

Objective

Anchor Problems - Problem 1

Anchor Problems - Problem 2

Anchor Problems - Problem 3

Anchor Problems - Problem 4

Anchor Problems - Problem 5

Anchor Problems - Problem 6

Anchor Problems - Problem 7

Problem Set

Target Task

Fishtank Learning

8th Grade MathUnit 7: Pythagorean Theorem and VolumeLesson 16

Objective

Anchor Problems - Problem 1

Anchor Problems - Problem 2

Anchor Problems - Problem 3

Anchor Problems - Problem 4

Anchor Problems - Problem 5

Anchor Problems - Problem 6

Anchor Problems - Problem 7

Problem Set

Target Task

8th Grade Math
Unit 7: Pythagorean Theorem and Volume
Lesson 16