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# Pre-Algebra Unit 5: Surface Area and Volume

last edited by 9 months, 1 week ago

# Pre-Algebra Unit 5: Surface Area and Volume

### Unit Driving Question

How are two dimensional and three dimensional objects related to each other in real-world situations?

### Essential Questions

1. How can formulas be used to better understand measurements of 3D objects?

2. What relationships exist between 3D figures, nets, surface area, and volume?

3. How are two dimensional and three dimensional objects related to each other?

### Big Ideas

1. Surface area and volume can be calculated for a rectangular prism.
2. Surface area and volume can be calculated for a cylinder.

# Technology Resources

#### 1 Lesson

• Slicing Solids (OpenUp): This lesson introduces the idea that slicing a three-dimensional figure with a plane results in a two-dimensional cross section. Slicing a fruit or vegetable, dipping the exposed face in paint, and stamping it on a paper helps students focus on the two-dimensional face that is created by the slice. Given two-dimensional representations of how objects are sliced, students practice visualizing the three-dimensional figures and the resulting cross sections.

# Big Ideas for Development Lessons

## Big Idea 1:  Surface area and volume can be calculated for a rectangular prism.

OAS-M: PA.GM.2.1, PA.GM.2.3

### Key Resources

1. Volume of Right Prisms (OpenUp): In this lesson, students learn that they can calculate the volume of any right prism by multiplying the area of the base times the height of the prism. Students make sense of this formula by picturing the prism decomposed into identical layers 1 unit tall. **Note: This activity covers other prisms, not only rectangular prisms.

2. Computing Volume Progressions 1-4 (Illustrative Mathematics): A series of 4 tasks that gradually build in complexity.  The purpose of this series of tasks is to build in a natural way from accessible, concrete problems involving volume to a more abstract understanding of volume.

3. New Boxes From Old (OER Commons):Students find the volume and surface area of a rectangular cardboard box (such as a cereal box), and then figure out how to convert that box into a new, cubical box having the same volume as the original.

### Evidence of Understanding

Evaluate rectangular prisms for their volumes

• Develop a formula to be understood and applied

• Solve Mathematical applications of volume

• Analyze Real-world problems involving volume of rectangular prisms

Evaluate rectangular prisms for their surface areas

• Develop a formula to be understood and applied
• Solve Mathematical applications of surface area

• Analyze Real-world problems involving surface area of rectangular prisms.

• Use decomposition and nets when working with surface area of rectangular prisms.

## Big Idea 2:  Surface area and volume can be calculated for a cylinder.

OAS-M: PA.GM.2.2 PA.GM.2.4

### Key Resources

1. The Volume of a Cylinder (OpenUp): The purpose of this lesson is for students to believe that the volume of a cylinder is the area of the base times the height, just like a prism.

2. Finding Cylinder Dimensions (OpenUp): In this lesson, students have opportunities to reason about V=r2h to solve a variety of problems. They not only compute volumes given radius and height, but also find radius or height given a cylinder's volume and the other dimension by reasoning about the structure of the equation

3. Cubed Cans(OER Commons): In this lesson, students will use formulas they have explored for the volume of a cylinder and convert them into the same volume for rectangular prisms while trying to minimize the surface area.

### Evidence of Understanding

Find the volume of a right cylinder

• Develop a formula to be understood and applied

• Solve mathematical applications of volume in terms of pi

• Analyze real-world problems involving volume of a right cylinder in terms of pi

Find the surface area of a right cylinder

• Develop a formula to be understood and applied

• Solve mathematical applications of surface area in terms of pi

• Analyze real-world problems involving surface area of a right cylinder in terms of pi

• Use of decomposition and nets when working with surface area or right cylinders

Use appropriate measurements and approximations of pi

# Unit Closure

#### 1 Week (includes time for probes, re-engagement, and assessment)

(Choose One)

Smoothie Box (Mars): In this task, you must figure out how to make a cardboard box just big enough for 12 bottles.

Sports Bag (Mars): In this task, you must figure out how to cut out the material to make a cylindrical sports bag.