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9-12 Geometry Unit 5

Gradeband

K-5 Math 6-8 Math •9-12 Math

Course

Algebra 1 •Geometry Algebra 2 Extra Support Materials for Algebra 1

Unit

Unit 1 Unit 2 Unit 3 Unit 4 •Unit 5 Unit 6 Unit 7 Unit 8

Modeling Prompts

K-5
6-8
9-12

Algebra 1
Geometry
Algebra 2
Extra Support Materials for Algebra 1

Integrated Math 1
Integrated Math 2
Integrated Math 3

Unit 1
Unit 2
Unit 3
Unit 4
Unit 5
Unit 6
Unit 7
Unit 8

Modeling Prompts

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Unit 5

Student Learning Targets

Geometry

Section ACross-Sections, Scaling, and Area

1

Solids of Rotation

I can draw the two-dimensional shape that creates a particular three-dimensional solid when rotated using a given axis.
I can identify the three-dimensional solid created by rotating a two-dimensional figure, using a linear axis.

2

Slicing Solids

I can identify the three-dimensional shape that generates a set of cross-sections.
I can visualize and draw multiple cross-sections of a three-dimensional figure.

3

Creating Cross-Sections by Dilating

I know that a pyramid’s cross-sections are dilations of its base, with scale factors ranging from 0 to 1.

4

Scaling and Area

I know that when figures are dilated by a scale factor of , their areas are multiplied by .

Section BScaling Solids

Section CPrism and Cylinder Volumes

Section DUnderstanding Pyramid Volumes

Section ELet’s Put It to Work

5

Scaling and Unscaling

I can use square root graphs and do calculations to interpret the relationships between scale factors and areas.

6

Scaling Solids

I know that when a solid is dilated by a scale factor of , its surface area is multiplied by and its volume is multiplied by .

7

The Root of the Problem

I can create and describe graphs that show relationships between volumes and scale factors.
I can work backward from a volume or surface area scaling to find a scale factor.

8

Speaking of Scaling

I can calculate scale factors for lengths, surface areas, and volumes if I’m given any one of the three factors.

9

Cylinder Volumes

I can calculate volumes of solids that are composed of cylinders.
I can explain how finding the volume of a prism relates to finding the volume of a cylinder.

10

Cross-Sections and Volume

I know that if two solids have equal-area cross-sections at all heights, they have the same volumes.

11

Prisms Practice

I can calculate volumes of right and oblique prisms and cylinders and figures composed of prisms and cylinders.

12

Prisms and Pyramids

I can explain the relationships between pyramids, cones, prisms, and cylinders.

13

Building a Volume Formula for a Pyramid

I can explain why the volume formula for pyramids and cones is .

14

Working with Pyramids

I can calculate volumes of pyramids and cones.
I can work backward from a given volume to find possible dimensions of a pyramid or cone.

15

Putting All the Solids Together

I can use the Pythagorean Theorem and trigonometry to help calculate volumes of prisms, cylinders, cones, and pyramids, including solids of rotation.

16

Surface Area and Volume

I can use surface area and volume relationships to solve problems.

17

Volume and Density

I can solve problems involving density and volume.
I know that the density of an object is the ratio between its mass and its volume.

18

Volume and Graphing

I can use cube root and square root graphs to solve geometric problems.