## Tree Modeling Word Problem.docx - Section 4: Modeling with Geometry - Density and Trees

# Pyramids and Spheres Exploration

Lesson 3 of 4

## Objective: Students will be able to derive volume formulas for pyramid and sphere and apply these.

*99 minutes*

#### Do Now

*10 min*

Students will complete a Do Now question reviewing how to find the volume of a cylinder. Students will be asked to find how much paint can be contained in a paint can with a given diameter. This Do Now will help students review what real-world situations to apply volume to, and also how to use the formula for volume of a cylinder. You may want to point out (or ask students to predict!) that a common mistake that students make in this problem is calculating the volume with diameter rather than radius.

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Before starting the play dough activity, it may be worthwhile to review some important ground rules using this manipulative. I also usually give students a minute or two just to play with it before we jump into our class notes; they are usually very excited about using this. I ask students not to make it into different shapes or crumble the play dough. I also like to demonstrate how to cut through the play dough cleanly using the plastic knife.

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In this section, students will have an opportunity to tackle a challenging problem involving rate, density, volume and modeling geometry in a real-world situation. Teachers with ESL students may want to consider preparing students for some new words, like timber, and also may want to review how to convert centimeters into meters. Get your calculators ready, this is a challenging task!

#### Resources

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**Practice**: After completing both the play dough activities and also the class examples of pyramids and spheres, there are 5 practice examples for students to work on in pairs or independently. If time is left in the class, students can write their work on the board and present this to their classmates.

**Exit Ticket****: **Students will find the volume of the Khufu pyramid in Egypt based on its real-world dimensions.

##### Resources (5)

#### Resources

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- UNIT 1: Introduction to Geometry: Points, Lines, Planes, and Angles
- UNIT 2: Line-sanity!
- UNIT 3: Transformers and Transformations
- UNIT 4: Tremendous Triangles
- UNIT 5: Three Triangle Topics
- UNIT 6: Pretty Polygons
- UNIT 7: MidTerm Materials
- UNIT 8: Circles
- UNIT 9: 3-D Shapes and Volume
- UNIT 10: Sweet Similar Shapes
- UNIT 11: Trig Trickery
- UNIT 12: Finally Finals