Pyramids and Spheres Exploration

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

Big Idea

Students will use play dough to discover the volume formulas for pyramids and spheres.

Do Now

10 minutes

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.    

Introduction to Play Dough Activity

4 minutes

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. 

Exploration for Pyramid and Sphere Volume

50 minutes

Modeling with Geometry - Density and Trees

20 minutes

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!

Practice/Homework and Exit Ticket

15 minutes

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 TicketStudents will find the volume of the Khufu pyramid in Egypt based on its real-world dimensions.