# Lesson 12

Prisms and Pyramids

### Lesson Narrative

In this lesson, students analyze relationships between prisms and pyramids. They categorize pyramids and cones as solids with a single base and an apex or central vertex, as opposed to cylinders and prisms which have 2 congruent bases. They extend their understanding of the terms right and oblique to apply to cones and some pyramids.

Then, students assemble a triangular prism out of 3 triangular pyramids, and they make initial observations about these solids. The pyramids they build will be used in the next lesson to develop the formula for the volume of a pyramid.

Students use language precisely (MP6) when they describe characteristics of pyramids, cones, cylinders, and prisms.

### Learning Goals

Teacher Facing

• Compare and contrast (using words and other representations) pyramids, cones, prisms, and cylinders.

### Student Facing

• Let’s describe relationships between pyramids and prisms.

### Required Preparation

Consider creating an extra few sets of nets and pyramids ahead of time. This ensures that all groups will have pyramids to work with even if students struggle to build the pyramids.

Students will reuse their assembled pyramids in the next lesson, so prepare a place to store the pyramids. In the next lesson, it's okay if students don’t use the specific pyramid they built—each group simply needs a complete set of 3 pyramids to manipulate.

### Student Facing

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

Building Towards

### Glossary Entries

• apex

The single point on a cone or pyramid that is the furthest from the base. For a pyramid, the apex is where all the triangular faces meet.