In this Warm-up, students apply the pyramid volume formula to explore how different sets of dimensions in solids can produce the same volume.

The goal is to make sure students understand how to apply the volume formula for a pyramid. Ask students to explain why the rectangular prism has the same volume as the pyramid. The prism has the same base as the pyramid, but it has the height. So, when we use for the prism and for the pyramid, the results are the same.

Math Community

After the Warm-up, display the revisions to the class Math Community Chart that were made from student suggestions in an earlier exercise. Tell students that over the next few exercises, this chart will help the class decide on community norms—how they as a class hope to work and interact together over the year. To get ready for making those decisions, students are invited at the end of today’s lesson to share which “Doing Math” action on the chart is most important to them personally.

The purpose of this activity is for students to practice solving problems that involve volumes of pyramids and cones. Monitor for various problem-solving strategies—in particular, for the problem in which students find the radius or height of a cone given a particular volume. Some students may substitute values into a formula and solve the resulting equation, and others may follow a process of deductive reasoning.

In this activity, students are building skills that will help them in mathematical modeling (MP4). They apply their understanding of pyramid volumes to find possible dimensions of a pyramid given its volume. They are asked to create multiple designs of an ice sculpture that meet the given criteria. 

In the digital version of the activity, students use an applet to create three-dimensional shapes that match given information about the volume. The applet allows students to first create a two-dimensional base before extruding it to a three-dimensional solid and checking its volume. The digital version may be preferable to help students visualize their pyramids accurately.

Monitor for students who start by using trial and error to find values, and for those who begin by setting one value and calculating the others.

Many students may use squares and rectangles for their bases. Listen for students who consider other shapes.

This is the first time Math Language Routine 6: Three Reads is suggested in this course. In this routine, students are supported in reading a mathematical text, situation, or word problem three times, each with a particular focus. During the first read, students focus on comprehending the situation. During the second read, students identify quantities. During the third read, the final prompt is revealed and students brainstorm possible starting points for answering the question. The intended question is withheld until the third read so students can make sense of the whole context before rushing down a solution path. The purpose of this routine is to support students’ reading comprehension as they make sense of mathematical situations and information through conversation with a partner.