##
* *Reflection: Staircase of Complexity
Making Sense of the Formula - Section 3: Closer

It seems like I have been working on the formula for volume forever! But, it really hasn't been that many lessons. I really enjoyed the progression of lessons I created in order to build a deep and flexible understanding of volume and its formula. Would it have been much easier to just tell students that when you look at a prism you just have to multiply the l x w x h to find the volume? Of course it would have. But, would have it built a background for understanding volume? No way. Sometimes taking the road less traveled is the right path.

*Finally!*

*Staircase of Complexity: Finally!*

# Making Sense of the Formula

Lesson 9 of 14

## Objective: Students will be able to use and understand the formula for determining volume for a right rectangular prism.

*60 minutes*

#### Opener

*15 min*

In this lesson students will be finally coming to terms with the formula for volume. The previous lessons in this unit have worked towards setting the scene for student self-discovery of the l x w x h formula for volume. I feel it was important to spend time building the background in order to create a deep and flexible understanding of the concept of volume.

Since we are on the path to uncovering the formula for volume, I start this lesson with a quick find the object game. I show the game on the projector and have the students help me uncover the hidden objects.

Amazing Adventures Around the World

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#### Practice

*30 min*

To start our final investigation of uncovering the formula for volume, I have students complete a simple investigation within their partnerships. I give students a copy of the worksheet that includes 10 different right rectangular prisms and four columns for recording answers. The partners need to determine the length, width, height and volume of each prism. While investigating each individual prism, students build the prisms using base ten cubes.

The students need to build the prism exactly as they see it on the worksheet. Then they need to determine the dimensions and volume. Again, the purpose of this investigation is that students come to the conclusion of the formula on their own by seeing why and how the formula works. As I ask them to determine the volume of each prism I am careful not to tell them how to determine the volume. In the previous two lessons the students used addition and multiplication strategies in order to determine the volume of prisms. The final step is to find the formula.

I allow the students time to work and complete the worksheet as I circulate the room and aid with struggling students. I wrap up the activity by facilitating a class discussion about patterns or observations students noticed. I ask probing questions if the formula for volume is reluctant to come out.

#### Resources

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#### Closer

*15 min*

Now that students have uncovered the volume formula and have a deep, flexible understanding of volume it is time to move on to applications. Students should now be able reason abstractly with situations involving volume of right rectangular prisms.

As way form of quick informal assessment I show students a Scholastic Study Jam that covers volume and provides it in a real world context. I show the video to students and pause along the way to ask clarifying questions to students to check for understanding.

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- LESSON 1: Attributes of Solid Figures
- LESSON 2: Naming Solid Figures
- LESSON 3: Practice with Solid Figures
- LESSON 4: Open Nets
- LESSON 5: Fixed Volume
- LESSON 6: The Unit Cube
- LESSON 7: Volume as Addition
- LESSON 8: Volume as Multiplication
- LESSON 9: Making Sense of the Formula
- LESSON 10: Finding Volume with Story Problems
- LESSON 11: Volume of Multiple Objects
- LESSON 12: Volume Task 1
- LESSON 13: Volume Task 2
- LESSON 14: Volume Review