Grade: 5/6

Lesson Title: Investigating the Volume of Rectangular Prism

Date: Dec 10

Curriculum Expectations gr.5 determine through investigation the relationship between the height, the area of the base, and the volume of a rectangular prismgr.6 solve problems involving the calculation of the volume of a rectangular prism

What do students need to know and be able to do? -grade 4-grade 6’s should know how to calculate volume using a formula alreadyLearning GoalsContent:To calculate volume of a rectangular prism, you need to know the area of the base and the height of the prism

Process:- select a strategy to communicate their findings

Lesson Components Anticipated Student Responses and Teacher

Prompts / QuestionsAction! Rationale:This would be an introduction to volume. We have not done any work on it yet.I want us to come up with an activity which would lead to students to making a rectangular prism with just one layer of blocks and then have them see that when we add another layer that the volume is the area of the base times two because we the height has doubles and if we add a third layer the volume is the area of the base times 3 because the height is 3…..this will hopefully lead them to discover (grade 5) or understand (grade 6) the formula for volume.

Investigation:Create a rectangular base using less than 20 cubes. What is the area of the base? Add another layer to your base. How many cubes are in the prism now?Add another layer. How many cubes are in the prism now?Describe what you notice.How many cubes would be in the 10th layer? The 35th layer?

Anticipated Student Responses and Possible Misconceptions

Sample Scaffolding Questions How else can you represent this?How are these ___the same or different?If I do ____, what will happen?How can you prove your answer or verify your estimate?How do you know?Have you found all the possibilities? How could you arrive at the same answer in a different way?

how will students record their information? (chart displays relationships between numbers well)

note relationship between area of the base and the number of the layers

in the 10th and 35th layer – can they develop a generalization, formula or algebraic expression?

* What is the area of the base?We wondered if introducing the work area here confused the concepts of volume and area. Might the question read, “How many squares made up the base of the prism?”

Minds-On AFL

Create a rectangular prism using 12 cubes.How are they the same? How are they different?

What are we listening and looking for from the student conversation and responses?

How do we know it is a rectangular prism?

Height Length and width Bottom/Base layers Unit? Cubes (rather

than squares) Listen for word

volume...Lesson ComponentAfter / Consolidation / Reflecting and Connecting

Consolidation Highlights and Summary(Uncover Learning Goal, Success Criteria)

The following student work was used to consolidate the key ideas in the investigation:

1. Students compared number of layers in the prism to the total number of cubes in the prism in a t-chart. They discussed the title of the right hand column which was “Area” originally. When asked they were able to express that the area was a 2-dimensional figure, like the bottom or face on the “base” of their shape. They then changed the title to “Cubes”, meaning “Number of Cubes in the Shape”.

2. This group used repeated addition and then multiplication to show the number of cubes in each layer of the prism that they created. The amount the prism grew was the same each time. They articulated that multiplication was a faster way to calculate the number of cubes in the solid.

3. The first chart that this group created included a lot of information. They were asked why they crossed out information in the second column; they had determined that the area of the base of their prism remained the same. It was the total number of cubes or the “Volume” that increased with each additional layer.

4. This work by the same group changed the first column as well, replacing the word base with layer. They noticed that the chart shows a pattern where the values increase by 8 and the

number of layers multiplied by the base area determines the number of cubes in the shape. They were then able to use the pattern to determine the number of cubes in the 10th and 35th rows.

Independent Practice: Exit Card Reflection Homework

Student Next Steps (Large Group/Small Group/Individual)

Create a rectangular base using 6 cubes. What is the area of the base? Add another layer to your base. How many cubes are in the prism now?Add another layer. How many cubes are in the prism now?How many cubes would be in the 37th layer?

Students all used a chart to show their thinking in the independent task.Next StepsLarge Group: extend the idea that the base area x height is the volume, and define volumeReinforce the units of measure for area vs volumeSmall Group focus: to recognize that the patterns on the chart can be generalized to determine the number of cubes for any number of layers in the prism.