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GIRL GUIDE COOKIES [DAY 3]

VOLUME OF RECTANGULAR PRISMS

Understand concepts of volume related to rectangular prisms.

Intentionality

Spark Curiosity

Fuel Sensemaking

During Moves

Student Approaches

Consolidation

Reflect and Consolidation Prompts

Resources & Downloads

Educator Discussion Area

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PRESENTATION MODE

Intentionality & Unit Overview

Length of Unit: 5 Days

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DAY 1
DAY 2
DAY 3
DAY 4
DAY 5

Students will determine the volume of a case of cookies measured in boxes of cookies. Students will be given the dimensions of both the case and the box of cookies using a standard unit of measure, centimetres.

Intentionality…

In this task, students will explore the volume of a rectangular prism by determining the number of boxes of cookies contained within the larger case. Students will be shown the dimensions of both the case and box in standard units. Students will have to consider the dimensions of the case and each box as they visualize how the boxes can be organized within.

This task will allow students to explore a concrete volume model and develop a deeper understanding of big ideas, including the following:

  • Volume and capacity can be measured using non-standard and standard units;
  • A rectangular prism has three views. It can be viewed from the top, front and side. Each of these three faces are two dimensional, with a length and a width;
  • A rectangular prism has three dimensions, which can be described using three linear measurements; the length, the width and the height;
  • The measurements of length, width, and height are used to determine volume;
  • Volume can be determined by multiplying the area of the base by the height of the prism;
  • Volume is related to the operations of multiplication and addition;
  • A solid figure which can be packed without gaps or overlaps using a quantity of unit cubes is said to have a volume of that same quantity of cubic units.

Spark Curiosity

What Do You Notice? What Do You Wonder?

Show students the video below displaying the case of cookies.

After showing the Spark video, consider leaving the following still image on the screen:

Girl Guide Cookies [Day 3] - How Many Boxes - 02 - Spark Image

Ask students to engage in a notice and wonder protocol. Anything and everything that comes to mind is fair game.

Write down all of the students’ noticings and wonderings. For example:

  • A box.
  • Are these cookies for a school fundraiser?
  • How many cookies are there?
  • How many boxes are in the case?
  • How much does it weigh?
  • How much does each box cost?
  • How much does the whole case cost?
  • And many others…

Take time to acknowledge the noticing and wondering your students have engaged in and try to answer any that you can address right away.

  • Yes, these are cookies from a fundraiser at school for the upcoming year end field trip.
  • There are individual boxes packed inside.
  • Each box costs $5.00

Estimation: Prompt

Land on the following question:

How many boxes of cookies are there in one case?

Make an estimate.

Follow up that question with:

How might we convince someone that the quantity you came up with is correct?

Girl Guide Cookies [Day 3] - How Many Boxes - 02 - Spark Image

Give them time to make estimates based on what they saw and share with their peers.

Ask students to estimate a number of boxes that they think is too high and a number of boxes that they think is too low before making their “best estimate”. Ask them to visualize how the boxes might be organized inside the case.

Encourage students to share their estimates and justification.

Estimation: Partial Reveal

Now, share the following image which gives students an opportunity to make a spatial comparison between an individual box of cookies and a case of cookies.

Girl Guide Cookies [Day 3] - How Many Boxes - 03 - Spark Update Estimate Image

Allow students to share their reasoning with their table groups.

Fuel Sense-making

Crafting A Productive Struggle: Prompt

After sharing out their estimates, have students improve the precision of their estimates by using the following images and they must convince their mathematical community of peers as well as the teacher.

Prompt:

Here are the dimensions of a box of cookies as well as the whole case. Without the use of a calculator, update your estimate. Consider using tools and representations to help you think as well as to represent your thinking.

Girl Guide Cookies [Day 3] - How Many Boxes - 04 - Sense Making - Prompt Image With Measurements

Set students off to work and construct their arguments for how many boxes of cookies can fit in a case.

During Moves

While Students Are Productively Struggling…

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Student Approaches

Student Approach #1: Linking Cubes with Skip Counting and Addition

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Student Approach #2: Pictorial Representation with Addition

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Student Approach #3: Area Model and Multiplication Using Distributive Over Addition and Over Subtraction

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Next Moves

Reveal

Once you have consolidated the learning and made connections across different student solution approaches, you can share the following reveal video:

Alternatively or after showing the video, you can show this still image.

Girl Guide Cookies [Day 3] - How Many Boxes - 08 - Next Moves - Reveal Image

Answer: 12 boxes of cookies.

Revisit the students’ answers. Ask students why their answers may or may not have been exact.

Consolidation

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Reflect and Consolidation Prompts

Provide students an opportunity to reflect on their learning by offering this consolidation prompt to be completed independently.

Consolidation Prompt #1:

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Consolidation Prompt #2:

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Consolidation Prompt #3:

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We suggest collecting this reflection as an additional opportunity to engage in the formative assessment process to inform next steps for individual students as well as how the whole class will proceed.

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