Middle School Mathematics UDL Instructional Unit- Lesson 5 - Culminating Lesson

Mathematics Geometry Unit Lesson 5: Culminating Activity

Objectives:

Students will:

• Determine the volume of rectangular prisms.
• Determine the surface area of rectangular prisms.
• Identify and quantify attributes of a problem that need to be measured.
• Draw a net of a rectangular prism.

Essential Questions:

1. What is the volume of a rectangular prism?
2. What is the surface area of a rectangular prism?
3. How do volume and surface area differ?
4. What is the net of a rectangular prism?

Vocabulary

Area - the measure of the size of the surface of a two-dimensional figure; measured in square units	Complex shape - a figure that includes the elements of two or more simple shapes (triangles, rectangles, squares, circles)
Cubic inch - the volume equal to a cube one inch on each side	Cubic unit - a unit of measurement of volume or capacity
Height - the perpendicular distance of a two- or three- dimensional shape from the base to the opposite vertex	Length - a measurement of the distance from one point to another
Rectangular prism - a three-dimensional figure of which all faces are rectangles	Square inch - the area equal to a square one inch on each side
Square unit - a unit of measurement of area	Surface area - the total area of all the faces or surfaces of a three-dimensional figure
Volume - a measure of the number of cubic units needed to fill the space inside an object	Width - the minimum distance between parallel lines of a figure

Materials:

Culminating Activity Resource Part A

Culminating Activity Resource Part B

Drawings

Grid paper

Tables

Introduction

Revisit/Review Unit and Lesson Objectives Remind the students that throughout these lessons they were to solve real-life and mathematical problems involving area, surface area, and volume.

1. Describe and understand what area measures and the correct units for area measure.
2. Determine the area of rectangles, squares, and triangles using graph paper/manipulatives and formulas.
3. Use appropriate known formulas for area.
4. Determine the area of complex shapes by composing and decomposing figures.
5. Construct the net of a rectangular prism.
6. Determine the surface area of a rectangular prism from a net or using a formula.
7. Describe when surface area is used and why it is important in real life.
8. Describe and understand what volume measures and the correct units for volume.
9. Determine the volume of rectangular prisms using manipulatives and formulas.
10. Describe and understand how surface area and volume of solids differ.
11. Describe when volume is used and why it is important in real life.

Conduct a class discussion on which skills were used to solve different types of problems. Talk about additional strategies they used to implement the skills and solve the problems.

Multiple means of representation: Along with posted lesson objectives in the classroom, students may refer to their individual copies of the objectives and their mathematics journals.

Multiple means of expression: Students can share what they have learned or strategies they used by showing different models, pictures, drawings, etc., used throughout the lessons.

Multiple means of engagement: Share ideas of how these skills have been useful in solving the problems

Additional Considerations for Emerging Readers and Emerging Communicators: As review is conducted, provide the student with all previously used materials, strategies, examples, and supports from previous lessons. Utilize the strategies were the most helpful. Pre-plan information for the student to contribute to the discussion using his/her preferred mode of communication.

Exit Assessment – Culminating Activity

Scenario: Mrs. Sweet owns Grandma's Candied Apples. She makes candied apples and sells them to small shops and large stores. Decisions must be made as to the best boxes for packaging multiple candied apples to be sent to small shops and large stores. Three designs have been presented to her for packaging her candied apples to sell to small shops. For small shops, each candied apple is in its own package, which measures 6 inches by 6 inches by 10 inches. For large stores, Mrs. Sweet needs to have a box designed and net drawn of that box for manufacturing. The candied apples will be packaged in threes. The candied apples box now measures 6 inches by 18 inches by 10 inches. Each large shipping box needs to hold 18 apples. To keep costs down, Mrs. Sweet knows that the boxes she selects must not have more volume than needed. Also, the box with the least surface area will cost less in materials to produce.

Tasks: Part A Select the best shipping box for small stores.

1. Determine how many candied apples will fit into Box A, Box B, and Box C.
• See Culminating Activity Resource Part A Worksheet for drawings of boxes and chart.
2. Determine the volumes of Box A, Box B, and Box C.
3. Determine the surface area of Box A, Box B, and Box C.
4. Make a chart of the above measurements.

	Box A	Box B	Box C
How many apples does the box hold?	12	12	12
Volume of the box	4320 in3	4320 in3	4752 in3
Surface area of the box	2424 in2	864 in2	1392 in2

5. Taking into account Mrs. Sweet wants a box without extra volume and the least amount of surface area, which box best fits Mrs. Sweet's needs? Why?

Tasks: Part B Design the best shipping box for large stores.

1. Design a shipping box that will hold 18 apples packaged in groups of 3.
2. Determine how many packages each shipping box will need to hold.(i.e. 18/3 = 6 packages of 3 apples each)
3. Make a chart showing the box dimension possibilities as well as the volume and surface area for each.

Dimensions - length, width, height	Volume	Surface Area
108 x 6 x 10	6480 in3	3576 in2
54 x 12 x 10	6480 in3	2616 in2
36 x 18 x 10	6480 in3	2376 in2
54 x 6 x 20	6480 in3	3048 in2
27 x 12 x 20	6480 in3	2208 in2
18 x 18 x 20	6480 in3	2088 in2
18 x 12 x 30	6480 in3	6480 in2

4. Taking into account Mrs. Sweet wants a box without extra volume and the least amount of surface area, which box from your designs best fits Mrs. Sweet's needs?
5. Draw a net of your box design that best fits Mrs. Sweet's needs.

Multiple means of representation: Allow students to refer to their mathematics journals and other notes as they solve the problem. Provide students with a copy of the word problem and the tables. Have drawings and manipulatives available for students to use.

Multiple means of expression: Allow students to solve the problem using formulas and/or models and record information into the tables using various formats (computer, paper/pencil, drawings, etc.)

Multiple means of engagement: Ensure each student is actively involved in solving the problem. Encourage students to consider options for solving the problem that will engage them. As you observe students work, use questioning to encourage students to explain their strategies.

Additional Considerations for Emerging Readers and Emerging Communicators

Tasks: Part A

As this is now assessment as opposed to all previous activities in this lesson, the student's first independent attempts solving the problems and answering the question should be observed and recorded for accuracy. If correct answers are required to answer subsequent questions, make a note if the student is not correct, supply the correct information, and move to the next part of the task. For example, if the student does not calculate volume correctly for one box, supply the correct answer so he/she has accurate information to answer the question about which box best fits Mrs. Sweet's needs.

• Provide the student with all previously used materials, strategies, examples, and supports including labeled representations of the boxes.
• Reduce the number of boxes.
• Provide the word problem in symbol-based text.
• Summarize the word problem.
• Highlight important information in the word problem.
• Read the problem to the student or have the student use text reader.
• Give the student step-by step instructions one at a time.
• Provide answer choices for the student to select from.
• Add formulas into chart.

Tasks: Part B

1. Provide access to all the supports used in Tasks: Part A.
2. Decrease the complexity of the task by providing the student with the dimensions of two boxes on the chart instead of requiring the student to create his/her own boxes. Add formulas, etc. to the chart and have the student determine volume and surface area of each (again, providing all supports used in Part A.
3. Provide pre-drawn/cut nets (one for each of the boxes) and have the student identify or select which net matches the box they chose in step 6.
4. As this is now assessment as opposed to all previous activities in this lesson, the student's first independent attempts solving the problems and answering the question should be observed and recorded for accuracy. If correct answers are required to answer subsequent questions, make a note if the student is not correct, supply the correct information, and move to the next part of the task. For example, if the student does not calculate volume correctly for one box, supply the correct answer so he/she has accurate information to answer the question about which box best fits Mrs. Sweet's needs.

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