Middle School Mathematics UDL Instructional Unit- Lesson 4
Contents |
Objectives
- Students will solve real-life and mathematical problems involving area, surface area, and volume.
Essential Questions
- How do we find the volume of a rectangular prism?
- Where is volume used in real life, and why is it important?
- What is the difference between surface area and volume?
Vocabulary
| Cubic foot - the volume equal to a cube one foot on each side | Cubic inch - the volume equal to a cube one inch on each side |
| Face - a flat surface of a three dimensional figure | 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 | 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 |
| Rectangular prism - a three-dimensional figure of which all faces are rectangles |
Materials
Cubes
- Centimeter cube
- Inch cubes
- Foot cubes
Box Grid paper Rubik's® cube
- Graphic representation of Rubik's® cube
Ruler Scissors Template of the formula for volume Water bottle Worksheet - Lesson 4 Practice
Introduction
Activate Previous Knowledge
- Remind students that they have been working on the concepts of area and surface area.
- Review with students the units used to measure area and surface area (square centimeters, square inches, square feet, and square meters).
- Discuss how they can use this knowledge to solve problems they encounter in the "real world".
- Present the students with a Rubik's® cube and a box.
- How would you find the surface area of each?
- How many Rubik's® cubes will fit in the given box?
- How can we find out how many Rubik's® cubes will fit in the given box?
Multiple means of representation: Use models and/or drawings during large group instruction. Allow students to have a copy of a drawing or model at their desks.
Multiple means of expression: Provide a list of formulas to determine surface area or provide options for using manipulatives and/or computer models.
Multiple means of engagement: Allow students to use paper/pencil, manipulatives, computer, etc.
Additional Considerations for Emerging Readers and Emerging Communicators If the student has had little to no experience with the concept of volume or the skill of calculating volume, it might be helpful to provide instruction using the Lesson 4 Concept Reinforcement Activity (CRA) prior to teaching the Introduction to Lesson 4.
- Provide the student with all materials and supports he/she has previously used in Lessons 1-3, including definitions, examples, formulas, etc.
- Provide examples in symbol-based text, with added visual and tactile characteristics, photos, digital animations with sound accessible through AT, etc.
- Allow the student to use all materials and supports to answer questions using his/her preferred mode of communication.
- Provide options for the student to select from.
- Allow the student to move the Rubik's® cube around in the box before estimating.
- Provide options for the student to select from.
b. Establish Goals/Objectives for the Lesson Inform students of the goals/objectives for this lesson. Share with them that they will make decisions as to the appropriate measurements and formulas to use in solving real world and mathematical problems involving the volume of rectangular prisms. Explain that they will:
- Describe and understand what volume measures and the correct units for volume measurements.
- Determine the volume of rectangular prisms using manipulatives and formulas.
- Describe when volume is used and why it is important in real life.
- Describe and understand how surface area and volume of solids differ.
Multiple means of representation: Along with posting lesson objectives in the classroom, provide individual copies for students.
Multiple means of expression: Allow students to record lesson objectives in different formats: mathematics journal, computer, graphic organizers (premade or original), etc.
Multiple means of engagement: Brainstorm ideas of how and when these skills might be relevant to "me."
Additional Considerations for Emerging Readers and Emerging Communicators
- Provide definition and unit measures for volume with or without symbol-based text, with textures, other tactile qualities, colors, etc. (resources such as Standard Tactile Symbol List available from the Texas School for the Blind www.tsbvi.edu/tactile-symbols may be useful in determining representations; some representations may need to be pre-taught (Rowland, 2012), but use of the same representations/symbols \[or the system\] during this and other lessons will reduce the need for pre-teaching).
- Provide definitions and images of rectangular prisms with or without symbol-based text, with textures, other tactile qualities, colors, etc.
- Provide formulas and examples of volume of rectangular prisms with or without symbol-based text with textures, other tactile qualities, colors, etc.
- Provide calculator (large button, handheld, talking, or computer-based).
- Provide manipulatives and concrete representation at least one rectangular prism to use in calculating volume. Add textures, color, sound, etc. as needed.
- Provide real-life examples of using volume with or without symbol-based text.
- Provide real-life examples of using volume with pictures.
- Provide real-life examples of using volume with animated digital displays including sound.
- Provide graphic organizer, such as a T- chart showing the differences between surface area and volume.
- Add symbol-based text to organizer and information.
- Put information on cards so the student can sort information into correct columns.
- Use hook-and-loop tape.
- Add texture to outline graphic organizer and background of column categories.
- Add color for interest.
- Color code information according to categories so the student can match colors to sort information.
- Provide graphic organizer digitally with sound so the student can manipulate information using AT.
Body
- Lead a discussion about what volume is: the measurement of space occupied in three dimensions.
- Show students that volume is the space taken up inside of something.
- Ask the students: When we put the Rubik's® cubes in the box, what were we finding?
- Give an example of a cubic unit such as a one-inch cube. Explain to students that since volume is a measurement made in three dimensions, the units used are cubic.
- Also show students a cubic centimeter and cubic foot.
- Ask students: What unit would you use when measuring the volume of a cereal box?
- Find the volume of a box using inch cube blocks and the formula.
- Have students see how many inch cube blocks it takes to fill a box.
- Ask the students: If the blocks fill all of the space in the box, what is the volume of the box?
- Ask the students:
- What is the length of the box?
- What is the width of the box?
- What is the height of the box?
- Show the students that the volume of the box can be found by multiplying length times width times height.
- Ask the students: How does the volume found using cube inch blocks compare to using the formula?
- Ask the students: What would be the volume of the pictured box?
- Discuss with students how surface area and volume measurements differ.
- Given the scenario of Sophia using wrapping paper to wrap a gift in a box, ask the students: What part relates to surface area? (the wrapping paper, because it covers the entire surface of the box)
- What part relates to volume? (the gift, because it must fit inside the box)
- What unit would you use to measure the wrapping paper?
- What unit would you use to measure the volume?
Multiple means of representation: Use models and/or drawings during large group instruction. Allow students to have a copy of a drawing or a model at their desk.
Multiple means of expression: Provide the formula to determine the volume of a rectangular prism, or provide options for using manipulatives and/or computer models.
Multiple means of engagement: Allow students to use paper/pencil, manipulatives, computer, etc., to complete exercises. Present information in context of student interests (pets, gardening, new bedroom floor plan, etc.).
Additional Considerations for Emerging Readers and Emerging Communicators
- Using the rectangular prism and manipulatives provided in the introduction, have the student mirror the teacher's demonstration of volume.
- Allow the student to use his/her preferred mode of communication.
- Give the student a one-inch cube.
- no additional supports
- Give the student concrete representations of a cubic centimeter and a cubic foot.
- Give the student a cereal box and have him/her explore which will fit inside – the inch cube or the foot cube.
- Provide the representations digitally, and provide access through AT.
- Allow the student to use his/her preferred mode of communication to answer.
- Give the student enough inch cubes to fill the cereal box.
- Provide the cubes and box digitally with access through AT.
- Cut the front from the box on three sides, leaving the bottom connected so that the front can be "hinged" or folded back. This will allow the student to fill the box while the box lay on its back, creating a more visually easy way to see when the box is full.
- Count the cubes that fill the box.
- Touch and count.
- Place the cubes on a number line.
- Use a calculator with the "+1" function.
- Allow the student to use his/her preferred mode of communication.
- Indicate where to find the length, width, and height of the box on the sides of the box (on digital access, too, if that is being used). Have the student measure (use any supports previously used in measuring) or line up the inch cubes to find the dimensions of the box (this may be digital, as well).
- Provide the formula.
- Allow the student to use a calculator.
- Provide choices of "same" or "different" so the student can choose the answer using AAC.
- Provide representations of the gift and wrapping paper (rectangular prism, net, photos, digital, etc.).
- Provide the student with the choices of "gift" and "paper" in his/her preferred mode of communication. Allow the student to select the answer. Correct as necessary demonstrating why the answer(s) is correct.
- Provide the choices of "inches" and "square inches" in the student's mode of communication. Allow the student to select the answer. Correct as necessary demonstrating why the answer(s) is correct.
- Provide the choices of "inches" and "cubic inches" in the student's mode of communication. Allow the student to select the answer. Correct as necessary demonstrating why the answer(s) is correct.
Practice
- Have students work in pairs on a variety of problems using different rectangular prisms with some students only using dimensions to determine volume. Use Lesson 4 Practice Worksheet.
- Give each student the formula for finding the volume of a rectangular prism:
- Bring the whole group back together.
- Have a student from each pair discuss how they found the answer to a question.
- After going over the practice, ask students: Is important to know how much an object holds?
- Is it important to know the measure of the surface? Why or why not?
Multiple means of representation: Provide students with a copy of the word problems and a template of the volume formula. Have drawings and manipulatives available for students to use.
Multiple means of expression: Allow students to solve the problems using formulas and/or models.
Multiple means of engagement: Ensure each student is actively involved in his/her partnership. Present different problems related to student interests. As you observe group work, use questioning to encourage students to explain their strategies.
Additional Considerations for Emerging Readers and Emerging Communicators
- Provide inch cube manipulatives, which can represent different cubic units of measure in the problems (inch, centimeter, foot, meter, etc.) and measurement, calculation, and writing supports previously provided (including, digital, AAC, and AT).
- Provide the formula using the same supports as previously provided.
- Preplan a discussion contribution using the student's preferred mode of communication.
- Allow the student to use previously provided examples to answer the question.
- Allow the student to use previously provided examples to answer the question.
Closure
Revisit/Review Lesson and Objectives Remind students of the lesson's objectives and expected student outcomes. Have students discuss which of the lesson's problems addressed the objectives below and what they learned from their experiences. Student will solve real-life and mathematical problems involving area, surface area, and volume.
- Describe and understand what volume measures and the correct units for volume measurement.
- Determine the volume of rectangular prisms using manipulatives and formulas.
- Describe when volume is used and why it is important in real life.
- Describe and understand how surface area and volume of solids differ.
Ask students: What are some examples of situations in which we use volume in real life?
Multiple means of representation: Along with posting lesson objectives in the classroom, students may refer to their individual copies.
Multiple means of expression: Students can share what they have learned in different formats through writing, drawing, creative expression, discussion, etc.
Multiple means of engagement: Share ideas of how and when these skills might be relevant to "me."
Additional Considerations for Emerging Readers and Emerging Communicators
- As review is conducted, provide the student with all previously used materials, strategies, examples, and supports.
- Preplan information for the student to contribute to the discussion using his/her preferred mode of communication.
Exit Assessment
Give students a new problem:
Students will be making models of an open cardboard box to find the greatest volume they can create from a piece of cardboard measuring 10 cm by 12 cm. The dimensions of the box are to the nearest whole centimeter. Students will use a piece of grid paper to make the model.
Steps:
- Cut out a 10-unit by 12-unit square from the grid paper.
- Cut a 1 by 1 square out of each corner and fold to form a box.
- Record the length, width, and height of the box in the chart and figure the volume.
- Cut 2-unit-by-2-unit squares from each corner and fold to form a box.
- Repeat steps two and three.
- Cut 3-unit-by-3-unit squares from each corner and fold to form a box.
- Repeat steps two and three.
- Cut 4-unit-by-4-unit squares from each corner and fold to form a box.
- Repeat steps two and three.
Use the table to answer this question: What are the dimensions of the box with the greatest volume?
| Length of side corner | Length of box | Width of box | Height of box | Volume of box |
| 1 cm | ||||
| 2 cm | ||||
| 3 cm | ||||
| 4 cm |
Multiple means of representation: Provide students with a copy of the word problem, drawn models of the situation, and/or formulas as needed/requested.
Multiple means of expression: Allow students to solve the problem using the formula, drawings, computer graphics, and/or models.
Multiple means of engagement: Create situations that include areas of interests to the students.
Additional Considerations for Emerging Readers and Emerging Communicators
- Provide all supports previously provided (measuring, calculating, definitions, formulas, worksheets, examples, writing, cutting, etc.).
- Provide visual/tactile/verbal cues for folding.
- Precut and pre-fold the paper into boxes.
- Provide digital representations of the boxes.
- Decrease the number of problems to solve.
- Provide answer selections.
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.
