- Lesson Plan Template: General Lesson Plan
Learning Objectives: What should students know and be able to do as a result of this lesson?
The students will work with surface area through the use of nets and volume with the use of cubes. The students will be able to determine if two rectangular prisms have the same surface area, if the volume is the same. They will also be able to determine if there is a general relationship between volume and surface area (one is always bigger or smaller than the other).
Prior Knowledge: What prior knowledge should students have for this lesson?
Students need prior knowledge of area, and should understand volume is how much is contained in a three-dimensional figure.
Guiding Questions: What are the guiding questions for this lesson?
If the volume of two or more rectangular prisms is the same, will the surface area be the same?
Is the surface area always bigger, or always smaller than the volume?
Teaching Phase: How will the teacher present the concept or skill to students?
1- Have the students cut out the rectangular prism net. While they are cutting, explain, "This graph is called a net. This net is an unfolded rectangular prism. When it is refolded, we can fill it up to show volume. The rectangular prisms and nets in this lesson are measured in centimeters."
2- Have the students fold the figures into a rectangular prism.
3- "Looking at your rectangular prism, what can you tell me about it?" (It has 6 faces (sides). It is constructed of rectangles. The opposite faces are the same size.)
4- "The opposite faces are the same size. Lightly color (so boxes can still be seen) the same faces A and D a color, B and E a second color, and finally C and F a third color."
5- "If we wanted to find the area of one face (side) of the rectangular prism, a rectangle, what would we do?" (Area = length times width)
6- "With your group, can you come up with a way to find the area of all six faces? This is called the surface area." The goal is to see the students multiply 2x4 for rectangles A and D then multiply by 2 to represent both the rectangles, then 3x4 times 2 for rectangles B and E, and 2x3 times 2 for rectangles C and F. (2lw + 2hw + 2lh). The surface area will be 52 square centimeters.
7- Give the students the manipulative blocks. Have the students refold their rectangular prism. Next to it have them construct a rectangular prism out of the centimeter manipulative cubes matching the paper rectangular prism. In their group, have students discuss ways to find the volume. (count the blocks, multiply the length, width and height.)
8- What is the volume of this prism? (2x3x4=24 cubic centimeters)
Guided Practice: What activities or exercises will the students complete with teacher guidance?
9- Give every student a copy of the chart worksheet. Have them fill in the answers to the example.
10- "This rectangular prism is 2x3x4. That is not the only way you can lay it out. Individually, create another rectangular prism that has a volume of 24. It can only use the 24 blocks you already have." Give the students a few minutes to brainstorm and lay out their new prism. Encourage them to be different than the others in the group.
11- "Decide which measurement is the length, width, and height. Write your name under the word "Sample" and enter these measures into your chart. We know the volume is still 24 cubic centimeters because we did not add or remove any cubes. This value is already filled in for you."
12- Give the students a piece of centimeter graph paper. Have them make their own net of the rectangular prism they just created out of the 24 cubes. Have them use the prior measures and net, to assist in creating this new net. Encourage them to seek help from the group first, before coming to you. Circulate through the room and make sure students are not getting frustrated and assist struggling students if needed.
13- Once the prisms are drawn, cut out, and folded; have the students share the prism with the group. (Hopefully, there should be variations including 1x2x12, 1x3x8, 1x1x24, and 2x2x6.) Is the prism that is 2x6x2 different than the 6x2x2 or 2x2x6? (Others can be demonstrated as well. It is easier with the folded net, than with the blocks on some of these combinations.) Point out variations between the groups if appropriate.
14- Have students trade the net prisms within the group and find the surface area. Write the information on the chart (include the name of the person who made the net). Compare with the creator to make sure the calculations are correct. (Can be repeated 2 more times as time allows).
Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the lesson?
15- Give the students more graph paper. Have them create another rectangular prism net. Encourage some of them to use as much of the paper as they can. They can also use scraps from the last prism they cut out. Provide tape if necessary. Again, all of the prisms should be different. Walk around the room and make sure the students and/or groups are not in need of help. This net should NOT have a volume of 24 cubic centimeters.
16- When constructed, the students should find the surface area of their net.
17- Before having students find the volume, have them lay out one layer of their blocks to represent the length and width (or base) of the figure. For the larger figures this could end up being more cubes than they have. A 6x6 base would take 36 cubes. Making it a height of 6 would require 216 cubes. "While it might have been practical in our original example of 24 cubic centimeters, do you still just want to count the number of cubes in the volume?" (For most the answer will be no). "Find the volume of your rectangular prism and record your results on the chart."
18- "Make sure your name is on your prism and trade with someone in your group. Find the surface area and volume for your new prism. Record findings on your chart. When you have completed the computations, check with the creator of the net to make sure you both have the same value."
19- Depending on time, students can trade multiple times and even between groups.
Closure: How will the teacher assist students in organizing the knowledge gained in the lesson?
20- Have the students complete the writing activity at the bottom of the worksheet. "Write a paragraph summarizing your groups findings. If the volume of two or more rectangular prisms is the same, will the surface area be the same? Is the surface area always bigger, or always smaller than the volume? Justify your answers."
The results of the worksheet will be used to determine mastery of the learning objectives.
Students will be observed in their groups while creating the nets and completing the chart. Students should complete the computations with paper and pencil, and be given feedback as needed, while working. First, the chart will be checked, with a key, for the proper surface area based on the length, width, and height choosen. Second, the students' explanation of the groups' findings (as supported by the chart) will be read and discussed with the student.
Feedback to Students
Students will provide feedback to each other. They will assist each other in completing the task. They will trade nets and see if classmates determine the same answer.
Students will be given feedback, as needed, while completing the chart and surface area nets.
Worksheet will be corrected. Explanation of findings and justification will be evaluated. Misconceptions will be corrected as needed and counter examples provided if necessary.