Standard(s)
Pioneer School
Understanding by Design Template
Teacher_CJ Hanson_________________ Grade____10th Grade Geometry
Date____Oct. 9, 2016________________ Subject____Geometry__________
|Stage 1- Desired Results |
|Established Goals: (TEKs) |
|Geometry |
|(10) Two-dimensional and three-dimensional figures. The student uses the process skills to recognize characteristics and dimensional changes |
|of two- and three-dimensional figures. The student is expected to: |
|b. determine and describe how changes in the linear dimensions of a shape affect its perimeter, area, surface area, or volume, including |
|proportional and non-proportional dimensional change. |
|(11) Two-dimensional and three-dimensional figures. The student uses the process skills in the application of formulas to determine measures |
|of two- and three-dimensional figures. The student is expected to: |
|d. apply the formulas for the volume of three-dimensional figures, including prisms, pyramids, cones, cylinders, spheres, and composite |
|figures, to solve problems using appropriate units of measure. |
| |
| |
|Understandings: (Enduring Understandings) |Essential Questions: |
|Students will understand that identical surface area can result in |How do different dimensions of a 3-D solid affect the volume of the |
|different volumes. |shape? |
| | |
|Students will understand that spatial reasoning can help us know that |If you use only one sheet of paper to fold into a 3-D solid, what |
|not all similar shapes will have identical properties. |shape has the greatest volume? The least volume? |
| | |
| | |
| | |
| | |
|Student will know that, given a sheets of paper (i.e. same surface |Students will be able to determine the volume of a rectangular prism |
|area), which shapes will result in larger/smaller volumes and which |or cylinder given the dimensions, or vise-versa with at least 95% |
|dimensions affect this property. |accuracy. |
| |Given information of a cylinder (i.e. dimensions or volume, students |
| |will be able to identify how each dimension of the cylinder affects |
| |the volume by listing the ratio of dimension change to volume change |
| |with no error. |
|Stage 2- Assessment Evidence |
|Performance Tasks: Students, in a group setting, will construct | Self-Assessments: Individually, the students will explore the |
|different shapes/solids using paper and determine their volumes using |various solids that can be made with the sheet of paper and determine |
|its dimensions. The groups will reflect on which shapes produces the |a shape that will maximize/minimize the volume created. |
|greatest/smallest volumes. | |
|Stage 3 Learning Plan |
|Popcorn, Anyone? |
|A technology integration lesson plan for 10th Grade Geometry |
|Designed by |
|CJ Hanson: chanson@twu.edu |
|[pic] |
|| Summary | Objectives| Duration | Type | Technology Integration | Procedures | Evaluation | Materials Needed | |
| |
| |
|Lesson Summary |
|In this lesson, students will discover and use different volume formulas and make predictions based on observations or conjectures. This |
|lesson uses two 3D shapes (prisms and cylinders) and discusses the difference in volume each produces using the same size paper to form each |
|shape (i.e. same surface area). |
| |
|Objectives |
|Students will be able to determine the volume of rectangular/square prisms and cylinders using information such as the height, radius, |
|circumference, etc. Students will also discover how changes in these pieces of information impacts the volume. |
| |
| |
| |
|Content Standard |
|TEKS |
|Geometry |
|(10) Two-dimensional and three-dimensional figures. The student uses the process skills to recognize characteristics and dimensional changes |
|of two- and three-dimensional figures. The student is expected to: |
|b. determine and describe how changes in the linear dimensions of a shape affect its perimeter, area, surface area, or volume, including |
|proportional and non-proportional dimensional change. |
|(11) Two-dimensional and three-dimensional figures. The student uses the process skills in the application of formulas to determine measures |
|of two- and three-dimensional figures. The student is expected to: |
|d. apply the formulas for the volume of three-dimensional figures, including prisms, pyramids, cones, cylinders, spheres, and composite |
|figures, to solve problems using appropriate units of measure. |
| |
|Duration |
|This lesson should take about 1 to 2 hours, so plan for at least 2 classes. |
| |
|Lesson Type |
| |
|Group activity (3-4 students per group) |
| |
| |
|Technology Integration |
|After the lesson, the students will explore more ways how each dimension of a 3D shape will impact the volume. This website provides an |
|interactive program that allows you to adjust the dimensions of each shape and compare two individual shapes simultaneously. |
|
|ea/explore_it.html |
|OR: |
|Go to learnalberta.ca |
|Select English to continue |
|Go to search bar (located on left side under “Find Resources”) |
|Type in “surface area” and press the enter button or select search |
|On the right, under “Resource Matching Your Criteria,” select the first result. It should be titled “Exploring Surface Area and Volume.” |
| |
|Instructional Procedures |
| |
|Students should work in pairs because they will work together to create the objects and in filling the objects with popcorn. Pass out the |
|Popcorn Prisms Anyone? activity sheet, a piece of white paper, a piece of colored paper, tape, and a ruler to each pair of students. It is |
|helpful to spend time showing students some model rectangular prisms, reviewing the volume formula, demonstrating the prism construction. |
|Popcorn should not be used for the demonstration, but students should be able to see how the prisms fit inside of each other. |
|Circulate around the room as students work through the activity sheet. After students finish Question 2, hand each group a bowl of popcorn and|
|a cup for transferring the popcorn. Suggest to students that one hold the rectangular prism as the other fills the tall prism without spilling|
|the popcorn into the shorter one. If availability allows, watch students during this part of the activity to see their reactions. |
|Question 6 may be difficult for some students. You may choose to guide students by asking them the dimensions of their rectangular prisms. |
|After students conclude that the bases are squares, ask for the formula for finding the area of a square. Students should be able to transfer |
|this knowledge to the volume formula. Ask more advanced students how to relate the side of the rectangular prism to the side of the |
|rectangular piece of paper use to form the prism and create a formula for volume based on this. They should find: |
|V = (w/4)2 · l |
|where l and w are the length and width, respectively, of the original rectangular paper |
|Question 7 can be used as enrichment for students who finish early. Have tactile learners use their original rectangular prisms to determine |
|the length and width by changing the dimension. Encourage students to play with the numbers and explain their methods for solving the problem.|
|At the conclusion of the activity, model the algebraic solution if no students found one. |
|The beginning of the cylinder activity should closely mimic the prism activity. Distribute the same materials and the Popcorn Cylinders |
|Anyone? activity sheet. Again, model the cylinders and have students follow the same steps as in the rectangular prism activity. Show students|
|how to measure the diameter, stressing it is only an estimate, and the lesson should run smoothly. |
|Students may struggle with Question 6. Direct them back to the prisms activity. The example in Question 6 is very important for helping |
|students see concrete examples before tackling the remaining questions. If they copy the answer from the prism activity, ask them why they can|
|substitute radius for side-squared. Once most groups have completed the activity, you should write the following formulas on the board: |
|V = πr2h |
|V = w2h |
|Provide initial values for the radius and the height and ask students how the volume changes as you increase each by one unit. Duplicate the |
|activity for the volume of a square prism. This is a good place to reinforce what the patterns implied with the activities. For enrichment, |
|provide models of square prisms and ask students to compute the change in volume as the sides and height are increased. |
|If time allows, the Comparing Cylinders activity sheet is available to help students understand the concept of calculating radius given |
|circumference and that the circumference of the popcorn cylinder was formed from the side of the rectangular paper. Have materials available |
|for students who want to recreate the cylinders. |
|It is suggested that Questions 1–9 be instructor-led with student input. Select students in different groups to help with the answers and |
|question the students as they build the cylinders. The student pairs should be able to complete Questions 10 and 11 based on the prior |
|questions. |
|To bring closure to this activity, a class discussion of the results is important. Questions for Students can be posted on the board and |
|groups walk around and add their comments for the class discussion. During the discussion, encourage both concrete examples and algebraic |
|reasoning. |
|- Jamie Chaikin (illuminations.) |
|These instructions are directly from Jamie Chaikin’s instructional lesson plan on Illuminations and I do not claim them as my words. |
| |
|Evaluation |
|Provide students with a different sized piece of paper (i.e. non-standard size) and have them compute the volume of the resulting rectangular |
|prism and cylinder. |
| |
|Materials Needed |
|Describe what's needed to implement this lesson. Some of the possibilities: |
|8.5×11 in. white paper |
|8.5×11 in. colored paper |
|Popcorn |
|Paper Plates |
|Cups |
|Tape |
|Rulers |
|Popcorn Prisms Anyone? Activity Sheet |
|Popcorn Cylinders Anyone? Activity Sheet |
|Comparing Cylinders Activity Sheet |
|Popcorn Prisms Anyone? Answer Key |
|Popcorn Cylinders Anyone? Answer Key |
| |
| |
|Works Cited |
|Alberta Learning. Exploring Surface Area and Volume. 2004. Web. 13 September 2016. |
|Chaikin, Jamie. Popcorn, Anyone? 1 January 2011. Webpage. 13 September 2016. . |
| |
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