This site includes public domain images or openly licensed images that are copyrighted by their respective owners. The Illustrative Mathematics name and logo are not subject to the Creative Commons license and may not be used without the prior and express written consent of Illustrative Mathematics. Spanish translation of the "B" assessments are copyright 2020 by Illustrative Mathematics, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0). The second set of English assessments (marked as set "B") are copyright 2019 by Open Up Resources, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0). Īdaptations and updates to IM 6–8 Math are copyright 2019 by Illustrative Mathematics, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).Īdaptations to add additional English language learner supports are copyright 2019 by Open Up Resources, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0). OUR's 6–8 Math Curriculum is available at. It is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0). IM 6–8 Math was originally developed by Open Up Resources and authored by Illustrative Mathematics®, and is copyright 2017-2019 by Open Up Resources. Privacy Policy | Accessibility Information The second method requires visualizing the solid in a different way, but we only needed to find the area of two different pieces (the long rectangle and base). While the calculations using this method were simple, there were more pieces. If not brought up in students’ explanations, explain to students that the first method requires finding the area of 6 different shapes (there are 7 faces, but the two bases are the same). “Could you solve for volume with the measurements given in the picture? If so, are there any unnecessary measurements? If not, what else would you need to know?”.“Do you need to know all of the measurements in the picture to solve for surface area?” (No, you just need to know the perimeter and area of the base and the height of the figure.).“Do you think you will prefer the same method for every problem? Why or why not?”.“Which method do you prefer for this problem? Why?”.“How many different shapes did you need to calculate the area of when using the second method (using perimeter of base)?”.“How many different shapes did you need to calculate the area of when using the first method (calculating area of all the faces)?”.“How did you find any other areas you needed to solve the problem?”.“How did you find the area of the base?”.To highlight the difference between the two methods, ask: Select previously identified students to share the discussion they had with their partner. Solids with holes, such as the triangular prism with a square hole, can use a variation on Elena’s method: two congruent triangles with holes for the bases, one rectangle for the outside side faces, and another rectangle for the faces forming the hole.Įxplain to students that they will have the opportunity in the next activity to practice using any of these strategies. For other shapes, such as pyramids, Noah’s method of finding all the faces individually or Elena’s method of combining those faces into identical copy groups will work. This can be more efficient than the other methods because students only need to calculate two areas (since the two bases will be identical copies). Prisms can always be cut into three pieces: two bases and one rectangle whose length is the perimeter of a base and whose width is the height of the prism.The length of the rectangle will be the same as the perimeter of the base and the width of the rectangle will be the height of the prism. Andre’s method does always work even if the rectangles have different widths.Elena’s method will not always work because the rectangles will not always be the same size, but we can notice that some shapes are the same and not have to work them all out individually.Noah’s method will always work, but it can be inefficient if there are a lot of faces.If not mentioned by students, be sure students understand: “Which of the students’ methods will work for finding the surface area of other three-dimensional figures that are not prisms?” (only Noah’s).“Which of the students’ methods will work for finding the surface area of any prism?” (Noah’s and Andre’s).“Which of the students’ methods will work for finding the surface area of this particular prism?” (all 3).Students may have trouble generalizing which method would work for any prism.
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