Comparison of Surface Area and Volume of Cubes

[b]Lesson[/b] [i]Launch
[/i] (5 minutes): I am going to double the size of this cube. What do you think will happen to the surface area? The volume? What are your predictions? [i]Explore[/i] (35 - 40 minutes): -Students will open up Geogebra file, and start recording their session using Screencast-o-matic. Students will play around with the slider to see how it is connected to the cube. -Students will answer the questions on the Surface Area and Volume Activity Sheet (they may collaborate with a partner, but each student should explore on their own). Teacher questions: *Around question 5 on the handout, ask students to explain their sketch, what restraints (if any) they put on it and why. *Originally the slider is set from 0 to 5, inquire what might happen to the graphs if we increase the value to 20. What information might we gain from doing this? *Keep an eye out for unique explorations and make a note so these students can share their method with the class later during the share/summarize (right or wrong). *What happens when you change the slider values? Larger numbers? What if we leave reality and imagine negative side lengths? How does this affect the graph of the function? Why would this happen? -The activity encourages students to investigate how the change in one dimension (length) can affect the change in other dimensions (2-D - surface area and 3-D - volume). [i]Share/Summarize (getting back to the big idea—not “assigning homework”)[/i] (5-10 minutes): Questions posed to students: *As one dimension changes, how are the other two dimensions affected? *Students should present their findings and elaborate on their methods. What interesting things did you come across during the exploration? *What function rule did you think was the best for point R? Why do you think that is the “best”? What about point T? [i]Homework / Formative Assessment:[/i] What if 2 cubes were stuck together? How would the surface area of this compare to the cube we explored in class? The volume? What if we just kept adding on cubes making one long rectangular prism?

 

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Resource Type
Activity
Tags
area  cubes  surface  volume 
Target Group (Age)
15 – 18
Language
English (United States)
 
 
GeoGebra version
4.0
Views
3651
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