Surface Area of Prisms and Pyramids
Lesson 6 of 8
Objective: SWBAT calculate surface area of prisms and pyramids.
Students enter silently according to routine. Do Now assignments are handed at the door and introduce students to the concept of nets. This word however, is not used. These figures are called composite figures, made up of more than one 2D shape. In each item, students are asked to find the area of each composite figure. Students will have 5 minutes to work independently and silently.
Once those 5 minutes have passed it will be time to review the answers. It is important here to push students to copy down the work as horizontal algebraic expressions, including initial formulas and substitutions. The prior skill needed to be able to complete the work this way includes evaluating algebraic expressions through substitution. This is a skill we will continue to refine throughout the next few days as it impacts surface area and volume of 3D figures. It is also important to emphasize MP6, attention to precision. A drop of a negative sign or misuse of parenthesis can lead to a wrong solution. Thus, checking your work is supremely important in these tasks.
After reviewing the answers to the Do Now, students are given 3d prisms and pyramids to explore. Each year I have collected 3D shapes that students have created and I use them to give to students the next year for observations. Students have 3 – 4 minutes to write 2 facts they’ve noticed while manipulating these 3D shapes. These facts can include the counting some part of the shape or noting the 2D shapes that make up their 3D figure. No names are yet given, not terms are used. Students are left to freely observe and describe what they hold. By introducing something concrete they can hold in their hands and exploring it before we begin throwing around new words, I hope students will build the connections to the new vocabulary on their own.
Next, students receive their classnotes. Any lettering in red font indicates words that must be copied by students off the board. We review the definitions of prisms and pyramids and I ask students to tell me the name of the 3D figure they were holding during the previous exploration, making sure to justify their answer using the vocabulary included in the notes. For example, I’m holding a pyramid. I know this because all of these are the sloping sides that meet at this top point called the vertex.
Finally, we reach the second page in the class notes. I ask students to read the first paragraph and example with their partners and attempt that problem, showing their work in the way specified by the notes (using algebraic expressions). I give students 3 – 4 minutes to do this before I stop everyone to make sure the algebraic expressions are written on their paper. The following is explained to students:
- The most common error happens when calculating the areas of each face and adding them, even if you use a calculator!
- This is why using algebraic expressions are so useful
- You can visibly check the expression to make sure you have the appropriate number of total faces/areas being added depending on the 3D figure
- Use this strategy to attend to precision (MP6)
Students will be asked to form groups of 4 to complete the Class work . Once they have selected their groups and are seated I will distribute the work sheet including surface area problems only. I will be working with a small group of students, selected during the Do Now because I noticed them struggling to write algebraic expressions. I will begin working with them on white boards before asking them to work on paper. I will also ask the first 4 groups to complete the class work correctly to write solutions up on the board. These solutions should include a drawing. This is a good opportunity to give the artist in class an opportunity to display a skill and practice the skill at the same time.
Once students complete this assignment, they will be handed an additional problem sheet to complete independently. This worksheet will include additional problems with evaluating algebraic expressions. Students are advised that these sheets will be graded. Those who cannot complete the assignment during class will be allowed to take it home to complete for homework.
Throughout this class work section it is important to ensure students are being pushed to show their work neatly and algebraically. I can be quite particular about the equal signs and parentheses students are asked to use in class, but I find it pays off because it lessens the likelihood of making small errors.
Students will receive an exit ticket and will have 10 minutes to solve. This is a somewhat complex problem and I want to be able to give students some feedback as they solve to see how far they can get in this problem. While everything we’ve been covering today is more skill and fluency driven, this example is closer to the type of common core problem solving needed for students to meet the new academic standards. Students should be reminded of any problem solving strategies we covered this year while they work.
Once students have completed the exit ticket they receive their HW and are asked to line up.