SURFACE AREA Agenda: 1. Do Now 2. 3 Act Lesson: Pop Boxes 3. Cubes Investigation 4. Debrief Learning Target: I can use 2D and 3D models to informally calculate the surface area. Do Now 4/20: Find the area of the polygon below.

3 ACT LESSON: POP BOXES Act 1: Coke vs. Pepsi Both of these boxes hold 12 cans of pop. What questions does the following video raise for you? Questions

3 ACT LESSON: POP BOXES Act 2: What do we have? What do we need? How can we proceed? Have (Given)Need (Unknown)Next Steps (Strategies) Pop Box Measurements

DEFINITION: PRISM Rather than “boxes”…. Prism – a 3D solid with two congruent ends, and sides made of parallelograms. (They are named for the shape of the congruent ends.) **MUST BE IN NOTES!**

CUBE INVESTIGATION 1.Take 2 minutes to play around with the cubes. 2.Use the blocks to create another “box”. Write down the dimensions. 3.Build the first three "boxes” in the table. 4.Use the dimensions to fill the blanks for number of cubes and number of squares on the outside. 5.Complete the rest of the table with your own "boxes”. (Find someone check your answers with!) 6.Look for shortcuts (rather than just straight counting!) BoxesDimensionsNumber of Blocks Number of squares 1 2

DEBRIEF Act 3: Back to Coke vs. Pepsi How can we use the shortcuts we came up with to answer the questions we raised about the Pop Boxes? Which box uses the most cardboard? PrismDimensionsNumber of CubesNumber of Squares Coke Pepsi

SURFACE AREA: NETS Agenda 1. Do Now 2. Finish Pop Boxes 3. Nets and Area 4. Debrief Learning Target: I can use 2D nets to determine the surface area. Do Now 4/21: Find the area of the figure below.

ACT 3: COKE VS. PEPSI Dimension of Coke Box: 12cm x 13cm x 40cm Dimensions of Pepsi Box: 20cm x 26 cm x 12cm

ACT 3: POP BOXES Method 1: Develop and use a pattern/rule Method 2: Draw the net PrismDimensionsNumber of CubesNumber of Squares Coke Pepsi

NETS OF SOLIDS Net - a 2D representation of the surface area of a 3D solid. 1.Measure and find the area of your own net. 2.What shortcuts can you use with the net to help you determine the surface area more quickly? **MUST BE IN NOTES!**

DEBRIEF What will all the nets of prisms have in common? What shortcuts can you use to determine the surface area of a prism with any shape base?

SURFACE AREA OF PRISMS AND PYRAMIDS Agenda 1. Do Now 2. Definition: Pyramid 3. Vertices, Edges, Sides 4. Euler’s Number 5. Debrief Learning Target: I can use the number of vertices, edges and sides to help draw the two dimensional nets of three dimensional figures (cylinder, prism, pyramid, cone). 8 m 4m 3 m

DEFINITIONS: PYRAMID Pyramid - a 3D solid with one polygon base and all side triangles. (Names for the shape of the base) Faces - the polygons that make up a 3D solid Edges - where two faces meet Vertices - where two or more edges meet

EULER’S FORMULA Euler was a Swiss mathematician who developed a way to quickly determine the properties of a solid. Use the nets provided to complete the table below.

DEBRIEF Can we write any rules yet about how to find surface area? What are some of the shortcuts we DO know to find the area of prisms and pyramids?

REVIEW: PERIMETER What is the perimeter of this shape? How do we find this? If the shape is regular, is there a faster way? A tri = ½bh x n P = b x n A all = ½ P x h 8 cm

USING THE PERIMETER TO FIND SURFACE AREA In each net, the sides of the base are also the sides of the rectangles or triangles that form the side (lateral) faces. When we add all of these together, they form the perimeter of the base. Steps to find Surface AreaFormula in a prismFormula in a pyramid 1. Find the area of the base and multiply times the number of bases 2(B.A.)1(B.A.) 2. Find the area of the side (lateral) faces and multiply by the number of side (lateral) faces (every side) x h or (P x h) ½ (every side) x (h) or ½(P x h) 3. Add all of the areas together 2(B.A.) + (P x h)B.A. + ½(P x h)