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23 A NCTM 2011, Indianapolis page 1 EDC, Think Math! published by School Specialty Math
24 A NCTM 2011, Indianapolis page 2 EDC, Think Math! published by School Specialty Math
25 E E E E NCTM 2011, Indianapolis page 3 EDC, Think Math! School Specialty Math
26 NET D: Cut along the heavy lines. Fold along the light dotted lines. D D D D NCTM 2011, Indianapolis page 4 EDC, Think Math! published by School Specialty Math
27 NET S: Cut along the heavy lines. Fold along the light dotted lines. NCTM 2011, Indianapolis page 5 EDC, Think Math! published by School Specialty Math
28 NETS R, T: Cut along the heavy lines. Fold along the light dotted lines. NCTM 2011, Indianapolis page 6 EDC, Think Math! published by School Specialty Math
29 NET P: Cut along the heavy lines. Fold along the light dotted lines. P P NCTM 2011, Indianapolis page 7 EDC, Think Math! published by School Specialty Math
30 NET PP: Cut along the heavy lines. Fold along the light dotted lines. PP NCTM 2011, Indianapolis page 8 EDC, Think Math! published by School Specialty Math
31 Area of a parallelogram NCTM 2011, Indianapolis page 9 Cindy Carter, Keith Civin, E. Paul Goldenberg
32 Why proof is important What is the area of this square? What is the area of this rectangle? Cut this copy on the heavy lines Dissect this copy of the square and try to fit the pieces back together to fill the rectangle above. What s going on?! NCTM 2011, Indianapolis page 10 Cindy Carter, Keith Civin, E. Paul Goldenberg
33 Find the area of the base and the volume of each of these rectangular prisms built out of inch cubes. = 1 cu. in. A B C Area of base: sq. in. Area of base: Area of base: Volume: cu. in. Volume: Volume: D E F Area of base: Volume: Area of base: Volume: Area of base: Volume: G H I Area of base: Volume: Area of base: Volume: Area of base: Volume: NCTM 2011, Indianapolis page 11 EDC, Think Math! published by School Specialty Math
34 Find the area of the base and the volume of each of these rectangular prisms built out of inch cubes. = 1 cu. in. J K 3 5 Area of base: Volume: Area of base: Volume: L M Area of base: Area of base: Volume: Volume: This shape is different. It is related to the rectangular prism shown in Problem M. Figure out its volume and explain your thinking. Volume: NCTM 2011, Indianapolis page 12 EDC, Think Math! published by School Specialty Math
35 Area of a triangle NCTM 2011, Indianapolis page 13 Cindy Carter, Keith Civin, E. Paul Goldenberg
36 Area of a trapezoid NCTM 2011, Indianapolis page 14 Cindy Carter, Keith Civin, E. Paul Goldenberg
37 Area of a circle NCTM 2011, Indianapolis page 15 Cindy Carter, Keith Civin, E. Paul Goldenberg
38 Dissect to find the area in inches 2. Note that the top of this figure is not a straight line! You may assume that segments that look parallel are parallel. The area under the curve can be approximated by computing the area of some trapezoids. What is that area, roughly, in cm 2? The base of this prism is a regular pentagram, with an area of roughly 1/2 cm 2. The height of the prism is about 2 cm. Calculate the volume. The area of the smaller octagon is about 81% of the area of the larger octagon. The stray poppy seed is dead center of the octagons. Roughly what is the area in cm 2 taken up by the chocolate chip cookie? No lake on earth has sides that go straight down like this. (But this one is unearthly!) Its sides are traced out by a line (segment) moving parallel to itself around the rim of the lake the way the sides of any prism or cylinder are, and its bottom is absolutely flat and congruent to its top. (Definitely unearthly!) If the lake s area is ~ 2.5 mi 2 and the depth is about 4 mi, about how much water does the lake contain? By the way, mathematicians refer to shapes like this as cylinders, though obviously not circular cylinders. NCTM 2011, Indianapolis page 16 Cindy Carter, Keith Civin, E. Paul Goldenberg
39 I. Each right triangular prism is sitting on its base. Use the dimensions to compute the volume. A SHOW YOUR WORK: Volume: cu. units B SHOW YOUR WORK: Volume: C SHOW YOUR WORK: Volume: NCTM 2011, Indianapolis page 17 EDC, Think Math! published by School Specialty Math
40 II. Each right triangular prism is sitting on a face other than its base. Use the dimensions to compute the volume. A SHOW YOUR WORK: Volume: B SHOW YOUR WORK: Volume: Show two ways to calculate the volume of this right triangular prism Volume: NCTM 2011, Indianapolis page 18 EDC, Think Math! published by School Specialty Math
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1 A student has a rectangular postcard that he folds in half lengthwise. Next, he rotates it continuously about the folded edge. Which three-dimensional object below is generated by this rotation? 4) 2
KCATM Geometry
Name School KCATM Geometry 9 10 2013 1) Find the minimum perimeter of a rectangle whose area is 169 square meters. a) 42 meters b) 13 meters c) 26 meters d) 52 meters 2) Find the coordinates of the midpoint