MASCOT PAINTING Use the picture on the left and enlarge it by using the grid below. Page 206 Classroom Strategies Blackline Master II - 64
Draw Me in 3-D Use cubes to construct the building described in the plan below. 3 1 2 1 1 In the building plan, the numbers in each square tell the height of the building over that square. Make an orthographic (top, side (end), front) drawing of your building. Top Front Side (end) Here is an orthographic drawing. Build the building. Top Front Right Side Now show the building plan. Make six block buildings. Draw building plans for three of them, and create an orthographic drawing for the other three. Exchange drawings with another student and try to reproduce the buildings, with cubes, from the drawings. Classroom Strategies Blackline Master II - 65 Page 207
Building with GeoBlocks Using the given orthographic drawings, build the 3-dimensional figure. 1. Top Front Left Side 2 Blocks Right Side Back 2. Top Front Left Side 3 Blocks Right Side Back Page 208 Classroom Strategies Blackline Master II - 66
Building with GeoBlocks continued 3. Top Front Left Side Back Right Side 2 Blocks 4. Top Front Right Side 2 Blocks Back Left Side 5. Top Front Left Side 3 Blocks Back Right Side Classroom Strategies Blackline Master II - 67 Page 209
more Building with GeoBlocks 6. Top Front Left Side 3 blocks Back Right Side 7. Top Front Left Side 3 blocks Right Side Back Page 210 Classroom Strategies Blackline Master II - 68
Make Your Own Graduated Cylinders Materials: Various transparent cylinders with vertical sides such as olive jars, perfume sample vials medicine bottles graph paper with grids of various sizes fine point marking pen that will write on glass or plastic one standard measure that can measure a liter or other convenient amount How to divide a length into ten equal parts Use 11 parallel lines that divide a section of a page into ten equal spaces. These lines can be from notebook paper or graph paper. The height from the top line to the bottom needs to be less than the length of the object you want to divide. Place the object that you want to divide so that the top edge is on the top line and the bottom edge is on the bottom line. Suppose we want to divide the part of this cylinder marked by a heavy line into ten parts. Tilt the cylinder, or a strip of paper cut to the same size, so that the top of the heavy line is on the top parallel line, and the bottom of the scale line is on the bottom parallel line. The parallel lines now show you positions to mark for the ten division lines. 1. Mark one of your containers so that each division line represents a deciliter (0.1 liter). 2. Are the lines far enough apart so that you can divide each space into ten equal parts? 3. Now measure a deciliter and pour it into a smaller container that is nearly the same size. Perhaps a large pill bottle would work. Divide this so that each mark represents a centiliter (0.01 liter). Are the lines far enough apart so that you can divide the spaces into ten equal parts again? If so these will be milliliters (0.001 liter). 4. Now measure a centiliter into a smaller container that is nearly the same size. (Some food coloring comes in plastic vials that may be about the right size. To use those, cut off the tops.) Divide this into milliliters. 5. Do you have a vial that you can divide into tenths of a milliliter? (A perfume sample vial might work.) 6. Keep making measuring containers that are more and more precise. What is the most precise container you can make? If you had smaller and smaller containers, what other factors might limit your precision or cause error? Classroom Strategies Blackline Master II - 69 Page 211
Precisely! Discuss each situation with your group. Other groups may have different ideas and answers. Be prepared to explain why you chose the answer you did. 1. Dr. Morton s lab has a ruler that can be used to measure to the nearest millimeter, a micrometer that can be used to measure to the nearest millionth of a meter, and a measuring stick that can be used to measure to the nearest centimeter. He also has a scale that can be used to measure to the nearest ten grams, and a balance that can be used to measure to the nearest tenth of a milligram. He has a dose spoon that can be used to measure to the nearestcentiliter, a cup that can be used to measure to the nearest deciliter, and a graduated cylinder that can be used to measure to the nearest milliliter. Which tool should he use to measure each of the following? Explain. a. Weight of a newborn baby e. Height of an elderly patient b. Weight of a headache powder he is prescribing f. Length of a antibiotic capsule c. The amount of water he wants to use in his tea pot. d. The amount of liquid penicillin he needs to add in making an antibiotic capsule. 2. Dr. Morton s three assistants are helping him make some anti-itch powder. Tom uses the scale and weighs out 320 grams of cornstarch to use as the base for the powder. Sue uses the balance and weighs out 50.2 milligrams of itch reliever for the powder. Ben uses the balance and weighs out 1.3 milligrams of perfumed salts to use in the powder. They mix this together, put it in a package, and label the package, Anti-itch Powder 320.0515 grams Is there an error here? 3. Dr. Morton has asked his assistants to measure a triangular region that showed up on an x-ray. The region is a right triangle, and Tom measures one leg to be 11 cm long. Ben measure the other leg and finds that it is 6 cm long. They both used the measuring stick. Sue uses the Pythagorean Theorem and reports that the hypotenuse is 12.529964 cm long. Is there an error here? 4. Discuss the best tools and techniques to use in mixing three ingredients to make a dry medicine that is combined by weight. The medicine is very strong and should be taken with extreme caution. 5. Discuss the best tools and techniques to use in measuring and constructing two congruent right triangles that will be used to hold up a shelf. The shelf is about the width of a notebook and should be about table height. 6. Discuss the best tools and techniques to use in measuring three liquids that will be used in a lotion used to soothe aching muscles. Page 212 Classroom Strategies Blackline Master II - 70
Similar Figures Find the square roots requested below. If the square root is not a whole number, give the decimal value to the nearest hundredth. 1. 16 2. 2 3. 81 Give the whole numbers that the square roots below fall between. Example: 10 is between 3 and 4. 4. 27 5. 145 6. 40 Use the values given to help find the missing side. 7. Side a = 3cm 8. Side c = 13cm Side b = 4cm Side a = 5cm Side c = Side b = b a c Solve each problem below. 9. The telephone pole has a cable attached to the ground. The cable is 100 feet long, the distance along the ground from the cable to the pole is 60 feet. How tall is the pole? 10. A bridge across a river is 120 feet long. Mark is standing at point M along the edge of the river, 50 feet from the end of the bridge. Joe is standing on the other side of the river at the other end of the bridge. How far is Mark from Joe? J B R I D G E M Classroom Strategies Blackline Master II - 71 Page 213
Surface Area and Volume 1. Select the situation which is related to surface area. A) How much soup will fit in a can? B) How much tin is needed to make a soup can? C) How many soup cans will fit on a shelf? 2. Select the situation which is related to volume. A) How much paper is needed to wrap a package? B) How much paint is needed to paint a water tower? C) How much water will a gold fish bowl hold? 3. The cracker box is 10 inches long, 5 inches deep and 5 inches tall. Find its surface area. 4. How much metal is needed to make a hollow rectangular column which is 20 feet tall, 3 feet deep, and 4 feet wide. Page 214 Classroom Strategies Blackline Master II - 72
Surface Area and Volume continued 5. How much metal is used to make a gas storage tank that is cylindrical with a height of 25 feet, and a radius of 10 feet? 6. How much velvet will Mary need to cover a metal tea box shaped like a cylinder, if the box has a diameter of 4 inches and a height of 7 inches? 7. A cylinder has a volume of 360 cubic inches. What is the volume of a cone with the same height and diameter? 8. What is the volume of a rectangular prism with the same base and height as a pyramid with a square base that has a volume of 90 cubic feet? V =? V = 90 ft Classroom Strategies Blackline Master II - 73 Page 215
Surface Area and Volume continued Find the volume of each of the following containers. 9. 10. 18 27 27 8 12 11. 12. 14 14 5 5 8 8 13. What happens to the volume of the prism in problem #9 if the height is doubled? 14. What happens to the volume of the cylinder in problem #10 if the diameter is doubled? Page 216 Classroom Strategies Blackline Master II - 74
Similar Figures 1. In which case or cases below are the figures always similar? A) all circles B) all squares C) all rectangles 2) Circle any letter beside similar figures. A) B) C) 3) The triangles shown below are similar. Find the length of the missing side. 18 in 9 in? 12 in 4 in 4) The quadrilaterals shown below are similar. Find the length of the missing side. 32 cm 24 cm 9 cm 9 cm? 15 cm 20 cm 5) To find out how far it is across a river, John builds a fire at the rivers edge directly across from point P. He then walks West 10 feet away from the fire. Then he walks South for 25 feet, stopping when his campfire is in a direct line with a cabin on the other side of the stream. He knows the cabin is 100 yards due North of point P. How wide is the river? Cabin 100 yd 10 Fire? P 25 River Classroom Strategies Blackline Master II - 75 Page 217
Similar Figures 1. Show the figure below after it has been rotated 90 clockwise around the origin. y B C A D x 2. Give the coordinates of the original figure (pre-image) and its image. A (, ) A (, ) B (, ) B (, ) C (, ) C (, ) D (, ) D (, ) Page 218 Classroom Strategies Blackline Master II - 76
Similar Figures 1. Show the figure below after it has been transformed according to this rule: For every coordinate (x, y), the new coordinate is (2x, 2y). y x 2. Describewhat happened to the figure. 3. What would happen to the figure if it was transformed according to the following rule: (x, y) (3 x, 3 y)? Classroom Strategies Blackline Master II - 77 Page 219