zMath 160  - Unit 19: Transformations, Tessellations, and Similar Triangles; Customary Units Conversions and Computations

Transformations

For problems #1 through #6, write the type of transformation shown, choosing answers from translation, reflection, or rotation.


1)

If a line is drawn down through the butterfly’s spine, what kind of transformation exists between the left side and the right side?


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2)

In creating this design, if the top section was created first, and then the right section was created next, what kind of transformation did the artist use to create it?


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3)

What kind of transformation did the artist use to create the shadow effect?


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4)

What kind of transformation was applied to the first triangle to get the second triangle.


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5)

What kind of transformation was applied to the first triangle to get the second triangle?


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6)

What kind of transformation was applied to the first triangle to get the second triangle?


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Tessellations


7)

Create a shape that tessellates the plane. Start with a square, equilateral triangle, or hexagon and cut off a piece in an interesting way, then translate it to the opposite side of the shape. You may cut more than one piece. Test the shape and create a nice design that covers the plane. Describe your design and describe how you created the pattern that tessellates the plane.


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8)

Research M.C. Escher and find one of his artworks in which he uses tessellations. Name the artwork and describe its appearance. Also give the website where the information is found.


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Similar Triangles


9)

In this triangle, measure the length of each of the sides. On paper, draw a similar triangle that is larger and has the 1:2 relationship between each of its sides. State the length of each of the sides of the given triangle and then state the corresponding lengths of each of the sides of the triangle you drew.


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10)

Are these two towers similar? Explain why you think they are or are not.


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Customary Units Conversions and Computations


11)

Find the following items in or near your home and then state the answer that will complete the statements. Write the letter of the statement and then the answer. a. Find a pint container in your home. Using a one-cup measure, fill up the pint container with water. How many cups of water does it hold? ______ b. Find a quart container. Using a pint container, fill it up the quart container with water. How many pints of water does it hold? ______ c. Find a gallon container. Using a quart container, fill it up the gallon container with water. How many quarts of water does it hold? ______ d. Find either a ruler or a yardstick. Find something in your home that is about 3 feet long. What is the object? ______ e. Find out from your mom, dad, or guardian how many miles it is to your grandma’s, aunt or uncle’s, or a friend’s house. State the distance in miles. Then express that number of miles into feet. Can you walk this distance? ______ f. Express how tall you are in feet and inches. Then, changing the feet to inches, express how tall you are in inches only. ______ g. If you are permitted to go to the school game which starts at 6:00 p.m. and the time is currently 4:15 p.m., how many minutes will you have to wait to see the beginning of the game?______ Also, express this answer in hours and minutes._____ 


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For problems #12 through #14, fill in the blank.


12)

10 qt = _______ gal


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13)

Solve.


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14)

7 yd = ________ ft


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15)

Add and simplify.


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16)

Subtract.


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17)

Borrow and Subtract.


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Review


18)

In the word MISSISSIPPI, what is the ratio of the occurrence of the letter “S” to all the letters in the word.


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19)

In the word MISCELLANEOUS every vowel is used. What percent of the letters in this word are vowels? Round to the nearest whole percent.


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20)

Timothy’s parents are going to buy a new home. They must have a 10% down payment to finance the house. If the house costs $80,000 how much of a down payment must they provide? 


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21)

Estimate a reasonable solution. Round to the nearest whole number.


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22)

Name a quadrilateral that has right angles and opposite sides are parallel.


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For problem #23, use the following triangle.


23)

For the triangle, fill in the blanks. State the answers in the same order as given in the problem.


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24)

Look around your room. Find an example of parallel planes. Do not use the walls, ceiling, or floor as an example. Describe the parallel planes you found.


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25)

How many sides do each of the polygons listed have? State the name of the polygon the number of sides. a. Pentagon = ? sides b. Octagon = ? sides c. Hexagon = ? sides d. Quadrilateral = ? sides e. Decagon = ? sides


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