5.1. Area and Perimeter The Dot Game. My Notes ACTIVITY


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1 Area and Perimeter SUGGESTED LEARNING STRATEGIES: Summarize/ Paraphrase/Retell, Think/Pair/Share, Use Manipulatives Have you ever played? Here is your chance to play a game during math class. Have fun. Game Board The game is played on a rectangular grid of dots. Object of the Game Each player tries to create as many squares as possible that have sides one unit long by drawing line segments that connect the dots on the game board. Playing the Game Two players are needed. (Find a partner in your class.) Decide who will have the first turn. Players take turns connecting two dots with a horizontal or vertical line segment that is one unit long. If a player completes a square, that player places his or her initial in the square and continues to play by drawing another line segment. A player s turn ends when he or she draws a line segment that does not complete a square. Play continues until all the dots are connected by line segments. The game board will be filled with squares, each containing the initial of the player who completed it. Game Board 1 Game Board 2 ACTIVITY 5.1 Winning the Game Count the squares for each player. The player who has completed the greatest number of squares is the winner. 1. Play the game two times with your partner. Use the game boards in the space. Tell who wins each game. 2. In each game, how many squares did you mark? Game 1 Game 2 3. In each game, how many squares did your partner mark? Game 1 Game 2 Unit 5 Geometry 243
2 ACTIVITY 5.1 Area and Perimeter SUGGESTED LEARNING STRATEGIES: Guess and Check, Quickwrite, Create Representations, Self Revision/Peer Revision 4. What is the combined number of squares for both players in each game? Game 1 Game 2 5. How many small squares make up the large square on a game board? 6. What is the area of a small square? 7. What is the area of the large square? MATH TERMS Adjacent squares must have at least one side and two vertices in common. Vertices is the plural of vertex. Game Board 8. Look at Game Board 1 from the first two games and identify the largest shape made with your initialed adjacent squares. Draw that shape in the space. Be sure to draw all the small squares. 9. What is the area of the shape above? How did you determine the area of the shape? 10. Rewrite the part of the directions labeled Winning the Game using the concept of area. 11. Look at the shape you drew for Question 8. Draw the shape again on the game board in the space, but do not draw any interior line segments. 244 SpringBoard Mathematics with Meaning TM Level 1
3 Area and Perimeter ACTIVITY 5.1 SUGGESTED LEARNING STRATEGIES: Quickwrite, Close Reading, Create Representations 1 2. How many oneunit line segments are there in the perimeter of the figure that you drew for Question 11? 13. Compare your answer for Question 1 2 to your partner s answer. Did the person who had the most squares on game board 1 also have the most line segments in Question 11? ACADEMIC VOCABULARY Perimeter is the distance around a figure. Game Board 1 Now play the game again. The rules for playing this time are the same, but the winner will be decided differently. Instead of the winner completing the greatest number of squares, the winner in this game will have completed adjacent squares that form a figure that has the greatest perimeter. 14. Betty and Andy played on a 4 cm 5 cm grid. Their results are shown below. Each segment drawn is 1 cm in length and each square has an area of 1 cm 2. A A A A A B B B B A B B B B A READING MATH 1 cm 2 is read as one square centimeter. Sometimes you will see 1 sq cm used for 1 cm 2. B B B B A Betty (B) claims she won, while Andy (A) claims he won. How can both be correct? Justify your decision. 15. Play the game twice with your partner. Remember, the player whose squares make up a shape made of adjacent squares that has the greatest perimeter is the winner. Game Board How did you determine the perimeter of your figure? Show your work. Unit 5 Geometry 245
4 ACTIVITY 5.1 Area and Perimeter SUGGESTED LEARNING STRATEGIES: Quickwrite, Group Presentation, Create Representations, Think/Pair/Share 17. For Betty and Andy s Dot Game, draw and describe the different units of measure used to decide who won the first round of and who won the second round. 18. Make a figure that has the same area as Betty s figure, but with a different perimeter. Use the grid in the space. You may also use square tiles to form a figure and then make a drawing of it in the space. 19. Use the grid in the space to draw the rectangles. Recall that opposite sides of a rectangle have the same measures. a. Draw a rectangle that is formed with 16 squares. What are the perimeter and the area of the rectangle? Include units in your answer and draw a diagram of your rectangle. b. Make a different rectangle with the same area but a different perimeter. Draw a diagram in the space. c. Can you make a different rectangle with the same perimeter as the rectangle in Part a, but with a different area? If so, draw a diagram in the space. 20. Write a rule, in words, to determine the area of a rectangle. 21. If a rectangle has length l, width w, and area A, write an equation that relates all three variables. 246 SpringBoard Mathematics with Meaning TM Level 1
5 Area and Perimeter ACTIVITY 5.1 SUGGESTED LEARNING STRATEGIES: Think/Pair/Share, Group Presentation 2 2. Write a rule, in words, to determine the perimeter of a rectangle. 23. If a rectangle has length l, width w, and perimeter P, write an equation that relates all three variables. 24. The drawing below is a composite figure. 2.3 cm 5.2 cm MATH TERMS A composite figure is made up of two or more figures. 3.9 cm 4.1 cm a. Find the measure of each side that is not labeled. b. Find the area of the composite figure. Show your work. c. Find the perimeter of the composite figure. Show your work. 25. Find the area and perimeter of the composite figure below. Show your work. 3 ft 5 ft 6 ft 9 ft 3 ft 2 ft Unit 5 Geometry 247
6 ACTIVITY 5.1 Area and Perimeter CHECK YOUR UNDERSTANDING Write your answers on notebook paper. Show your work. 1. Colleen and David played I. Their game card is shown below. Who won? Explain how you know. C D D C D D C C D D D D C C D C C D D C 4. Make a rectangle that is formed using 24 squares and has a perimeter of Find the area and perimeter of a rectangle that has a length of 23 meters and a width of 17 meters. Show your calculations. 6. Find the area and perimeter of the figure below Sammi and John played the Dot Game II. Their game card is shown below. Who won? Explain how you know S J J J J J 8 S J J S S S S S S J 3. Marcy found the area and perimeter of this rectangle. Label the area and perimeter with the appropriate units. 3 m 4 m A = 12 P = 14 J J 7. MATHEMATICAL REFLECTION What are the dimensions of a rectangle that has a perimeter of 16 cm and has the greatest possible area? 248 SpringBoard Mathematics with Meaning TM Level 1
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