Here is a picture of the spinner that came in a game Alex bought.

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Curtis Quinn
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1 Here is a picture of the spinner that came in a game Alex bought. 5 people play the game, and each chooses a color. When the spinner lands on the player s color, the player may advance on a game board. When Alex looked at the spinner, he realized it would not give each person a fair chance of winning. Alex decided to make a new spinner for his game using the same 5 colors. What could Alex s spinner look like? Be sure to explain your mathematical thinking. 1 of 12

2 Suggested Grade Span 3 5 Grade(s) in Which Task Was Piloted 5 Task Here is a picture of the spinner that came in a game Alex bought. 5 people play the game, and each chooses a color. When the spinner lands on the player s color, the player may advance on a game board. When Alex looked at the spinner, he realized it would not give each person a fair chance of winning. Alex decided to make a new spinner for his game using the same 5 colors. What could Alex s spinner look like? Be sure to explain your mathematical thinking. Alternative Versions of Task More Accessible Version: Here is a picture of the spinner that came in a game Alex bought. 2 of 12

3 4 people play the game, and each chooses a color. When the spinner lands on the player s color, the player may advance on a game board. When Alex looked at the spinner, he realized it would not give each person a fair chance of winning. Alex decided to make a new spinner for his game using the same 4 colors. What could Alex s spinner look like? Be sure to explain your mathematical thinking. More Challenging Version: Refer to the original version of the task, and... What if the spinner was made for 6 players? 7 players? 10 players? Write a rule for determining the size of each section for any number of players. Be sure to explain your mathematical thinking. Teacher Note: See page 7 of the PDF to print a complete worksheet with graphics. NCTM Content Standards and Evidence Data Analysis and Probability Standard for Grades 3 5: Instructional programs from prekindergarten through grade 12 should enable all students to... Understand and apply basic concepts of probability. NCTM Evidence: Describe events as likely or unlikely and discuss the degree of likelihood using such words as certain," equally likely" and impossible." Exemplars Task-Specific Evidence: This task requires students to describe the probability of landing on each color of a spinner. Geometry Standard for Grades 3 5: Instructional programs from pre-kindergarten through grade 12 should enable all students to... 3 of 12

4 Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships. NCTM Evidence: Identify, compare and analyze attributes of two- and three-dimensional shapes and develop vocabulary to describe the attributes. Exemplars Task-Specific Evidence: This task requires students to identify that there are 360 degrees in circle and to use that information to create congruent sections. Time/Context/Qualifiers/Tip(s) From Piloting Teacher This is a short- to medium-length task. To print a copy of the more accessible version of the task with the graphic image, refer to page 6. To print a copy of the more challenging version of the task with the graphic image, refer to page 7. Links This task could link to studies of games of chance. The following two Web sites have interactive spinner activities students can play to learn more about spinners and probability: Common Strategies Used to Solve This Task Most students will solve the task with diagrams supported by computation. Possible Solutions The spinner should have five equal sections that are 72 degrees each. More Accessible Version Solution: The spinner should have four equal sections that are 90 degrees each. 4 of 12

5 More Challenging Version Solution: Number of Players Task-Specific Assessment Notes Number of Degrees in Each Section n 360 ã n General Notes This task requires a rudimentary understanding of probability but focuses more on a student s understanding of a circle. Novice The Novice will have some basic mathematical understanding about fairness, but the number of degrees in a circle and a knowledge of spinners may be lacking. Some communication may be evident, but it may lead more to confusion than to clarification. No connection will be made. Apprentice The Apprentice will have some parts of the task correct. An attempt to address fairness will be demonstrated along with an understanding of fractions, percents or degrees in a circle. Some correct reasoning will be evident, and some communication will be used. Math representations will be attempted. Practitioner The Practitioner will achieve a correct answer, and work will be shown and labeled. A mathematically accurate solution will be presented, and mathematically relevant observations will be made. Expert The Expert will demonstrate extensive knowledge about fractions, percentages and degrees in a circle. An efficient approach will be used to solve the task, and of prior knowledge will be used throughout. Precise math language will be used to communicate ideas, and a sense of purpose and audience will be communicated. Math representations will be used to analyze relationships. 5 of 12

6 More Accessible Version Worksheet Here is a picture of the spinner that came in a game Alex bought. 4 people play the game, and each chooses a color. When the spinner lands on the player s color, the player may advance on a game board. When Alex looked at the spinner, he realized it would not give each person a fair chance of winning. Alex decided to make a new spinner for his game using the same 4 colors. What could Alex s spinner look like? Be sure to explain your mathematical thinking. 6 of 12

7 More Challenging Version Worksheet Here is a picture of the spinner that came in a game Alex bought. 5 people play the game, and each chooses a color. When the spinner lands on the player s color, the player may advance on a game board. When Alex looked at the spinner, he realized it would not give each person a fair chance of winning. Alex decided to make a new spinner for his game using the same 5 colors. What could Alex s spinner look like? What if the spinner was made for 6 players? 7 players? 10 players? Write a rule for determining the size of each section for any number of players. Be sure to explain your mathematical thinking. 7 of 12

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Emma thought of a math challenge for her classmates to solve. Then Emma asked her classmates the following question:

Emma thought of a math challenge for her classmates to solve. She gave them the following directions: Draw a square on your paper. Draw in the lines of symmetry. Then Emma asked her classmates the following