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Subject

Math, Science & Technology

Materials

Various manipulatives such as:
pattern blocks/color tiles/ fraction strips/spinners/Cuisenaire rods, craft material such as construction paper, markers, tape, etc.

Authors

The Core Curriculum Companion For The New York State Mathematics Resource Guide Writing Team.

Duration

4-5 lessons

Procedure

DOING THE INVESTIGATION

• Students will discuss the concept of a "fair game."
• Students will work in groups to find fractions of a set and fractional parts of a whole.
• Students will identify equivalent fractions.
• Students will demonstrate and apply their ability to add fractions.

Students will work in groups to:

• Design a game board and divide it into fractional parts. Each part should reflect one of the possible outcomes.
• Discuss rules that will make their game fair.
• Write rules for playing the game.

POSSIBLE SOLUTIONS

Design a spinner and spin it 25 times

• If it lands on 1/2, player A gets a point
• If it lands on anything else, player B gets a point

OR

• If it lands on 1/2 no one gets a point
• If it lands on 1/4 player A gets a point
• If it lands on 1/8 player B gets a point

Vocabulary

Probability, fair game, unfair game, outcome, equivalent

Description

Students will design a carnival game in which there are 4 possible outcomes. The likelihood of each outcome is as follows:
1/2, 1/4, 1/8, 1/8.
Write rules for this game so two players will have an equally likely chance of winning.

WHAT'S THE MATHEMATICS?

• express probability as a fraction
• use fractional notation to express probability of an occurrence
• find equivalent fractions

Extending the Activity

Design a game that has several possible outcomes. Explain how you arrived at your answer.

Assessment 1

Using the spinner to the right, what is the probability of landing on yellow?
a) 1/2
b) 1/4
c) 1/6
d) 1/8

Ans. a) 2 of the 4 equal segments are yellow. The probability of landing on yellow is 2/4 = 1/2.

Assessment 2

Is this spinner fair? Explain your answer.

Ans. The spinner is not fair. Two of the five equal segments are blue. The probability of landing on blue is 2/5. The probability of landing on red is 1/5, the probability of landing on yellow is 1/5, and the probability of landing on green is 1/5.

Additional Notes

For additional information and activities, see pages 48-49 and 60 in the New York State Core Curriculum/Mathematics Resource Guide.

About The Core Curriculum Companion

Source

The Core Curriculum Companion For The New York State Mathematics Resource Guide Writing Team. “Investigation - Uncertainty”. In The Core Curriculum Companion For The New York State Mathematics Resource Guide, 125-127.

Related New York City Performance Standards

• M1d Describe and compare quantities by fractions.
• M4e Predict results and find out why some results are more likely, less likely, or equally likely.
• M5a Formulation
• M5b Implementation
• M5c Conclusion
• M7c Explain solutions to problems clearly and logically.

Related Academic Standards

New York State

NY-4.NF.1 Explain why a fraction a/b is equivalent to a fraction a × n/b × n by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.

NY-4.NF.5 Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100.

NY-4.MD.4 Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots.

4.NF.1 Explain why a fraction a/b is equivalent to a fraction (n * a)/(n * b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.

4.NF.5 Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100.

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