# State Curriculum - Mathematics

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Standard 5.0 Knowledge of Probability: Students will use experimental methods or theoretical reasoning to determine probabilities to make predictions or solve problems about events whose outcomes involve random variation. Standard 5.0 Knowledge of Probability: Students will use experimental methods or theoretical reasoning to determine probabilities to make predictions or solve problems about events whose outcomes involve random variation. Standard 5.0 Knowledge of Probability: Students will use experimental methods or theoretical reasoning to determine probabilities to make predictions or solve problems about events whose outcomes involve random variation. Standard 5.0 Knowledge of Probability: Students will use experimental methods or theoretical reasoning to determine probabilities to make predictions or solve problems about events whose outcomes involve random variation. Standard 5.0 Knowledge of Probability: Students will use experimental methods or theoretical reasoning to determine probabilities to make predictions or solve problems about events whose outcomes involve random variation. Standard 5.0 Knowledge of Probability: Students will use experimental methods or theoretical reasoning to determine probabilities to make predictions or solve problems about events whose outcomes involve random variation. Standard 5.0 Knowledge of Probability: Students will use experimental methods or theoretical reasoning to determine probabilities to make predictions or solve problems about events whose outcomes involve random variation. Standard 5.0 Knowledge of Probability: Students will use experimental methods or theoretical reasoning to determine probabilities to make predictions or solve problems about events whose outcomes involve random variation.
A. Sample Space A. Sample Space A. Sample Space A. Sample Space A. Sample Space A. Sample Space A. Sample Space A. Sample Space
1. Identify possible outcomes
1. Identify possible outcomes
1. Identify possible outcomes
1. Identify possible outcomes
1. Identify a sample space
1. Identify a sample space
a. Recognize that a real life situation may have more than one outcome such as a coin having heads or tails
a. Identify some possible outcomes that make up the sample space such as on a number cube rolling a 2
a. Identify possible outcomes that make up the sample space for a given real life situation
a. Determine possible outcomes of independent events
Assessment limit:
• Use two independent events with no more than 4 outcomes each and an organized list or tree diagram
a. Determine the number of outcomes
Assessment limit:
• Use no more than 3 independent events with a sample space of no more than 6 outcomes in each event.
a. Describe the difference between independent and dependent events
b. Identify possible outcomes that make up the sample space for a given experiment such as: flipping a coin, spinning a spinner, and rolling a number cube
b. Determine the number of outcomes
Assessment limit:
• Use no more than 5 dependent events with no more than 10 outcomes in the first event
B. Theoretical Probability B. Theoretical Probability B. Theoretical Probability B. Theoretical Probability B. Theoretical Probability B. Theoretical Probability B. Theoretical Probability B. Theoretical Probability
1. Identify the probability of one simple event
1. Determine the probability of one simple event comprised of equally likely outcomes
1. Determine the probability of one simple event comprised of equally likely outcomes
1. Determine the probability of one simple event comprised of equally likely outcomes
1. Determine the probability of an event comprised of no more than 2 independent events
1. Determine the probability of an event comprised of no more than 2 independent events
a. Describe the probability of an event using words
Assessment limit:
• Use probability terms of more (or most) likely, less (or least) likely, or equally likely
a. Express the probability as a fraction
Assessment limit:
• Use a sample space of no more than 6 outcomes
a. Make predictions and express the probability as a fraction
Assessment limit:
• Use a sample space of no more than 20 outcomes
a. Express the probability of an event as a fraction.
a. Express the probability of an event as a fraction, a decimal, or a percent
Assessment limit:
• Use a sample space of no more than 35 outcomes and decimals with no more than 2 decimal places
a. Express the probability of an event as a fraction, a decimal, or a percent
b. Express the probability of an event as a decimal
Assessment limit:
• Use a sample space of 10, 20, 25, or 50 outcomes

c. Express the probability of an event as a percent

2. Determine the probability of a second event that is dependent on a first event of equally likely outcomes
a. Express the probability as a fraction, a decimal, or a percent
Assessment limit:
• Use a sample space of no more than 60 outcomes
C. Experimental Probability C. Experimental Probability C. Experimental Probability C. Experimental Probability C. Experimental Probability C. Experimental Probability C. Experimental Probability C. Experimental Probability
1. Analyze the results of a probability experiment
1. Analyze the results of a survey or simulation
1. Analyze the results of a survey or simulation
a. Make predictions and express the experimental probability as a fraction, a decimal, or a percent
Assessment limit:
• Use no more than 30 results in the sample space
a. Make predictions and express the probability of the results as a fraction, a decimal with no more than 2 decimal places, or a percent
Assessment limit:
• Use results of 25 or 50
a. Make predictions and express the probability of the results as a fraction, a decimal with no more than 2 decimal places, or a percent
Assessment limit:
• Use 20 to 500 results
2. Conduct a probability experiment
2. Conduct a probability experiment
2. Conduct a probability experiment
3. Compare outcomes of theoretical probability with the results of experimental probability
3. Compare outcomes of theoretical probability with the results of experimental probability
3. Compare outcomes of theoretical probability with the results of experimental probability
4. Describe the difference between theoretical and experimental probability
4. Describe the difference between theoretical and experimental probability
4. Describe the difference between theoretical and experimental probability

Note: Highlighted assessment limits will be tested in the no calculator section of MSA. In the assessment limit, (0-10) or (-10 to 10) means all numbers in the problem or the answer will fall within the range of 0 to 10 (including endpoints) or -10 to 10 (including endpoints), respectively. All content standards are tested in MSA but not all objectives. Objectives that have an assessment limit are tested on MSA. Objectives without an assessment limit are not tested on MSA.

MSDE has developed a toolkit for these standards which can be found online at: http://mdk12.org/instruction/curriculum/mathematics/vsc_toolkit.html.

June 2004