DPS Unit Map Grade 7 – Math Unit 6: Probability 18 Days

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Stage 1: Examine and Unpack Standards

UNIT FOCUS STANDARDS 7.SP.5 Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. 7.SP.6 Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. 7.SP.7 Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.

a. Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. b. Develop a probability model (which may not be uniform) by observing frequencies in data

Transfer Goal

Students will be able to independently use their learning to…

investigate chance processes and develop, use, evaluate probability models.

Making Meaning

UNDERSTANDINGS Students will understand that…

Probability is the likelihood of an event occurring.

Theoretical probability is the likelihood of an event happening based on all possible outcomes.

Experimental probability is the probability of an event occurring after an experiment was conducted.

Probability can often be represented by a visual display of data.

Models can be used to represent the sample space of a compound event in order to connect and build understanding of the probability calculations.

ESSENTIAL QUESTIONS

Will it happen?

How do you make predictions based on data?

How can chance processes be investigated?

How do you develop, use, and evaluate probability models?

How do people use data to influence others?

Acquisition

KNOWLEDGE Students will know…

The probability of a chance event is a number between 0 and 1.

Larger numbers (closer to 1) indicate greater likelihood of an event occurring.

The benchmark of ½ can be used to determine if an event is more likely or less likely to occur.

the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.

Theoretical and experimental probabilities and proportional reasoning are used to make predictions.

Equivalent fractions (and prior fraction knowledge) are used for making predictions.

Probability in a uniform probability model is the number of favorable outcomes as 1 (numerator) out of the number of all possible outcomes (denominator). For example – probability of rolling a 5 on a regular die is

SKILLS Students will be able to… • Represent the probability of a chance event as a

number between 0 and 1. (7.SP.5) • Use the terms “likely”, “unlikely,” to describe

the probability represented by the fractions used. (7.SP.5)

• Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency. (7.SP.6)

• Predict the approximate relative frequency of a chance event given the probability. (7.SP.6)

• Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. (7.SP.7)

• Develop a probability model (which may not be uniform) by observing frequencies in data

DPS Unit Map Grade 7 – Math Unit 6: Probability 18 Days

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generated from a chance process.

7.SP.8 Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.

a. Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs. b. Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., “rolling double sixes”), identify the outcomes in the sample space which compose the event. c. Design and use a simulation to generate frequencies for compound events.

1/6.

Probabilities of compound events are found by first finding the probabilities of each independent event. Then multiply the probabilities of the independent events.

Multiplication of fractions can be used to find probabilities of compound events.

Sample space represents all possible outcomes

Models of probability – area model, tree diagrams, organized lists, table

generated from a chance process. (7.SP.7) • Compare probabilities from a model to observed

frequencies. (7.SP.7) • If the agreement between a model and observed

frequencies is not good, explain possible sources of the discrepancy. (7.SP.7)

• Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. (7.SP.8)

• Represent the probability of a compound event as the fraction of outcomes in the sample space for which the compound event occurs. (7.SP.8)

• Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. (7.SP.8)

• For an event described in everyday language (e.g., “rolling double sixes”), identify the outcomes in the sample space which compose the event. (7.SP.8)

• Design and use a simulation to generate frequencies for compound events. (7.SP.8)

Academic Vocabulary

Stage 2: Calibrate Rigor and Design Assessment

Evaluative Criteria for Assessment District Provided Assessment Tasks

Objective Multiple Choice

Common District Assessments (administered at the end of the unit)

DPS Unit Map Grade 7 – Math Unit 6: Probability 18 Days

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Stage 3: Plan and Deliver Instruction This instructional pacing and sequencing represents one best practice option.

Professional Resources Instructional Resources

Learn Zillion: https://learnzillion.com/courses/43?collection_id=552#collection_545 Teachers to Watch: https://www.youtube.com/watch?v=_J9WHw4swSE&feature=player_embedded https://www.youtube.com/watch?v=MDnBzOf79FA&feature=player_embedded https://www.youtube.com/watch?feature=player_embedded&v=upSeQhv_CJk https://www.youtube.com/watch?v=euZUdpPiM8s&feature=player_embedded https://www.youtube.com/watch?v=aDJklK_nb78&feature=player_embedded

Connected Math Project Resources: CMP: How Likely Is It? CMP: What do You Expect? Georgia: https://www.georgiastandards.org/Common-Core/Common%20Core%20Frameworks/CCGPS_Math_7_7thGrade_Unit6SE.pdf Howard: https://grade7commoncoremath.wikispaces.hcpss.org/Unit+5+Statistics+and+Probability

Summary of Key Learning Events, Opportunities, and Instruction # of

Days Lesson Focus / Student Learning Target(s)

Standard Support

1 2 probability of simple events; likelihood 7.SP.5

2 3 relative frequency of simple events 7.SP.6

3 5 theoretical probability, experimental probability 7.SP.7

4 5 compound events, representations of compound events, simulations

7.SP.8

Rubric in task

DPS Performance Task http://www.insidemathematics.org/common-core-math-tasks/7th-grade/7-2003%20Fair%20Game.pdf (This task will be administered at the end of the unit)

Other Evidence – Embedded Stage 3 Learning Events

Teacher designed PLC designed

Additional Performance Tasks

Minute by Minute Assessments Concept Specific Common Formative Assessments http://mathgoodies4u.wikispaces.com/7+Statistics+and+Probability

DPS Unit Map Grade 7 – Math Unit 6: Probability 18 Days

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5 1 Common District Assessment (CDA) Deadlines YR: _5/11/15___, TR: _5/4/15_____

7.SP.5-8

6 1 Unit 5 and 6 Q4 Performance Task

Deadlines YR: _5/12/15___, TR: __5/5/15____

7.SP.1,4 7.SP.5-8

7 1 CDA review and targeted corrective instruction

7.SP.5-8