DPS Unit Map Grade 7 – Math Unit 5: Inferences 15 Days

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Stage 1: Examine and Unpack Standards

UNIT FOCUS STANDARDS 7.SP.1 Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. 7.SP.2 Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. 7.SP.3 Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. 7.SP.4 Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations.

Transfer Goal

Students will be able to independently use their learning to…

Collect, analyze, and interpret data to communicate information about the real world.

Create inferences about a population(s) based on evidence and reasoning.

Making Meaning

UNDERSTANDINGS Students will understand that…

statistics can be used to gain information about a population by examining a sample of the population.

generalizations about a population are only valid if the sample is representative of that population.

mathematics can give us tools that we can apply to complex problems that involve numbers, but it rarely answers all our questions or addresses all the needs in a situation

sometimes different mathematical approaches yield different solutions.

not all solutions to real-world uses of mathematics are perfect or beyond criticism. Often, we must defend our solutions using both mathematical and non-mathematical evidence and reasoning.

ESSENTIAL QUESTIONS

• How do we measure accurately? • How can the formulation of questions and

conjectures be prompted by the analysis of data?

• How can data be organized so that inferences and predictions can be developed and evaluated?

Acquisition

KNOWLEDGE Students will know…

Random sampling tends to produce representative samples.

Finding a valid, representative sample will enable valid inferences to be made about a population.

What it means to have a valid, random sample representative of a population(s).

Inferences about a population are only valid if the sample is random and representative.

Proportional reasoning is used to make estimates or predictions about a population.

Having multiple samples for the same population allows

SKILLS Students will be able to… • Recognize and identify that different sampling

techniques must be used in real life situations, because it is very difficult to survey an entire population. (7.SP.1)

• Select appropriate sample sizes based on a population in real-life situations and explain why generalizations about a population from a sample are valid only if the sample is random and representative of that population. (7.SP.1)

Collect data from a sample population in order to predict information about a population.

DPS Unit Map Grade 7 – Math Unit 5: Inferences 15 Days

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for gauging the variation of estimates or predictions.

Measures of center can be used to compare data and measure variability between data sets.

Data displays are used to visually compare data sets and draw informal comparative inferences.

Box plots are way to show measures of variability such as the range (Other data displays may highlight other measures of variability).

Mean absolute deviation is an element of a data set that is the absolute difference between that element and a given point. Typically the point from which the deviation is measured is a measure of central tendency, most often the median or sometimes the mean of the data set.

(7.SP.1) • Interpret data from a random sample to draw

inferences about a population with an unknown characteristic of interest. (7.SP.2)

Generate multiple samples (or simulated samples) of the same size to determine the variation in estimates or predictions by comparing the samples. (7.SP.2)

• Identify the degree of overlap between two numerical sets of data. (7.SP.3)

• Visually compare two numerical data distributions with like ranges. (7.SP.3)

Measure the difference between the centers of two different data distributions and express this difference as a multiple of a measure of variability. (7.SP.3)

• Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. (7.SP.4)

Key Vocabulary

Tier 3 Vocabulary Words random sampling, population, representative sample, inferences, variation/variability distribution, measures of center, measures of variability

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 5: Inferences 15 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?feature=player_embedded&v=Ly1ZPFogHps https://www.youtube.com/watch?v=odtB9tOKhvg&feature=player_embedded https://www.youtube.com/watch?v=NulMM5qQSpo&feature=player_embedded https://www.youtube.com/watch?v=U63odI5EBko&feature=player_embedded https://www.youtube.com/watch?v=HACE5QPUDXs&feature=player_embedded

Connected Math Project Resources: CMP2- Samples and Populations- Inv. 2 and 3 CMP2- Data Distributions-Inv. 1-3 CC Investigation 5: Variability Georgia Tasks: https://www.georgiastandards.org/Common-Core/Common%20Core%20Frameworks/CCGPS_Math_7_7thGrade_Unit4SE.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 3 population, random sampling, and inference 7.SP.1

2 3 multiple samples, inference, making predictions, gauging variation

7.SP.2

3 3 Informal comparison of data 7.SP.3

Rubric in task

DPS Performance Task http://www.insidemathematics.org/common-core-math-tasks/7th-grade/7-2005%20Ducklings.pdf

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 5: Inferences 15 Days

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4 4 Formal comparison of data 7.SP.4

5 1 Common District Assessment (CDA) Deadlines YR: _4/17/15___, TR: __4/9/15____

7.SP.1-4

6 1 CDA review and targeted corrective instruction

7.SP.1-4