SFUSD Mathematics Core Curriculum Development Project · 3 SFUSD Mathematics Core Curriculum, Grade...

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SFUSD Mathematics Core Curriculum, Grade 7, Unit 7.6: Samples and Probability, 2014–2015

SFUSD Mathematics Core Curriculum Development Project 2014–2015

Creating meaningful transformation in mathematics education

Developing learners who are independent, assertive constructors of their own understanding

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Grade 7 7.6 Samples and Probability

Number of Days

Lesson Reproducibles Number of Copies

Materials

1 Entry Task CM2 How Likely? Labsheet 1.1 1 per pair Coins (1 per group or student) 6 Lesson Series 1 CM2 How Likely? 1.2 (2 pages)

CM2 How Likely? 1.3 (3 pages) CPM CCC2 1.2.1 (4 pages) CPM CCC2 1.2.1A Resource Page CM2 How Likely? 1.4 (2 pages) CPM CCC2 5.2.1 (2 pages) CPM CCC2 5.2.3 (3 pages) CM2 How Likely? HW 1 (10 pages)

1 per pair 1 per pair 1 per pair 1 per pair 1 per pair 1 per pair 1 per pair 1 per student

Coins (2 per group) Paper Cups (1 per group) Colored pencils, markers, or crayons Spinners (paper clips or bobby pins) Colored cubes and a clear plastic bag

1 Apprentice Task Fair Game 1 per student 5 Lesson Series 2 CM2 How Likely? 2.2

CPM CCC2 5.2.4 (3 pages) CPM CCC2 5.2.5 (4 pages) CM2 How Likely? 2.3 & 2.4 (4 Pages) CPM CC2 5.2.6 (4 pages) CPM CC2 5.2.6 Resource Page CM2 How Likely? HW 2 (9 pages)

1 per pair 1 per pair 1 per pair 1 per pair 1 per pair 1 per pair 1 per student

2 Number Cubes Spinners (paper clips or bobby pins)

1 Expert Task Cereal Pens 1 per pair Playing Cards; 4 Sided Dice Colored blocks; Spinners

9 Lesson Series 3 CPM CCC2 8.1.1 (3 pages) CPM CC2 8.1.2 (2 pages) CPM CC2 8.2.1 (4 pages) CM3 Samples: 2.2 scenarios Using Random Sampling to Draw Inferences CPM CC2 8.2.2 (2 pages) CPM CC2 8.2.2 Resource Page

1 per pair 1 per pair 1 per pair 1 per pair 1 per pair 1 per pair 1 per pair

Rulers Measuring Tape Envelopes (1 per pair) Scissors Poster Paper

1 Milestone Task Milestone Task Provided by AAO

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Unit Overview

Big Idea

The probability of events can be expressed as a number between 0 and 1. Random sampling allows for better generalization and drawing more accurate inferences about a population. The bigger the population sample the more accurate the prediction.

Unit Objectives

● Students will understand and use random sampling to draw inferences about a population. ● Students will be able to draw informal comparative inferences about two populations. ● Students will investigate chance processes and develop, use, and evaluate probability models.

Unit Description

Students begin by developing an intuitive sense of probability through a coin-tossing experiment. Then they are introduced to the idea that probability can be used to predict outcomes and that not all outcomes are equally likely. Students began to look at the difference between experimental and theoretical probabilities and learn to develop theoretical probabilities using probability trees. Students understand that games are only fair if each participant has the same probability of winning. As they develop the understanding that experimental probabilities are more representative as the number of experiments gets larger, they take that understanding and apply it to data samples, i.e., that data sampling is more representative as the sample gets larger. They compare two populations based on inferences made from data samples. Finally, students find the mean average as a typical sample size and use that information to make predictions in situations involving scale.

CCSS-M Content Standards

7.SP – Statistics and Probability Use random sampling to draw inferences about a population. 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. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be. Draw informal comparative inferences about two populations. 7.SP.3 Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers

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by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable. 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. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book. Investigate chance processes and develop, use, and evaluate probability models. 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. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times. 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. 7.SP.7a Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected. 7.SP.7b Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies? 7.SP.8 Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. 7.SP.8a 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. 7.SP.8b 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. 7.SP.8c Design and use a simulation to generate frequencies for compound events. For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood?

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Progression of Mathematical Ideas

Prior Supporting Mathematics Current Essential Mathematics Future Mathematics

In earlier grades students have been using data to answer simple statistical questions, but have paid little attention to how the data were selected. Students begin to represent and analyze distributions using dot plots, line plots, histograms, and box plots, and develop a deeper understanding of variability and more precise descriptions of data distributions, using numerical measures of center and spread, and terms such as cluster, peak, gap, symmetry, skew, and outlier. There is no formal work in probability before seventh grade.

Students move from concentrating on analysis of data to production of data, understanding that good answers to statistical questions depend upon a good plan for collecting data relevant to the questions of interest. Students must develop some knowledge of probability before launching into sampling. Their introduction to probability is based on many opportunities to develop the connection between theoretical probability models and empirical probability approximations. The connection forms the basis of statistical inference. Students begin to differentiate between the variability in a sample and the variability inherent in a statistic computed from a sample when samples are repeatedly selected from the same population.

In eighth grade, students apply their experience with the coordinate plane and linear functions in the study of association between two variables related to a question of interest. Students extend their understanding of the univariate case to bivariate measurement data. They summarize bivariate categorical data using two-way tables of counts and/or proportions, and examine these for patterns of association. In high school, students develop a more formal and precise understanding of statistical inference as they learn that formal inference procedures are designed for studies in which the sampling or assignment of treatments was random and that these procedures may not be informative when analyzing non-randomized studies. Students extend their knowledge of probability, learning about conditional probability, and using probability distributions to solve problems involving expected value.

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Unit Design All SFUSD Mathematics Core Curriculum Units are developed with a combination of rich tasks and lessons series. The tasks are both formative and summative assessments of student learning. The tasks are designed to address four central questions: Entry Task: What do you already know? Apprentice Task: What sense are you making of what you are learning? Expert Task: How can you apply what you have learned so far to a new situation? Milestone Task: Did you learn what was expected of you from this unit?

1 Day 6 Days 1 Day 5 Days 1 Day 9 Days 1 Day

Total: 24 days

Lesson Series 1

Lesson Series 2

Lesson Series 3

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Entry Task Choosing Cereal

Apprentice Task Fair Game?

Expert Task Cereal Pens

Milestone Task Putting it all Together

CCSS-M Standards

7.SP.6 7.SP.5, 7.SP.6, 7.SP.7, 7.SP.8 7.SP.5, 7SP.6, 7.SP.7, 7SP.8 7SP.1, 7SP.2, 7SP.3, 7SP.4

Brief Description of Task

Discussion of probability (with KWL or PowerPoint) and then use coin toss problem 1.1 to observe results.

Students use probability to judge the fairness of a game.

Students design and carry out a simulation to predict probabilities.

Offensive Linemen Students analyze data from two college football teams.

Source Connected Mathematics 2: How Likely Is It?

MARS Adapted from Illustrative Mathematics

Illustrative Mathematics

Lesson Series 1

Lesson Series 2

Lesson Series 3

CCSS-M Standards

7.SP.5, 7.SP.6, 7.SP.7 7.SP3, 7.SP6, 7.SP8 7.SP.1, 7.SP.2, 7.SP.3, 7.SP.4

Brief Description of Lessons

Students develop an intuitive sense of probability through experiments, develop strategies for finding experimental probability, understand that probabilities are useful for predicting what will happen over the long run, and understand the concepts of equally likely and not equally likely. Tossing Paper Cups; One More Try; What if there is more than one event?; What are the chances?; Analyzing Events; Is it a fair game?

Students compare experimental and theoretical probabilities, use organized lists and tree diagrams to find theoretical compound probabilities, and understand that larger samples are better estimates. Exploring Probabilities; How can I find all the outcomes?; Winning the Bonus Prize; What if there are more than two events?; What if the events are not equally likely?

Students will compare two populations by making inferences from samples, based on the median and the interquartile range (IQR) of each sample. Students begin to use surveys and learn about sampling methods. Students also draw inferences and gauge the variation in sample statistics by creating multiple samples of a given population. In doing so, they continue to investigate the limitations of samples and statistics in accurately describing an entire population. Which tool is more precise?; Can I Compare the Results?; Is the Survey Fair? ; How Close is My Sample?

Sources Connected Mathematics 2: How Likely Is It? CPM Core Connections Course 2

Connected Mathematics 2: How Likely Is It? CPM Core Connections Course 2

CPM Core Connections Course 2

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Entry Task

How Likely Is It?

What will students do?

Mathematics Objectives and Standards Framing Student Experience

Math Objectives: ● Students develop an intuitive sense of probability through a

coin-tossing experiment. CCSS-M Standards Addressed: 7.SP.6 Potential Misconceptions:

Launch: You might begin by discussing questions in Getting Ready to informally assess students. Discuss decision-making and chances. During: Section A: - Show students a task list showing each step of the activity. - Model the first few tosses, how to record on chart, and how to write as a fraction and calculate as a percent. - Monitor groups to ensure they are recording data correctly. - Instruct students to, as they finish recording data, answer Part A, Question #2 (provide sentence frame). Early finishers: - As groups finish collecting their data, have them find another group who is finished. Groups should compare their data, then combine the results of how many times heads was tossed; find the percent. - Groups can keep combining with other groups as needed. Section B: - Once all or most groups have finished, have each group share out their answers to Question #2. Students can predict what will happen as the class data gets combined. - Have each group share out the number of heads that were tossed. Add and calculate as a fraction and decimal for the whole class. - Have students discuss questions for Part B in groups, as a class before answering. Closure/Extension: Students answer Part C in their groups. Discuss as a class. Introduce and discuss the concepts of “equally likely” versus “not equally likely” as it relates to the coin toss experiment.

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How Likely Is It?

How will students do this?

Focus Standards for Mathematical Practice: 4. Model with mathematics.

Structures for Student Learning: Academic Language Support:

Vocabulary: probability, fraction, percent, prediction, data, approximately

Sentence frames: Pre-task prediction: I predict that Kalvin will eat Cocoa Blast cereal _____ days out of _____ total days in June. I predict that the probability of Kalvin eating Cocoa Blast cereal each day in June will be ________. (fraction/decimal/percent) A. Question #2: As I add more data, the percent of tosses that are heads ________. (what happens?) B. Question #1: The total class number of tosses shows that ________% were heads. As the class adds more data, the percent of tosses that are heads ________. (what happens?) In June, the number of times Kalvin will eat Cocoa Blast cereal is approximately _________. Based on this, I expect Kalvin to eat Cocoa Blast Cereal in July for ________ days because ________. C. When Kalvin’s mother said that his chance of a coin showing heads is ½, this does/doesn’t (circle one) mean that for every two tosses he will always get one head and one tail because ________.

Differentiation Strategies: Suggested task list for the activity:

● Step 1: Create a chart with the five columns shown in “Coin Toss Results.” Then draw 30 rows for the 30 days of June, labeling each row with the date (1, 2, 3, 4, etc,, up to 30).

● Step 2: Toss a coin. ● Step 3: Record the result of the toss, H for heads or T for tails, in the labeled column. ● Step 4: Count how many times heads has been tossed so far; record in the labeled column. ● Step 5: Use the number of heads tossed and the total tosses to write the fraction of heads so far; record in the labeled column. ● Step 6: Use this fraction to calculate the percent of heads so far; record in the labeled column. ● Repeat steps 2–6 until you have tossed the coin 30 times. ● Model the first few tosses, how to record on chart, and how to write as a fraction and calculate as a percent. ● Provide an individual copy of the task list of steps for those who may have trouble tracking steps from the board. ● As groups begin to work in their on tossing and recording, model more rounds of tossing and recording for those students who need more support. ● Provide an already drawn chart to students with fine motor, visual-motor, or attention difficulties. ● Review how to change a fraction to a percent. ● Model/chart of writing a probability: Number of possibilities for item or number of total possibilities.

Participation Structures (group, partners, individual, other): Partners or groups of three, allowing for each partner to take turns tossing, record data, and discuss results of the data.

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Lesson Series #1 Lesson Series Overview: Students develop an intuitive sense of probability through experiments, develop strategies for finding experimental probability, understand that probabilities are useful for predicting what will happen over the long run, and understand the concepts of equally likely and not equally likely. CCSS-M Standards Addressed: 7.SP.5, 7.SP.6, 7.SP.7 Time: 6 days

Lesson Overview - Day 1 Resources

Description of Lesson: Toss paper cups to find an experimental probability where the outcomes are not equally likely. Understand that probabilities are useful for predicting what will happen over the long run. Notes: Provide a graphic organizer.

Connected Mathematics 2: How Likely Is It? Lesson 1.2: Tossing Paper Cups Suggested HW: Choose from CM HW (Applications, Connections, Extensions, etc.)


Description of Lesson: Develop strategies for finding experimental probabilities for a situation that involves tossing two coins, and explore the notion of fair and unfair. Use CPM CCC2 5.2.3 Problem 5-43 to summarize results and practice (c) organizing the possibilities. Notes: Provide a graphic organizer.

Connected Mathematics 2: How Likely Is It? Lesson 1.3: One More Try Suggested HW: Choose from CM HW


Description of Lesson: Powerpoint of possible or impossible can be substituted for CPM CCC2 Problem 1-50. Students understand and practice that probability is a fraction. Students are introduced to theoretical probabilities and build on experimental probabilities.

CPM CCC2 Lesson 1.2.1 - What are the Chances? (Introduction to Probability) Suggested HW: Choose from Review & Preview

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Description of Lesson: Students understand the concepts of equally likely and not equally likely.

Connected Mathematics 2: How Likely Is It? Lesson 1.4: Analyzing Events Suggested HW: Choose from CM HW


Description of Lesson: Students will practice writing probabilities of events and non-events and decide the fairness of the outcome.

CPM CCC2 Lesson 5.2.1: Is it a fair game? Probability Games Suggested HW: Choose from Review & Preview


Description of Lesson: Students continue to discuss independent events with the rock-paper-scissors activity.

CPM CCC2 Lesson 5.2.3 Problem 5-44 through 5-47- What if there is more than one event? Compound Independent Events Suggested HW: Choose from Review & Preview

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Apprentice Task

Fair Game?



Math Objectives: ● Students use probabilities to represent sample space for simple and

compound events. ● Students estimate the probability of future events and construct

arguments about the fairness of a game. CCSS-M Standards Addressed: 7.SP.5, 7.SP.6, 7.SP.7, 7.SP.8 Potential Misconceptions:

● The score students find in problem 1 is not the number of squares they are moving on the game board.

● Students may or may not include 2 as a prime number.

Launch: Discuss the task with students. Explain scoring that Chris and Jack are using. Then have students either complete the task individually or in pairs. Review prime numbers if they don’t remember what this is. ● Demonstrate/model for students how the first three results were obtained,

using the scoring chart (supplement with simplified rules for scoring chart). ● As a class, review the chart to ensure all students have correct responses.

Review incorrect responses and how they came to that answer (common misconceptions).

During: Walk around and help students with questions. Closure/Extension: Review task or ask students to share their strategies for solving. What is considered fair or unfair?

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Fair Game?


Focus Standards for Mathematical Practice: 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics.


Vocabulary: prime number, “twice” and “two more than” (relate to math operations), trial Sentence frames: For Question #3: If they play ____ times total, then probably: Chris will get to move ____ times (___ squares). Jack will get to move ____ times (___ squares).

Differentiation Strategies:

● Provide a list of prime numbers. ● Model/chart of writing a probability

○ Number of possibilities for item or number of total possibilities ● Simplify the rules for scoring chart::

○ H = Number Cube x 2 ○ T = Number Cube + 2

● Simplify the rules for moving squares: ○ Prime = Chris moves 2 spaces ○ Composite/Not Prime = Jack moves 1 space

Participation Structures (group, partners, individual, other):

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Lesson Series #2

Lesson Series Overview: Students compare experimental and theoretical probabilities, use organized lists and tree diagrams to find theoretical compound probabilities, and understand that larger samples are better estimates. CCSS-M Standards Addressed: 7.SP3, 7.SP8, 7.SP6 Time: 5 days


Description of Lesson: Students learn about some of the properties of probability as a mathematical concept. They also explore how probability changes if the sample size changes.

Connected Mathematics 2, How Likely Is It? Problem 2.2 – Exploring Probabilities Suggested HW: Choose from CM HW (Applications, Connections, Extensions, etc.)


Description of Lesson: Students are introduced to one method for organizing outcomes by using the probability table.

CPM CCC2 Lesson 5.2.4 - How can I find all the outcomes? Probability Tables Suggested HW: Choose from CM HW or CPM Review & Preview


Description of Lesson: Students make and use tree diagrams to determine theoretical compound probabilities and compare them with experimental probabilities. Use Connected Mathematics Problem 2.3 and 2.4 Introduction to show probability trees, then if there is time, move into CPM. Students practice with the tree diagram to find probabilities of independent events. Students are introduced to “mutually exclusive.”

Connected Mathematics 2, How Likely Is It? Problem 2.3 – Designing a Fair Game Problem 2.4 - Winning the Bonus Prize Optional: CPM CCC2 Lesson 5.2.5 Probability Tree: What if there are more than two events? Suggested HW: Choose from CM HW or CPM Review & Preview

Lesson Overview - Day 4 and 5 Resources

Description of Lesson: Students calculate probabilities of compound events where the outcomes are not equally likely by using a probability table. This will take 1 to 2 days.

CPM CCC2 Lesson 5.2.6 Compound events Suggested HW: Choose from CM HW or CPM Review & Preview

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Expert Task

Cereal Pens



Math Objectives: ● Students design and carry out a simulation ● Students use the results of the simulation to make statements about

probabilities of different events CCSS-M Standards Addressed: 7SP.8, 8a, 8c Potential Misconceptions Note to teachers from Illustrative Math Website: Modeling with simulation follows four steps: state assumptions about how the real process works; describe a model that generates similar random outcomes; run the model over many repetitions and record the relevant results; write a conclusion that reflects the fact that the simulation is an approximation to the theory.

Launch: Present task to whole class, clarifying as needed. Provide a selection of the following materials to help with simulation: - playing cards - 4 sided dice - spinners - construction paper squares/bags - website/computer random generators Give students 10 minutes to discuss in groups of 2-4 a plan for a simulation. During: After 10 minutes, have groups share and discuss whether each simulation will work, why or why not, allowing groups to modify their plan as necessary. Discuss how many trials to have. Groups then perform the simulation and record their results, then answer the questions, justifying their conclusions. Closure/Extension: Discuss results and methods for solving.

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Cereal Pens


Focus Standards for Mathematical Practice: 1. Make sense of problems and persevere in solving them. 2. Use appropriate tools strategically


Vocabulary: Sentence frames:

Differentiation Strategies: Participation Structures (group, partners, individual, other): Whole class, pairs and small groups

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Lesson Series #3

Lesson Series Overview: Students will compare two populations by making inferences from samples, based on the median and the interquartile range (IQR) of each sample. Students will begin to use surveys and learn about sampling methods. Students will also draw inferences and gauge the variation in sample statistics by creating multiple samples of a given population. In doing so, they continue to investigate the limitations of samples and statistics in accurately describing an entire population. *Note – IQR should be replaced by Mean Absolute Deviation (MAD) as the measure of choice. The new standards indicate this starting in 6th grade. CCSS-M Standards Addressed: 7.SP.1, 7.SP.2, 7.SP.3, 7.SP.4 Time: 9 days

Lesson Overview - Day 1 & 2 Resources

Description of Lesson: Students will measure a length using different measuring tools and generate two sets of data. They will compare the data by creating histograms and box plots to analyze center, shape, spread, and outliers. This is new for students this year although this lesson already assumes students know how to construct the plots. Spread this lesson over two days. Notes: You may have to spend time teaching how to make a box plot/box and whisker plot. Vocabulary with interquartile range, mean, median, mode should be reviewed.

CPM CCC2 Lesson 8.1.1 Which tool is more precise? Suggested HW: Choose from Review & Preview


Description of Lesson: This lesson focuses on comparing distributions of data using box and whisker plots and some histograms.

CPM CCC2 Lesson 8.1.2 Can I Compare the Results? Suggested HW: Choose from Review & Preview

Lesson Overview - Days 4 & 5 Resources

Description of Lesson: Students are introduced to convenience sampling, voluntary response sampling, representative sampling, and cluster sampling. Begin with 8-29 as introduction, then use CM Problem 2.2 scenarios for students to discuss the different types of sampling. Continue with 8-31 in CPM. You can create a foldable and have a card sort to differentiate the different sampling methods.

CPM CCC2 Lesson 8.2.1 Is the Survey Fair? Connected Mathematics 3: Samples and Populations Problem 2.2 Scenarios

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Description of Lesson: Students examine samples for bias by categorizing scenarios in the warm-up and then use random samples to predict outcomes in larger populations.

Using Random Sampling to Draw Inferences Poster paper (optional)


Description of Lesson: Students discuss random sampling and use this sampling strategy to compare populations. Teachers need to prepare a class set of cutouts from the Resource Page for random sampling.

CPM CCC2 Lesson 8.2.2 How Close is My Sample? Suggested HW: Choose from Review & Preview

Lesson Overview – Days 8 & 9 Resources

Description of Lesson: Students design an experiment and collect answers using sampling. Sampling Project Directions:

1. You are the designer. Your job is to design an experiment based on a question you would like to find the answer to. You need to collect responses and data using one of the sampling methods.

2. Think of a question, then come up with an hypothesis. 3. Develop a way to collect data. 4. Display your data results in graph form. 5. Share your conclusion by poster or PowerPoint.

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Milestone Task

Putting it all together



Math Objectives: ● Students will compare data from two college football teams and

analyze teams based on the data. CCSS-M Standards Addressed: 7.SP.2, 7.SP3, 7.SP4 Potential Misconceptions:

Launch: Constructed Response – there are 3 constructed response questions. Offensive Linemen – this will serve as the Performance Assessment for the last CLA. If you have not discussed mean absolute deviation (MAD), then only ask students to find the mean in part b of Offensive Linemen. During: Walk around and answer questions. Closure/Extensions: Counting Trees - Give students this assignment as an individual assessment. Answer any questions before the students begin.

● Students will choose an appropriate sampling method and collect data and record on a table.

CL 4-129 CPM CL 8-117 CPM Part of Georgia Travel Times X marks the spot - Lesson for Learning

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Putting it All Together


Focus Standards for Mathematical Practice: 1. Make sense of problems and persevere in solving them. 3. Construct viable arguments and critique the reasoning of others.


Vocabulary: mean absolute deviation (MAD), average, random sampling Sentence frames:

Differentiation Strategies: Participation Structures (group, partners, individual, other): Individual

SFUSD Mathematics Core Curriculum Development Project · 3 SFUSD Mathematics Core Curriculum, Grade...

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Transcript of SFUSD Mathematics Core Curriculum Development Project · 3 SFUSD Mathematics Core Curriculum, Grade...