Welcome to Common Core High School Mathematics Leadership Summer Institute 2014 Session 1 • 16 June 2014 Getting the Big Picture & Describing a Distribution

Today’s Agenda Introductions, norms and administrative details CCSSM background MKT assessment Grade 9, Lesson 1: Distribution and Their Shapes Reflecting on CCSSM standards aligned to lesson 1 Break Grade 9, Lesson 2: Describing the Center of a Distribution Reflecting on CCSSM standards aligned to lesson 2 Homework and closing remarks Timing for our purposes: Introductions, norms, admin: 3:30 CCSSM background: 4:15 MKT assessment: 4:30 Dinner arrives at 5:00; eat as you work Lesson 1: content work 5:30, reflection 6:30 Break: 6:45 Lesson 2: content work 7:00, reflection 8:00

Activity 1 introductions, norms and administrative details Where do you teach? What do you teach? How long have you been teaching? What challenges does your district face related to high school mathematics? What is your experience/background with the CCSSM? What do you hope to learn about the CCSSM from this project?

Activity 1 introductions, norms and administrative details Start on Time  End on Time Name Tents Attention signal Raise hand!! Silence cell phones. No texting or Wi-Fi. Restrooms No sidebar conversations . . . Food Administrative fee

Activity 2 ccssm background www.corestandards.org

CCSSM Design Principles Focus: Unifying themes and guidance on “ways of knowing” the mathematics. CCSSM Design Principles Coherence: Progressions based on mathematics and student learning. Understanding: Deep, genuine understanding of mathematics and ability to use that knowledge in real-world situations. Image: www.kidsgeo.com/geology MPES Conference 2011/D. Huinker

by Conceptual Categories Standards for Mathematical Practice Standards for Mathematics Content Make sense of problems & persevere in solving them Reason abstractly & quantitatively Construct viable arguments & critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for & make use of structure Look for & express regularity in repeated reasoning K–8 Standards by Grade Level High School Standards by Conceptual Categories ________________________ Domains Clusters Standards Insert a screenshot / have participants find this in their standards document on pp. 6 - 8

Standards for Mathematical Practice 1. Make sense of problems and persevere in solving them. 6. Attend to precision. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. Reasoning and Explaining 4. Model with mathematics. 5. Use appropriate tools strategically. Modeling and Using Tools 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. Seeing Structure and Generalizing William McCallum, The University of Arizona

K-8 Domains & HS Conceptual Categories William McCallum, The University of Arizona

Why the Engageny/Common Core books? First curriculum designed from the ground up for Common Core (not an existing curriculum “aligned” to the standards) Features tasks of high-cognitive demand that require students to think, reason, explain, justify, and collaborate Contains substantial teacher implementation support resources: lesson plans, notes on student thinking, assessments and rubrics Developed by an exceptional group of educators Source material is available free and could be integrated with existing programs your district may have

Activity 3 Statistics Knowledge Assessment MKT Assessment Go to: http://bit.ly/UWM-LOCUS orhttp://dev- artist.gotpantheon.com/quiz/djqJoGPi9u Access code: djqJoGPi9u

Learning Intentions and Success Criteria We are learning to… Use informal language to describe shape, center, and variability of a distribution displayed by a dot plot, histogram, or box plot. Recognize that the first step in interpreting data is making sense of the context. Make meaningful conjectures to connect data distributions to their contexts. Calculate and interpret the mean and median based on the shape and spread of the data Explain why the mean and the median are approximately the same for a data distribution that is nearly symmetrical and are not approximately the same for a skewed distribution.

Learning Intentions and Success Criteria We will be successful when we can: use appropriate language to describe and interpret a data set by its shape, its center, and its variability. describe the context of a data set, based on the center and variability of a data distribution. explain why we have (at least) two measures of the center of a data set, and when it is appropriate to use one rather than the other.

Activity 4 Lesson 1: distributions and their shapes Review of data distributions and representations EngageNY/Common Core Grade 9, Lesson 1

Activity 4 Lesson 1: distributions and their shapes

Activity 4 Lesson 1: distributions and their shapes

Activity 4 Lesson 1: distributions and their shapes

Activity 4 Lesson 1: distributions and their shapes Reflecting on CCSSM standards aligned to lesson 1 Review the following CCSSM High School content standards: S-ID.1 S-ID.2 S-ID.3 Where did you see these standards in the lesson you have just completed? What would you look for in students’ work to suggest that they have made progress towards these standards?

Activity 4 Lesson 1: distributions and their shapes S-ID.1: Represent data with plots on the real number line (dot plots, histograms, and box plots). S-ID.2: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. S-ID.3: Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliners).

Activity 4 Lesson 1: distributions and their shapes Reflecting on CCSSM standards aligned to lesson 1 Read MP2, the second CCSSM standard for mathematical practice. Recalling that the standards for mathematical practice describe student behaviors, how did you engage in this practice as you completed the lesson? What instructional moves or decisions did you see occurring during the lesson that encouraged greater engagement in MP2? Are there other standards for mathematical practice that were prominent as you and your groups worked on the tasks?

Activity 4 Lesson 1: distributions and their shapes CCSSM MP.2 engageny MP.2 MP.2 Reason abstractly and quantitatively Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. MP.2 Reason abstractly and quantitatively. Students pose statistical questions and reason about how to collect and interpret data in order to answer these questions. Student form summaries of data using graphs, two-way tables, and other representations that are appropriate for a given context and the statistical question they are trying to answer. Students reason about whether two variables are associated by considering conditional relative frequencies.

Activity 4 Lesson 1: distributions and their shapes Closing questions for lesson 1 What are some of the favorite televisions shows for high school students? Do the commercials connect with the viewers? You walk into a store. You estimate that most of the customers are between 50 and 60. What kind of store do you think it is? Why? You are going to take a trip to Kenya. Do you think you will meeting several people ninety or older? Why or why not?

Break

Activity 5 Lesson 2: Describing the center of a Distribution Measures that summarize data distribution shape EngageNY/Common Core Grade 9, Lesson 2

Activity 5 Lesson 2: describing the center of a distribution Individually, and then with your small group, consider: What do you think a center should tell us about a data distribution? How are centers used in our summary of a data distribution?

Activity 5 Lesson 2: describing the center of a distribution Can we assume that all students will interpret the question “How many pets do you currently own?” in the same way?

Activity 5 Lesson 2: describing the center of a distribution Why would the same hallway have different reported measures of length? What measure of the length of the hallway do you think are the most accurate from the data set? Why?

Activity 5 Lesson 2: describing the center of a distribution What number would you use to describe the typical age of cars in years by the car owners in this group?

AN overview of the high school conceptual categories Algebra Functions Modeling Number & Quantity Geometry Statistics & Probability

The Modeling Framework The Modeling Conceptual Category (pages 72-73 of your Standards book)

Activity 5 Lesson 2: describing the center of a distribution Reflecting on CCSSM standards aligned to lesson 2 Review the following CCSSM High School content standards: S-ID.1 S-ID.2 S-ID.3 Where did you see these standards in the lesson you have just completed? What would you look for in students’ work to suggest that they have made progress towards these standards?

Activity 5 Lesson 2: describing the center of a distribution S-ID.1: Represent data with plots on the real number line (dot plots, histograms, and box plots). S-ID.2: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. S-ID.3: Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliners).

Activity 5 Lesson 2: describing the center of a distribution Reflecting on CCSSM standards aligned to lesson 2 Read MP1, the first CCSSM standard for mathematical practice. Recalling that the standards for mathematical practice describe student behaviors, how did you engage in this practice as you completed the lesson? What instructional moves or decisions did you see occurring during the lesson that encouraged greater engagement in MP1? Are there other standards for mathematical practice that were prominent as you and your groups worked on the tasks?

Activity 5 Lesson 2: describing the center of a distribution CCSSM MP.1 engageny MP.1 MP.1 Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. MP.1 Make sense of problems and persevere in solving them. Students choose an appropriate method of analysis based on problem context. They consider how the data were collected and how data can be summarized to answer statistical questions. Students select a graphic display appropriate to the problem context. They select numerical summaries appropriate to the shape of the data distribution. Students use multiple representations and numerical summaries and then determine the most appropriate representation and summary for a given data distribution.

Activity 5 Lesson 2: describing the center of a distribution Closing questions for lesson 2 Sketch a dot plot in which the median is greater than the mean. Could you think of a context that might result in data where you think that would happen? Sketch a dot plot in which the median and the mean are approximately equal. Could you think of a context that might result in data were you think that would happen?

Learning Intentions and Success Criteria We are learning to… Use informal language to describe shape, center, and variability of a distribution displayed by a dot plot, histogram, or box plot. Recognize that the first step in interpreting data is making sense of the context. Make meaningful conjectures to connect data distributions to their contexts. Calculate and interpret the mean and median based on the shape and spread of the data Explain why the mean and the median are approximately the same for a data distribution that is nearly symmetrical and are not approximately the same for a skewed distribution.

Learning Intentions and Success Criteria We will be successful when we can: use appropriate language to describe and interpret a data set by its shape, its center, and its variability. describe the context of a data set, based on the center and variability of a data distribution. explain why we have (at least) two measures of the center of a data set, and when it is appropriate to use one rather than the other.

Activity 6 Homework and Closing Remarks Complete the Lesson 2 Problem Set in your notebook (pages S.14-S.16) Extending the mathematics: Sketch a histogram or dot plot or box plot of data collected from an imaginary population (ages of people in a church or temple, ages of people attending a movie, number of text messages sent per day from a grade 9 math class). Do not indicate the population of your graph. In our next class, we will guess the population based on your graph. Reflecting on teaching: Consider a typical class of 9th grade algebra students in your district. What aspects of these two lessons are likely to connect to their prior knowledge? What concepts in these lessons might be new to them?