Beyond Slope and Points David Harris, Escondido USD/K12 Alliance Susan Gomez Zwiep, CSU Long Beach/K12 Alliance CMC Palm Springs Oct, 2013 Lesson Available: Science Teacher Magazine (March 2013 Issue) David Harris, Escondido USD/K12 Alliance Susan Gomez Zwiep, CSU Long Beach/K12 Alliance CMC Palm Springs Oct, 2013 Lesson Available: Science Teacher Magazine (March 2013 Issue)

We will… Experience part of a lesson series Connect to the CCSS Math Discuss the Cross-Cutting Connections to Science Experience part of a lesson series Connect to the CCSS Math Discuss the Cross-Cutting Connections to Science

(Observation n ) Use your powers of observation to describe this. Looking at this object, assume you were describing it to someone who had common knowledge of the world but did not know what this was and could not see it as you describe it. How would you describe it?

Objective 1 Given a relationship between two variables in a real situation, I can connect the qualitative description of that relationship to quantitative description.

Sort Of Describe It Take what you have in the envelope and sort by putting together those you see as belonging together. (No need to over-think this)

I want to Belong Consider that a new rectangle is dropped on your table. Describe what would make it fit into each, but not all, category.

Common Two Categories

Categorization by shape: Required using more than one quantitative attribute to describe the category of rectangles Used a ratio of two measures as a category’s defining characteristic One length alone would not define a category

Objective 2 I can explain what a point (x, y) on the graph of a relationship means in terms of the situation from which the data points were derived.

Graphic stack of a Category On a piece of paper, prepare an x-y coordinate grid. For the sake of time we will define the length as the longer side of a rectangle. Take one rectangle and place it on the grid such that one vertex is tucked into the origin of the graph.

And, your point is...? What data points could you derive from this display? Which of these points describe the shape best?

Plot Plot the data points from each rectangle of the category for which (x, y) represents (length, width). There does not need to be any numbers to do this. If there is one, sketch a line of best fit.

Repeat Follow the same steps for the other set(s) of rectangles. You may make a new set of axes or use the same one as before.

Mathematical Similarity Figures that have the same shape but not necessarily the same size. Ratios internal to and between two similar figures are equal.

Our Story

What if…

Further Applications There are concepts in science and math where the quantitative description is a relationship between two variables (bivariate data) rather than a single measure.

Does volume have to go on the x axis (or time)? Why do we put time on the x-axis for motion graphs and volume for density graphs? How does a science concept and slope suggest the axis for each measure?

Our Story Board

Objectives 3 and 4 Participants can describe the equation and graphic representation of a linear relationship. Participants can determine from data points whether a relationship is linear or nonlinear.

Common Core Back Map We will start from 8 th grade Common Core standards and map back to 6 th to analyze connections to the activity.

Common Core Standards for Mathematics Two Types of Standards Mathematical Practice (recurring throughout the grades) Mathematical Content (different at each grade level)

Standards for Mathematical Content K-8 How the grade level standards are organized Standards Clusters Domains

Standards for Mathematical Practice 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning

8 th Grade

Analyze the Progression Given Standards 8.F.5; 8.SP.1 and 8.SP.2 as the Standards connected to our learning targets, what content standards from 7 th and then 6 th were part of a student’s progression to exploring these standards?

Algebra 1 Critical Area #4 Building upon their prior experiences with data, students explore a more formal means of assessing how a model fits data. Students use regression techniques to describe approximately linear relationships between quantities. They use graphical representations and knowledge of context to make judgments about the appropriateness of linear models. With linear models, they look at residuals to analyze the goodness of fit.

Analyze the Practices Which of the mathematical Practice standards (MPS) best describes the type of work a student would be doing in these activities?

Analyze the Practices Which of the mathematical Practice standards (MPS) best describes the type of work a student would be doing in these activities? Choose one of the MPS. What types of prompts would a teacher give to focus student work/thinking on that particular mathematical practice?

Assessing an Objective Learning Target: Given a qualitative description involving the relationship between two variables I can give a quantitative representation in words, numbers and graphs. Assessment

Assessing an Objective Learning Target: Participant can explain what a point (x, y) on the graph of a relationship means in terms of the situation from which the data points were derived. Assessment