Beyond Slope and Points

Beyond Slope and Points

David Harris, Escondido USD/K12 AllianceSusan Gomez Zwiep, CSU Long Beach/K12

Alliance

CMC Palm SpringsOct, 2013

Lesson Available: Science Teacher Magazine (March 2013 Issue)

David Harris, Escondido USD/K12 AllianceSusan Gomez Zwiep, CSU Long Beach/K12

Alliance

CMC Palm SpringsOct, 2013

Lesson Available: Science Teacher Magazine (March 2013 Issue)

We will…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

(Observationn)

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 8th grade Common Core standards and map back to 6th 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

8th Grade

8th Grade

8th Grade

8th 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 7th

and then 6th were part of a student’s progression to exploring these

standards?

Algebra 1Critical 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