Beyond Slope and Points David Harris, Escondido USD/K12 Alliance Susan Gomez Zwiep, CSU Long...
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Transcript of Beyond Slope and Points David Harris, Escondido USD/K12 Alliance Susan Gomez Zwiep, CSU Long...
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