May 3^{rd}, 2013

Algebra 1

Yi

Standard/CLE

D.2.C.A1 Given a scatter plot, determine an equation for a line of best fit (DOK 2 MA 3 1.6)
D.3.A.A1 Make conjectures about possible relationships between 2 characteristics of a sample on the basis of scatter plots of the data (DOK 3 MA 3 3.5)

Standard/Common Core

8.SP: Statistics and Probability: Investigate patterns of association in bivariate data.
1: Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.
2: Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.
3: Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height.
4: Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a twoway table. Construct and interpret a twoway table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores?

Essential Question

Drowning deaths and ice cream sales are positively correlated. A politician sees the data and decides to ban ice cream. Does that make sense?
How can we predict the outcome of events? What are the uses and limitations of such predictions?

Lesson Objective

9.3 I can analyze scatter plots to recognize correlation and use them as predictive models.

Notes for Teacher

This activity ties together multiple aspects of Algebra. A real life situation is presented, then students must collect data and explore the relationships between the variables at length. Before the lesson, students would have had one day of instruction on identifying correlation, and constructing lines of best fit, and had a brief quiz on the material. This second day of instruction is to give students an opportunity to apply their learning in an authentic way, while addressing misconceptions identified on the quiz day before.
During the lesson, students will get to work in small groups or pairs, translating between situations, algebraic equations, tables, and graphs. The focus is that students try to make sense of the situation using algebra rather than rote skills.
At the end of the lesson, students have a chance to reflect on their learning, and take another quiz so the instructor can assess their growth and understanding.

Starter Activity

Correct homework assignment 9.3A and work on review questions

Explicit Instruction

After going over the do now and covering any homework questions, have students engage in a whole discussion about the key question in slide 5.
On slide 7, follow up by showing students how reading ability and shoe size is positively correlated. Feel free to utilize a write pair share to engage further student talk.
Have students take notes as instructor moves through the example on slide 9.

Guided Practice

Banana Bungee
In this activity, students will work in partners to simulate a bungee jump using a banana and rubber bands.
Materials needed:
Bananas
Equal sized rubberbands
Paper clips
Measuring Tape
A safe ledge to conduct the final bungee jump
After introducing the activity, but before getting into groups, have students draft their hypothesis on their own. Once in groups, have students share and discuss their reasoning behind their hypothesis.
Next, students will need to tie an “anchor” rubber band to the stem of the banana and attach the paperclip to the other end. Teacher should establish one way to connect rubberbands together.
After data has been collected, students will continue to work in groups until the final test off the 110 inch ledge. Teachers are encouraged to create an incentive for the team who gets closest to the ground without touching.

Independent Practice

Students will individually reflect on the experiment (2 question in the classwork packet) before taking their quiz, and working on the homework assignment.

Checks for Understanding &
Assessment

As students work, ask students about the way they are collecting data and how that may affect their results. Do students notice a trend? How would they classify their data (linear, exponential, quadratic)?
Data from the experiment, students reflections, and quizzes are all means to assess student understanding and growth.

Modifications/Accomodations

Extended time
Enrichment: Give students classwork sheets with less structure such as blank tables with no suggested values for x, or simply blank grid paper for students to organize their own data.

Closure

Class Discussion of reflection questions.
· How close did the banana get to the ground?
· Was your prediction accurate? Explain why or why not.

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