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Authors’ Names: Jesse Green and Sharon Parker
Title of Lesson: Scatter plots
Date of Lesson: 2/22/2010
Length of Lesson: 50 mins
Name/Level of Course: 7th Grade Algebra 1 A
Appropriateness for Middle School Students: The exploration depends on the maturity of the middle schoolers to safely push another student on the crash cart. Students will also be using graphing calculators and will be expected to follow the written directions with little to no further instruction.
Source of the Lesson: Cooperative Learning and Algebra 1: Secondary Activities. Becky Bride 2007 Kagan Publishing. Find my x- and y-intercepts 224 and 233
Graphing Resources: Line Graphs and Scatter Plots © Copyright NC State University 2004
Sponsored and funded by National Science Foundation
Concepts
Students will learn that lines of best fit do not necessarily need to cross all points on a scatter plot, and how to find the line that best represents the correlation of data.
A scatter plot is usually made up of two variables: the independent (usually the x) and the dependent (usually the y). The independent variable is the one that you can manage and change, to see what happens to the dependent variable, which is observed. For scatter plots both variables are measurable in order to make distinct points. When plotting the points, order the independent variable from least to greatest, or in some kind of order, and plot the points. The points most likely won’t be on an exact line, but if there is a linear correlation, then there exists a line such that the trend of the data can be represented.
The possible types of correlation are positive, negative, vertical, horizontal, and no correlation, depending on what the slope is. Most correlations are either positive or negative, which gives the kind of trend two variables have on each other.
Performance Objectives (students will be able to…)
• Relate a real life example to scatter plots and lines of best fit
• determine lines of best fit for four basic graphs
• determine positive and negative correlation.
SSS Addressed
• MA.912.A.3.11- Write the equation of a line that models a data set, and use the equation or the graph to make predictions. Describe the slope of the line in terms of the data, recognizing that the slope is the rate of change.
• MA.912.A.3.12- Graph a linear equation or inequality in two variables with and without graphing technology. Write an equation or inequality represented by a given graph.
• MA.7.A.1.4- Graph proportional relationships and identify the unit rate as the slope of the related linear function.
Safety
* students need to stay clear while cart is in motion
* Students need to push cart carefully not to injure another student.
* Student sitting on cart needs to keep hands and feet on the cart to avoid running over fingers/ toes.
Supplementary Materials, Handouts
* 22 copies of pre test
* 22 copies of assesment
* transparency of instructions
* 22 copies of data sheet
* Small to medium sized bag of starburts
* Crash cart
* Stop watch
* Measuring tape
* 1000 pennies (or some other type of unit that varies in weight more)
|ENGAGEMENT Time: 10 mins | | |
|What the Teacher Will Do |Probing Questions |Student Responses and Potential Misconceptions |
|Before starting lesson tell students that today |How many pennies do you think this is? |500, 200 ect… |
|we will be raising our hands to answer all | |[1000] |
|questions. Show the students the pennies. | | |
|Tell them there are actually 1000 pennies. Show |If we wanted to make a graph comparing |Pennies on the side, weight in the jar on the bottom. |
|the students a jar. Pass out graphs for all the |the weight in the jar compared to how |[Number of pennies on the bottom, weight in the jar on the side] |
|students and have one overhead. |many pennies are in it, how would we | |
| |graph that? | |
| |Ask one of the students who answered |[The weight of the jar is affected by how many pennies are in the jar] |
| |correctly why they got that answer. | |
|Have an empty jar. Have a student weigh the jar |“Where would this weight go on our |[on the y-axis, because there are no pennies in the jar yet] |
|and tell the class. |graph?” | |
|Add 250 pennies. Have another student tell you |“Where would this go on the graph?” |[at the 250 mark and wherever the weight is] |
|the weight. | | |
|Repeat until all the pennies are in the jar. |Is it more likely or less likely that |[More likely] |
| |the more pennies in the jar the more | |
| |weight? | |
|Look at the graph. |Which way does the slope go on the |[Like an uphill] |
| |graph? | |
| |So what kind of slope is this? |[positive] |
|EXPLORATION Time: 25 min | | |
|What the Teacher Will Do |Probing/Eliciting Questions |Student Responses and Misconceptions |
|Have the crash cart, measuring tape, and |We are going to be doing an activity today to collect | |
|starburst ready in the hall. |data for a scatter plot. Class please stand back behind | |
| |me and will (two students Mrs bairley has chosen) please | |
| |come up? Now will one of you sit on the cart? The other | |
| |is going to push you at a steady speed for 30 seconds | |
| |Miss oarker will call out every two seconds as a cue for | |
| |you to drop a starburst. | |
| | | |
| | | |
|Have two volunteers measure where each starburst |Class record these numbers on your data sheet and please |Students go inside. |
|fell along the measuring tape. |quietly and calmly return to your seats in the classroom.| |
|Have instructions posted on over head. |Now follow the steps on the instruction sheet. | |
|Stop students before they graph line of best fit.|How can we graph this data? |Connect all the points [line of best fit] |
|Have students finish final steps graphing line of| | |
|best fit and the formula provided of their line. | | |
|Have the crash cart, measuring tape, and |Class please stand back behind me and will (two students | |
|starburst ready in the hall. |Mrs bairley has chosen) please come up? Now will one of | |
| |you sit on the cart? The other is going to push you at a | |
| |steady speed for 30 seconds Miss oarker will call out | |
| |every two seconds as a cue for you to drop a starburst. | |
| | | |
| | | |
|Have two volunteers measure where each starburst |Class record these numbers on your data sheet and please |Students go inside. |
|fell along the measuring tape. |quietly and calmly return to your seats in the classroom.| |
|Have instructions posted on over head. |Now follow the steps on the instruction sheet. | |
|EXPLANATION Time: 5 mins | | |
|What the Teacher Will Do |Probing/Eliciting Questions |Student Responses and Misconceptions |
|Explain why connecting all points would be |What would happen if we tried to connect every dot on this|A squiggly line. |
|impossible and improbable. |graph? |You couldn’t see a relation to anything there |
| |Why would that not be helpful? |would just be random lines. |
| |So why should we draw a line of best fit? |To see a clear relationship in the data |
| |Does anyone know what that relationship is called? |Correlation. |
|ELABORATION Time: 5 mins | | |
|What the Teacher Will Do |Probing/Eliciting Questions |Student Responses and Misconceptions |
|Have example graphs on over head. |Does anyone know what the line of best |Lines. |
| |fit for this graph would be? | |
| |Does anyone know what the correlation |Positive negative none. |
| |for this graph would be? | |
|Have example graphs on over head. |Does anyone know what the line of best |Lines. |
| |fit for this graph would be? | |
|EVALUATION Time: 10 mins | | |
|What the Teacher Will Do |Probing/Eliciting Questions |Student Responses and Misconceptions |
|Pass out quiz | | |
| | | |
Pre-Assessment Quiz.
Draw the line of best fit and write the whether there is a positive negative or no correlation.
1.[pic] Correlation____________
2.[pic]Correlation_______________
3.[pic]Correlation_______________
4.[pic]Correlation__________________
Post assesment
1.[pic]Correlation______________________
2.[pic]Correlation_______________________
3.[pic] Correlation_____________________
4.[pic]Correlation______________________
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