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Learning Objectives: What should students know and be able to do as a result of this lesson?
Students will interpret the y-intercept of the line of best fit on a scatter plot with respect to the context of the problem.
Students will interpret the slope (rate of change) of the line of best fit on a scatter plot within the context of the problem.
Prior Knowledge: What prior knowledge should students have for this lesson?
Students need to know how to find the slope given two points.
Students need to know how to count the slope using "rise over run" when the line is given on a graph.
Students need to know how to identify the slope and y-intercept from a linear equation in slope-intercept form.
Guiding Questions: What are the guiding questions for this lesson?
How can you describe the relationship between the two quantitative variables?
How can you describe the y-intercept and the slope in the context of the problem?
Teaching Phase: How will the teacher present the concept or skill to students?
Bell-ringer (warm-up) – the students will be given 5 equations in slope – intercept form and asked to state the slope and the y-intercept for each. (if necessary – use practice problems about slope-intercept form)
Display the first example of hours and dollars scatter plot, line of best fit and the equation. The students will discuss with a partner what the axis labels represent and how they relate to the slope and the intercept in the context of the example.
How does hour affect the dollar amounts?
Once the students have discussed what they think, they will write their answers on the dry-erase boards. The teacher records their answers on chart paper or on the board then discusses the responses with the class. The teacher also will need to discuss how meaningful the y-intercept is for this example and the real-life application of the scatter plot. (The y-intercept is meaningful since no hours worked would have no dollars).
Guided Practice: What activities or exercises will the students complete with teacher guidance?
Display the second example of shoe size and height scatter plot, line of best fit and equation. The students will discuss with the same partner (or the teacher could have them change partners) what the axis labels represent and how they relate to the slope and the intercept in the context of the example. The teacher needs to clarify that the line of best fit is for this sample of the data. The y-intercept is not meaningful for the entire population.
Once the students have discussed what they think, they will write their answers on the dry-erase board. The teacher records their answers on chart paper or on the board then discusses the responses with the class. The teacher also will need to discuss how meaningful the y-intercept is for this example and the real-life application of the scatter plot. (The y-intercept is not meaningful since you cannot have a height of 48 inches with a shoe size of zero, this because we are looking at sample data.)
Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the lesson?
The students will work on two practice problems about the height and weight of females and males independently first on dry-erase boards. Once they work on their own, they will pair up with another student with the other problem and discuss their answers.
The students will be given an exit slip dependent on their work on the height and weight scatter plots.
Closure: How will the teacher assist students in organizing the knowledge gained in the lesson?
After discussing the two problems given, the teacher will give the students an exit slip. These will be turned in as the students leave the classroom. Once the teacher sorts them and reviews the responses, the teacher will use the information for the next day's lesson. This bell-ringer could be similar to all three exit slips. Or the bell-ringer for the following day could address any misconceptions discovered from review of the exit slips.
The Exit slip with a scatter plot and line of best fit given will be used as a summative assessment. Students will describe the relationship of the slope and the y-intercept in the context of the problem.
An answer key for the slope and y-intercepts descriptions is given for each of the exit slip levels. This can be graded as a mini-quiz. (The interpretation of slope and y-intercept for a scatter plot should be reviewed in future lessons.)
The teacher will walk around as the students are working on the bell-ringer. The teacher can ask questions such as "how did you determine the slope and y-intercept for each linear equation?" This is where the teacher can determine if the students understand which values represent the slope and y-intercept in slope-intercept form. If there are students not quite sure about finding the slope and y-intercept, the teacher can adapt the guided practice to address the concern. See guiding questions.
During the discussion on the examples presented, the teacher will walk around to pairs of students as they discuss the relationship of the variables, monitoring progress and providing feedback.
Think-pair-share time – the students will individually think about and work through their given problem. Then they will pair up with another student and the pair will share how they interpreted each of their problems. The teacher will walk around as the pairs discuss their work to aid in discussion and offer feedback.
The teacher will have the students discuss their results. Before the end of class, an exit ticket will be given (see attachments - Three Exit Slips and answers). There will be three levels of exit tickets dependent on the information gathered as the teacher observed the student's discussion. (Check the last bullet in the Teaching Phase section on how to decide which exit ticket to give each student based on their understanding from the examples, practice problems and discussions).
Feedback to Students
The students will be working with a partner after completing the problems given (Practice Problems and answers attachment). This discussion could be based on their observation of the scatter plot. If the problems given are different in the pair, then each student would need to explain their own interpretation for their own problem. The students need to address what the slope is and what it represents in the scatter plot. They also need to discuss the meaning (if one) of the y-intercept. They should come to a consensus on what their interpretations are. The teacher will observe the student pairs, possibly asking questions about what the students are discussing or helping the students clarify their thinking as they record their answers on their dry-erase boards.
The teacher feedback on the exit slips would depend on what the student wrote describing the scatter plot and the interpretation of the slope and the y-intercept. The teacher might ask for clarification on a given response or ask for more information. If the student provides slope and has not given what they feel the slope means, then the teacher would need to ask for more information. The teacher should group the exit slips based on any misconceptions, lack of a clear response, or complete/correct responses. Since the exit slips are used as a summative assessment, the teacher might want to allow those students with any misconceptions or a lack of a clear response to do a "mini-quiz correction." These can be done in small groups or individually. Another way to provide feedback for the exit slips could be that the teacher talks with those students with misconceptions or a lack of a clear response. The exit slips need to be returned to the students the next day.
Accommodations & Recommendations
If needed, have the students complete some additional practice problems determining the slope and y-intercept from equations in slope-intercept form (like the warm up document). They can answer on dry-erase boards or sheet protectors.
The exit slips will be used to differentiate, dependent on what the teacher hears and sees during the work and discussion of the practice problems. These exit slips are based on the cost and selling price of merchandise.
Use the scatter plots to find the residuals and then make residual plots.
Suggested Technology: Document Camera, Computer for Presenter, LCD Projector
Special Materials Needed:
Dry-erase boards or the clear page protectors and dry erase markers
Chart paper and markers
Create a worksheet of the students' scenarios. Make sure that they include the data.
Math practice standards:
2 - Reason abstractly and quantitatively.
3 - Construct viable arguments and critique the reasoning of others.