General Information
Subject(s): Mathematics
Grade Level(s): 9, 10, 11, 12
Suggested Technology:
Basic Calculators
Instructional Time:
59 Minute(s)
Resource supports reading in content area:Yes
Freely Available: Yes
Keywords: Slope, yintercept, real world examples, slope intercept form
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Lesson Content

Lesson Plan Template:
General Lesson Plan

Learning Objectives: What should students know and be able to do as a result of this lesson?
Students will be able to:
 Interpret the slope as a rate of change in the context of real world examples;
 Interpret the yintercept modeled by real world examples;
 Understand that real world examples can be modeled by a linear function or equation of a line;
 Make predictions using a linear equation.

Prior Knowledge: What prior knowledge should students have for this lesson?
The students should be proficient in:
 Given two points, find the slope of the line that contains them;
 Working with slope intercept form;
 Identifying slope and yintercept from a graph;
 Solving equations when given an input value for either x or y;
 Write the equation of a line.

Guiding Questions: What are the guiding questions for this lesson?
 How can a real world situation be modeled with a linear function involving slope and yintercept? (both variables change at a constant rate with respect to one another)
 "You were given $100 for your birthday. Your family then decided to start giving you a $10 allowance every week. If you begin to save all your money from then on, how much money will you have in 11 weeks?"
 What does the slope represent in this real world example?
 "The slope represents the amount of money you are consistently adding to your account each week, $10."
 What does the yintercept represent in this real world example?
 "The yintercept is the amount of money you had before you started receiving an allowance. Meaning at week 0, before you had earned your first weeks allowance, you already had $100. Therefore, $100 is your yintercept."
 How can we use this model (equation) to make predictions about this situation?
 "The problem asks you to predict how much money you will have after eleven weeks of saving your allowance. We can model this linear function with the equation y=10x+100. We will plug in 11 for x, the number of weeks we have been earning $10, in order to calculate the total amount of money you will have at that future point in time. y=10(11)+100, after 11 weeks of accumulating $10, you would have accumulated $110, plus the $100 you already had before you started getting allowance. You will have $210 after 11 weeks of saving your allowance, if you have not spent any money."

Teaching Phase: How will the teacher present the concept or skill to students?
 The teacher will begin by having a student come to the board and solving the problem of the day. (EX: Solve for the slope between (1,5) and (6,9).)
 Teacher will then review slope intercept form, explaining that m is the slope and b is the yintercept. This equation can be used in many real world examples to help you understand a trend.
 Next, the teacher will explain that slope is a rate of change. The change in y over the change in x can be seen in a real world examples such as change in height over change in time, or the distance traveled over time.
 The teacher will allow 3 minutes of group discussion about slope in the real world and will use a random name generator to choose students to give real world examples of slope.
 Once the students understand the concept of slope in the real world, the teacher will begin explaining how the yintercept can be used in real world examples as well.
 The teacher will explain that the yintercept is the value of y when x is zero.
 Examples of the yintercept in a real world problem will be given to the students, for example, the starting value in a bank account before you buy clothes, or the initial amount of clothes in your closet before you begin donating items to Goodwill.
 The teacher will allow the students time to discuss and create their own real world examples involving the yintercept and will choose the students at random using a name generator on excel.
 In order to put the two concepts together the teacher will give a word problem and ask them to write the equation and then make a prediction based on the data. (Example: A student is eating ice cream at the park that is 12.7cm tall. It is extremely hot outside and the ice cream starts to melt at a constant rate of 2 cm/minute. If the student didn't eat any of the ice cream and it started to melt, how much would be left after 3 minutes?)
 The teacher will now explain how to display this word problem as a linear equation. Let the students know that since the ice cream is melting at a constant rate, that will be our slope and it will be negative. Then explain that since the yintercept is our beginning value before any melting occurred, 12.7, is our b. Plugging this into y=mx+b will give us the equation y=2x+12.7.
 In order to solve the word problem and make the prediction, the teacher will explain to the students that because the ice cream is decreasing in size (2cm/minute) and we want to find how much ice cream is left after 3 minutes, we will plug in 3 for x. y=2(3)+12.7. y=6+12.7. Therefore, y=6.7.
 Explain to the students what y represents. It means that after 3 minutes the ice cream will have melted to a new height of 6.7cm from the original 12.7cm.
(PowerPoint slides 19)
Slope_and_Yintercept_in_Real_World_Examples.pptx

Guided Practice: What activities or exercises will the students complete with teacher guidance?
 Before beginning this activity, the teacher will have acquired enough water bottles for all the students and create a small hole towards the top of the bottle near the cap.
 The students will be paired into groups and given the materials needed for the project.
 The teacher will give each group a 500ml empty bottle (with a small hole), a cylinder that measures in ml, water, and a stopwatch.
 The teacher will circulate the classroom and ensure that the students have the correct materials.
 The students will then measure out 400ml of water and pour it into their bottle.
 They will then start the stopwatch and turn the water bottle upside down over the cylinder and watch it fill up.
 Every 10 seconds the students will note how much water was in the cylinder creating coordinates.
 One student should be holding the water bottle and stopwatch above the cylinder telling his partner when 10 seconds have elapsed.
 The other student should be watching the cylinder and noting how much water is in the cylinder at each time interval.
 Each coordinate will be graphed on a coordinate plane so that the students may see the linear relationship between the two.
 Time is the independent variable and will be graphed on the xaxis.
 The amount of millimeters will be graphed on the yaxis.
 The teacher will look at the various graphs and ensure they were all graphed correctly and represent a linear relationship.
 Once all the data is graphed, the teacher will now instruct the students to solve for the rate of change between two of the coordinates.
 After the students have calculated the slope, the students will write the linear equation representing this situation. (EX: y=mx).
 Various students will share their findings and the class will discuss the project.
 Students should analyze the graph and realize the yintercept was 0 because the cylinder started empty.
 The students should also be able to analyze that the slope is positive because as time passed the amount of milliliters in the cylinder increased.
(PowerPoint slides 1012)
Leaky_Lines_Project_Worksheet.docx

Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the lesson?
The teacher will now ask a critical thinking question based on the project.
 Had we been measuring the rate at which the water left the bottle, would the slope have been positive or negative? What would the yintercept have been? Write an equation expressing this linear relationship using m for slope.
In order to review for the quiz the teacher will ask a few simple word problems.
 Your family is taking a trip to Disney and is driving at a constant rate. After one hour, you have traveled 60 miles, and after 2 hours you have traveled 120 miles. How fast is the car going?
 You are selling candy bars for a fundraiser. You have raised $50 so far and sell each candy bar for 75 cents. How much money will you have made after selling 30 candy bars?
 The graph shows the amount of money you have at the beginning of the month. How much money did you begin with? How much money do you earn each week? How much money will you have after 3 weeks?
(PowerPoint slides 1315)
Independent_Practice_with_answer key.docx

Closure: How will the teacher assist students in organizing the knowledge gained in the lesson?
The teacher will have a brief discussion focusing on the main ideas of the lesson. The discussion will entail how students can identify the slope and yintercept in a real world example. Referring to the last three examples in the independent practice, the students and teacher will discuss the equations to ensure they understand how to express them and solve them. Students should be able to explain that slope is a rate of change and can be found from two coordinates. They should also be able to identify the yintercept in the example as the initial value. The students should then be able to write a linear equation and make predictions based upon this information. The teacher will review writing a linear equation from a graph and asking the students what this equation and graph are actually expressing. The teacher will ensure the students recall that all these equations are based upon the slope intercept form of line.

Summative Assessment
See worksheet attached and give as a summative assessment the day after the lesson to measure mastery of the learning objectives.
Slope_and_yintercept_Summative_Assessment.docx

Formative Assessment
Throughout the lesson the teacher will be posing questions and giving students prompts. While students formulate answers and discuss within small groups, the teacher will circulate and monitor the students' responses to check for understanding. Intervention and additional explanation can be provided for support where needed. During the teaching phase when students are sharing their ideas and engaging in whole class discussion, the teacher will again be able to monitor and assess students' progress toward the learning objectives. This will inform the teacher as to whether the lesson can proceed or if more examples or clarification is needed.

Feedback to Students
When students are in groups, working individually, or going to the board to solve an example, the teacher will be able to observe and give feedback to individuals and to the whole class. The teacher can point out common errors and also reiterate the correct interpretation of both slope and yintercept.
Assessment
 Feedback to Students:
When students are in groups, working individually, or going to the board to solve an example, the teacher will be able to observe and give feedback to individuals and to the whole class. The teacher can point out common errors and also reiterate the correct interpretation of both slope and yintercept.
 Summative Assessment:
See worksheet attached and give as a summative assessment the day after the lesson to measure mastery of the learning objectives.
Slope and yintercept Summative Assessment.docx
Accommodations & Recommendations
Additional Information/Instructions
By Author/Submitter
This lesson aligns with the following Math Practice Standards:
MP.1 Make sense of problems and persevere in solving them.Â
MP.2 Reason abstractly and quantitatively.
MP.4 Model with mathematics.Â Â
MP.5 Use appropriate tools strategically.Â
MP.6 Attend to precision.Â
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Source and Access Information
Contributed by:
Yasemin Gurgan
Name of Author/Source: Yasemin Gurgan
District/Organization of Contributor(s): MiamiDade
Is this Resource freely Available? Yes
Access Privileges: Public
* Please note that examples of resources are not intended as complete curriculum.