Word Problems - Slope Intercept Form

NC SCOS Objective:

5.01 – Develop an understanding of function.

a)      Find, identify, and interpret the slope (rate of change) and intercepts of a linear relation.

 

Rationale:

The students have started graphing lines given tables and linear functions. They have also learned how to write linear equations in slope intercept form. Now, it is time for the student to interpret what the equations and lines mean that they have learned to graph and develop.  In the real world, knowing the slope of places or stairs or mountains is very important. For example, if someone wants to build a house on the side of a mountain, but they cannot do this if the slope is too steep. When a builder is building a house the stairs cannot be too steep or they will be difficult to climb. Slope is an important concept for the students to learn that will be used in life at some point. This lesson will be focusing on working with word problems and interpreting what a linear equation means.

 

Lesson Objective:

This lesson will demonstrate how to break down word problems to write linear equations and graph the line of the linear equation.

 

Student Objective:

Students will be able to write linear equations given a word problem and breaking it down into information that is usable.

 

Focus and Review:

There will be a bell ringer that will be up when the students enter the classroom will review the information that they will be using in the lesson today. This problem will review how to find slope and how to use slope and a point to write the equation of a line. Then use that information to graph the line. This is all information that they have learned in the past couple of weeks and they are going to use today to solve word problems.  

 

Point A: (2, 5) & Point B: (4, 2)

1.       Use these points to find the slope of the line.

2.       Use the slope and ONE of the points to write an equation for this line in slope intercept form.

3.       Then use your equation to graph the line.

 

The students will have a few minutes after they get settle to do this. We will then talk about it as a class. As I said before this will be a review of the information that we will be using today in breaking down and solving word problems.

 

Procedures:

Teacher Input/Guided Practice

·         I will show the students the plan for the day so they know what to expect.

·         After we have discussed and reviewed the information in the bell ringer that we are going to be using, then we are going to do an example word problem.

ADVERTISING, Student Council wants to buy posters advertising the school’s carnival. The Design Shoppe charges $15 to prepare the design and $3 for each poster printed. The total cost y can be represented by the equation y = 3x + 15, where x represents the number of posters.

1.      Graph the equation. (Find the slope and the y-intercept)

2.      Use the graph to find the cost for 10 posters. (Locate 10 on x-axis and follow it up to the line and then see where that lays on the y-axis. $45 dollars)

3.      Describe what the slope and the y-intercept represent. (The slope 3 represents the cost per poster, which is the rate of change. The y-intercept 15 is the one-time charge for preparing the design.)

Independent Practice

·         The students are going to be broken into groups and each group will be given a word problem that they are going to have to find the slope, write an equation, graph the equation, and interpret the information from the graph. This will help the students to use their problem solving skills to break down a word problem and interpret their information. They will be using poster paper and markers to write the information on.

I am going to group the students randomly by their birthday months. However, Before the students are grouped and start to move around I will go over what is expected out of them within their groups.

·         Within each group there needs to be roles for each student.

1.      Recorder – Someone who is going to write the information for the group.

2.      Facilitator – Someone who is going to make sure the group stays on task.

3.      Time Keeper – Someone who is going to make sure the team is on time with the time restrains I give them.

4.      Resource Manager – Someone who gets the materials for the team, at the beginning and throughout the time they are in their groups.

**Every student will help answer the problem that they are given.**

·         Within the word problem the students are given the equation of a line and they are going to have to graph the line and interpret the information shown in the graph.

1.      Write the word problem given to the group.

2.      Write the equation that was given and then label the slope and the y-intercept.

3.      Use a piece of graph paper and markers and graph the equation. Then tape this graph onto the poster paper. Explain the process of use the slope and y-intercept to graph the line.

4.      Interpret the information shown on the graph. What does the slope and y-intercept represent?

·         After all the groups are done, they will present their findings as a group in front of the class. There posters that they made will then be hung in the hallway for other students to see.

Extended Practice

Homework: If there is time then the students will be given a worksheet with 6 word problems dealing with the slope formula. They will be told to use the slope they find and a point to write the equation of the lines for numbers 1, 3, and 4. This will be a review of slope and using the slope and a point to write the equation of a line. This worksheet will also give them practice with graphing linear equations as well.

Lesson Closing

·         The students will fill out the student reflection on group work.

Assessment and Evaluation

·         The students will show by doing the worksheet dealing with slope and the additions that I am going to add with writing linear equations whether they understand the information or not. The student reflection on group work will also tell me what they learned from the lesson that day.

Plans for Individual Differences

·         There will be an example for the students who need to see what they are doing before they are given the task. The students will be working together in groups so they will be helping one another. They will also be learning from their group members when they present their findings to their classmates.

Resources, Materials, and Technology

Materials:

·         Poster Paper

·         Markers

·         Worksheets (Group Word Problems, Slope formula Worksheet, and Student reflection worksheet)

·         Graph paper

·         BRAIN!!! Ha!

Technology:

·         Powerpoint

·         Active board

Resources:

·          Glencoe Mathematics Applications and Concepts Course 3

DifferentiatedInstuctional Strategies: One Size Doesn’t Fit All (2nd Edition) by Gayle H. Gregory and Carolyn Chapman
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