My Graph Is ...

This is a Math lesson adapted from Marcoplo.


Basic Information
Summary:
This lesson is designed to allow students to select their own real-life data to plot and interpret. Interpreting the meaning of the slope and y-intercept

Grade/Level:
9-12

Time Frame:
45 minutes

Subject(s):
Mathematics

Topic(s):
The slope of a line

Notes:
It is important that the students be given the opportunity to graph and interpret their own sets of data. This will reinforce the skills introduced in the first two lessons of this Unit Plan. It will also give the teacher another opportunity to observe the students at work and assess their understanding of the material in the previous lessons.Divide the class into pairs of students. Give each student another copy of the handout Graphing Real-Life Data. Each pair of students is to think of two sets of data that will be linear when graphed. These might include such items as how many pounds of ground beef are purchased vs. the total cost, the number of hours worked vs. gross pay, and the number of marbles removed from a bag vs. the weight of the bag. Encourage the students to do one graph with a positive slope and another with a negative slope. (The students could be encouraged to find sets of data on the Internet. There are numerous sites that provide statistical data. The students might be interested in sports records, consumer consumption of products, etc.)Once each pair of students has decided what they want to graph and collected the data set if necessary, they should go to the Web site: http://illuminations.nctm.org/index_d.aspx?id=454 and plot their first set of data points on the applet. Students should use no more than 8 data points. This may require them to change the window settings. After plotting the data, they should have the applet draw the least squares regression line and calculate the correlation coefficient. Each student should record all this information on his or her own copy of the handout and then collaborate with his or her partner to complete the other information on the handout for the first graph. After completing the first graph, the students should follow the same procedure to complete their second graph.The students should then tape one copy of their a href="lessons/9-12/reallife/sheet1.pdf">Graphing Real-Life Data recording sheet to the classroom wall. These will be used during Lesson Four of this Unit Plan.

Standards and Key Concepts
Standards:
NY- New York City Performance Standards
• Subject: Mathematics
• Grade Range : High School
• Standard M3: Function and Algebra ConceptsThe student demonstrates understanding of a mathematical concept by using it to solve problems, by representing it in multiple ways (through numbers, graphs, symbols, diagrams, or words, as appropriate), and by explaining it to someone else. All three ways of demonstrating understanding—use, represent, and explain—are required to meet this standard.
Key Idea M3a: Models given situations with formulas and functions, and interprets given formulas and functions in terms of situations.
Key Idea M3b: Describes, generalizes, and uses basic types of functions: linear, exponential, power, rational, square and square root, and cube and cube root.
Key Idea M3c: Utilizes the concepts of slope, evaluation, and inverse in working with functions.
Key Idea M3d: Works with rates of many kinds, expressed numerically, symbolically, and graphically.
Key Idea M3e: Represents constant rates as the slope of a straight line graph, and interprets slope as the amount of one quantity (y) per unit amount of another (x).
Key Idea M3f: Understands and uses linear functions as a mathematical representation of proportional relationships.
Key Idea M3h: Defines, uses, and manipulates expressions involving variables, parameters, constants, and unknowns in work with formulas, functions, equations, and inequalities.
Key Idea M3i: Represents functional relationships in formulas, tables, and graphs, and translates between pairs of these.
Key Idea M3m: Uses equations to represent curves such as lines, circles, and parabolas.
Key Idea M3n: Uses technology such as graphics calculators to represent and analyze functions and their graphs.

Understandings:
select linear data to investigate plot data points interpret the slope of a line as a rate of change in the context of real-life data interpret the y-intercept of a line in the context of real-life data

Essential Questions:
1. What set of data when graph could represent a linear graph?2. What set of data may represent a positive slope? negative slope?

Knowledge and Skills:
Select data that is linear in nature Correctly plot data points, both by hand and on the applet Interpret the meaning of the slope of a line as a rate of change in the context of real-life data Interpret the meaning of the y-intercept of a line in the context of real-life data Correctly label the axes on the graph of real-life data Correctly scale the axes for a set of real-life data

Performance Tasks and Assessment
Performance Task:


Performance Prompt:


Assessment/Rubrics:
1. What factors did you consider when selecting sets of data that might be linear when graphed? 2. What mathematical knowledge did you need to be able to select data sets that might be linear when graphed? 3. What additional knowledge and skills are required when plotting the data using the Web-based tools? 4. What caused you trouble? Why do you think it was a problem for you? 5. How would you explain to a younger student the characteristics of data sets that might be linear when graphed?

Learning Experiences and Resources
Sequence of Activities:


Differentiated Instruction:
The sudents will be placed in groups of three. They will form collaborative groups to help each other within the groups. Each group will be formed by students with different skill levels. A graphing calculator will be provided to each student.

Resources:
Technology resources:AppleWorks
The number of computers required is 5.

TECHNOLOGY IN MATHEMATICS

I have had the opportunity of visiting several classes where technology is an important component of them. In one of the classes I visited, the students were searching pictures for their Advanced Spanish class. Those pictures had to resembled their reflections about a poem the students had chosen previously. The students used different search engines as Yahoo, Google, and AsKJeeves. Most of the students demonstrated great knowledge navigating through the internet and finding what they needed. Certainly, the use of computers and the internet have eased the development of many lessons for teachers that can have access to these powerful tools.
In my case, as a mathematics teacher, the story is a little different. In my shool, all the computer rooms are assigned to teach computer classes. It is very difficult to find an open Lab that we can use to teach a lesson. The technology in our department has been limited to the use of a graphing calculator TI83plus. I use the graphing calculator everyday and my students can benefit of its use doing a lot of things they never thought they could. My hope is that not to far in the future, my school can facilitate a room were the math teachers feel welcome and take advantage of all kind of programs available to teach mathematics, and our students find mathematics a subject where they can have fun too.