UNIT TITLE: Old McDonald had a Farm

Author: Sheila Roth E-Mail Address: SheilaR04@aol.com School: Neuqua Valley High School, Naperville, Illinois

THEME : Graphing Linear Equations

BROAD CONCEPT: Motivation and Survival

GRADES: 9th Grade Algebra 1 Students

INTEGRATED SUBJECTS: Reading, Language Arts, Mathematics, Science

UNIT GOALS AND PURPOSE: Students must be able to represent data through geometric models as well as with algebraic equations. Students must be able to look at a graphic representation of information since so much information is presented through tables and graphs. Students will see that, while many relationships are linear, there are some that are not and those relationships cannot be represented with a line graph. The purpose of this unit is for students to learn to graph linear equations and apply their knowledge of graphing to real-world situations

This graphing unit qualifies as an Engaged Learning unit for several reasons. The students choose some tasks and they have a picture of what they will learn because they have a task to complete. The students will develop new ideas and understanding while working with others. The problems and activities pertain to the real world. The task is difficult enough to be interesting, but is not totally frustrating. The unit involves integrating disciplines. The students will be reading a lot if information about the farming industry, they will be writing a presentation, and they are exploring weather and climate of different areas of the country. The technology is responsive to the students’ needs. The teacher acts as a facilitator much of the time, monitoring work, but not taking control. Students have the opportunity to explore new ideas. Students are encouraged to teach others in both informal and formal contexts.

Technology is an important component of this unit because students will use the graphing features of the calculator once they can graph on their own using pencil and paper. Students use the calculator to check their work. The students may use the calculator to show work to the rest of the class. Students will have Internet sites available for their use. Students will use given Internet sites to look for data and get some information for their culminating project. Students will use a spreadsheet to display information and KidPix Deluxe Studio to present their consultation for the McDonald family.

This project is authentic because it deals with an issue that is important to everyone. The students will be challenged to work together and to use knowledge to complete the project.

Here is the situation for the student: You are a consultant and you get lots of different kinds of clients. The McDonald family is a farming family. They come to you and tell you that they live in Louisiana and they would like to move to a city in the United States that is good for farming corn. Mr. McDonald would like you to choose three major cities and to tell him which city would be the best to move to. You will need to investigate times for growing corn, what kind of climate is necessary for farming corn, and the amount of precipitation necessary. You will choose three cities to investigate, choose the best city for the McDonald’s to move to, and write a convincing argument for Mr. McDonald. You should include any and all information and display your findings graphically. You will also do an oral presentation for the McDonald family using the KidPix Deluxe software.

TIME FRAME: 10 days

OBJECTIVES:

In this unit, students will:

· graph ordered pairs on a coordinate plane · MATERIALS: · General materials and equipment: Geoboards

· Technology tools: Computer, Graphing Calculator

· Software Used in this Unit: Word Processing (MS Word )

Spreadsheet ( Excel )

CD-ROM Encyclopedia ( Encarta )

Multimedia ( KidPix Deluxe )
 
 

 STATE STANDARDS ADDRESSED BY THIS UNIT: Mathematics Standards Goal 6: Number sense

Goal 7: Estimate, use measurement of objects

Goal 8: Use algebraic and analytical methods to identify and describe patterns and relationships in data, solve problems, and predict results

Goal 10: Collect, organize, and analyze data and predict results

 English Language Arts Standards Goal 1: Reading

Goal 3: Writing

Goal 4: Listening and speaking

Goal 5: Research

 Science Standards Goal 12: Concepts and principles

Goal 13: Science, technology, and society

 N.C.T.M. STANDARDS ADDRESSED BY THIS UNIT:

Standard 1: Mathematics as Problem Solving

Standard 2: Mathematics as Communication

Standard 3: Mathematics as Reasoning

Standard 4: Mathematics as Connections

Standard 5: Algebra

Standard 6: Functions

Standard 8: Geometry from an Algebraic Perspective

Standard 10: Statistics

STUDENT ACTIVITIES WHICH WILL PROMOTE ENGAGED LEARNING:

Activity 1: Use the coordinate system to create a picture

Students will learn about the Cartesian Coordinate System and how to plot points.

For the activity, students will draw a picture with straight lines on graph paper. After they have completed their picture, they will write ordered pairs on the vertices of the line segments. Students will list the ordered pairs in the order that they should be plotted as well as when to connect the dots and when to break the line. Now each student will hand their picture to another student and that student will draw the picture by following the directions, plotting the ordered pairs, and connecting the dots. This activity will give the students the opportunity to practice plotting ordered pairs. Students will be challenged to be creative in drawing a picture and writing specific directions for a classmate to follow. Activity 2: Slope of a line Students can begin to understand the concept of slope by looking at a staircase and explaining how they move their feet to get upstairs. This process leads to the definition of slope as rise over run. Students will demonstrate finding slope given two points on a line. Students will apply the concept of slope to real world situations by discussing the grade of the road and the incline of a wheelchair ramp. Activity 3: Determine the slope of a graph Students will graph 14 equations using their graphing calculators. Students will work in groups of two to complete the activity. Students will discover the relationship between the slope and the equation of line. After the students finish graphing the lines, the teacher will lead a discussion about their findings, emphasizing the effects of negative and positive slopes on the graph. Students will notice that all of the graphs pass through the origin. Students will also discuss the slopes and equations of vertical and horizontal lines. Students will use geoboards to model line segments and find the slopes of those segments. Activity 4: Discover Slope-Intercept of a Line Students will work in groups of two. The students will be given five equations of lines. The students will be asked to write down everything that they know about the line, including the graph of the line, the slope, the y-intercept, the x-intercept, etc. Students will also find ordered pairs that lie on the line. Students will present these pairs using Excel spreadsheet. After the pairs are finished, the teacher will assign each pair to a line. The pair will write all the information on an overhead transparency and will present this to the class. A chart will be drawn on the board and the students will look for the relationships between the information about the line and the equation of the line. The students will be challenged to see the relationship, y = mx + b, between the slope and y-intercept and the equation. The students will then be challenged to write the equation in standard form and point-slope form. Activity 5: Graph linear equations using the x- and y-intercepts or the slope and y-intercepts. Students will use the graphing calculator to graph the equations. Students will graph equations using the x- and y-intercepts and using the slope and y-intercept. Students can discuss real-world situations that can be represented by linear equations.
 
  Activity 6: Describe a situation that may be modeled by the graph Students will work in groups of four. Each group of students will be given a graph. The graph will have some variation in slope, y-intercept, or both. The students will write a scenario of what the graph represents. Students will take into account why the slope changes and what may account for that. The students will be challenged by the activity because they will have to relate the real world to the problem. This activity is switched around from the way that students usually see. Students are usually given the problem and they need to come up with the model. In this activity, students formulate the problem and that can be challenging. Activity 7: Write the equation of a line in slope-intercept, point-slope, and standard form. Once students know the slope-intercept form of the equation of a line, y= mx +b, students will be given two points to plot using their graphing calculators. The students will then be asked to write the equation of the line in slope-intercept form, using what they know about slope and the y-intercept. Once each student writes the equation, students will break up into pairs to compare the equations. Students will then write the equations in both point-slope and standard form Activity 8: Find the common characteristic Students will work in groups of three or four. The students will take cards that have three linear equations written on them. The students will be responsible for graphing the lines using the graphing calculator and coming to agreement on the common characteristic. Once the students decide on the common characteristic, they will then write another equation with the same characteristic. Students will be challenged to find the common characteristic. This activity can be used to lead to a discussion on parallel lines. Students may notice what is true about the equations of parallel lines. Students will see that they have the same slopes. Student groups will present information to the class. Students would then be challenged to find out what is true if two lines are perpendicular. Activity 9: Scatter Plot Students will select a city in the United States. The students will collect data on the average rainfall for the city for the months of January and July for the past 15 years using the Internet. Students will represent their information in a scatter plot. Students will write the equation for the line of best fit. Students will be challenged to collect the data, create the scatter plot, write the equation for the line of best fit. Students will make predictions based on the collected data as to whether the next few years will be wet or dry. Activity 10: Is it a linear relationship? Students will be given data on the amount that a car is worth over a 15-year time period. Students will plot the information on a graph. Students will then decide whether or not there is a linear relationship. Students would then discuss other situations where the relationship between two things is not linear. Ongoing Activity: Farming Consultant As the graphing unit goes on, students will be working in assigned groups of three students. Students will be looking up information about growing corn using the Internet sites and the other sources. Students will also be using the given Internet sites to select the cities in the United States and find the best city for growing corn. Students will have time to work with the data and the students will write a presentation for the client using Microsoft Word. Each group of students will present their work to the entire class using KidPix Studio Deluxe. Students will use extra class time each day to complete the final project. SHARE YOUR IDEAS: Students will present their final project to the class. The culminating project for the unit will be a multimedia presentation to the class as well as a written presentation for the teacher. The students will tell the McDonald family which cities they chose and which city is the best choice for farming corn. The students will display all of their information graphically and they will be convincing in their argument. The rubric for the activity is as follows:
 
 
 
 
 
 
 
 
 
 
 
  Rubric
 

Criteria 
4
3
2
1
Construction of graphs 
 Identifies all important elements and shows complete understanding of problem. Chooses appropriate strategy for solving problem. Gives evidence of a complete solution. Identifies most of the important elements of the problem and shows some understanding of the problem. Chooses appropriate strategy to solve problem. Solution is almost complete.  Identifies some of the important elements of the problem and shows little understanding of the problem. Chooses appropriate strategy. Gives some evidence of solution process, but not a complete solution.  Does not identify important elements of the problem and does not show understanding of the problem. Chooses inappropriate strategy to solve the problem. Does not give a solution.
Interpret and draw conclusions from graphs
 Provides a complete and correct graphic representation, including all information found. Explanation is supported by evidence, facts, and concepts of mathematics  Provides a mostly complete and correct graphic representation, including most information found. Explanation is supported by most of facts, evidence, and concepts of mathematics.  Provides an incomplete graphic representation, including some information found. Explanation uses only some of the evidence with little attention to facts and concepts of mathematics. Does not provide graphic representation. Does not include information found. Does not give explanation. 
Predict and justify trends
 Shows complete understanding of math concepts. Uses appropriate math terminology. Gives complete written explanation with justifications. Presentation thorough and complete. Shows nearly complete understanding of mathematical concepts. Uses nearly correct math terminology. Gives nearly complete written explanation with some justification. Presentation is nearly complete. Shows some understanding of mathematical concepts. Uses little correct math terminology. Gives incomplete written explanation with little justification. Presentation nearly incomplete.  Shows limited understanding of the mathematical concepts. Does not use correct math terminology. Gives little or no written explanation and no justification. No presentaion.
STUDENT AND TEACHER ROLES:

Students will lead much of their work because they will be working together. They will be setting daily goals for themselves and they have the big picture of what the unit is about. The teacher is not dependent on rewards. The students develop new ideas and understanding in conversations with others. The tasks are authentic, challenging, and multi-disciplinary. The students have the opportunity to be explorers. The students become the teachers for their small groups and the class as a whole. Students become producers in that they develop products of use. The teacher will serve as a facilitator by encouraging discussion among group members. The teacher is a guide by modeling different concepts for the students. The teacher also acts as a learner by constantly learning new things.

 ADDITIONAL REFERENCE PRINT RESOURCES STUDENTS MAY USE :

World Book Encyclopedia
 
 

FOR ADDITIONAL ONLINE INFORMATION AND MEDIA PERTAINING TO THIS UNIT, TEACHERS MAY WANT TO USE THE FOLLOWING INTERNET ARTICLES:

Title 1: Engaged Learning URL 1: http://www.k12.il.us/learning/engaged/engaged_learning.htm

Description 1: This web site gives information about engaged learning and provides many useful links.

 Title 2: Graphs

URL 2: http://forum.swarthmore.edu/alejandre/spreadsheet.html

Description 2: This web site gives descriptions of using spreadsheets and making

different kinds of graphs.

Title 3: Graphing in Excel

URL 3: http://www.sinc.sunysb.edu/stu/brfranke/lessons/graphing.htm

Description 3: Gives some instructions for graphing in Excel

Title 4: If I teach this way, am I doing my job?

URL 4: http://206.58.233.20/L&L/archive/vol27/no1/feature/

Description 4: Gives perspective about engaged learning in the classroom.

Title 5: Relations and functions

URL 5: http://www.ucs.mun.ca/~mathed/Algebra/intro25a.htm

Description 5: Lessons on graphing

Title 6: K-12 Internet Resources

URL 6: http://forum.swarthmore.edu/algebra/k12.algebra.html

Description 6: Resources for teachers that want to use the Internet

 RELEVANT INFORMATION, STUDENTS WILL VISIT THE FOLLOWING WEB SITES: Title 1: The Weather Channel URL1: http://www.weather.com/education/safeside/resources/history.html Purpose of Use 1: Gives the students a chart that they can use for data.

Description1: This site gives weather information.

Title 2: Glossary URL 2: http://www.weather.com/glossary/wx_glossary_t.html Purpose of Use 2: Students can look up terms related to weather

Description 2: Glossary of meteorological terms

Title 3: World Climate

URL 3: http://www.worldclimate.com/. Purpose of Use 3: To find data on temperature and rainfall in different cities

Description 3: Students select cities and find temperature and rainfall levels.

Title 4: Corn Connection - Environmental Topics

URL 4: http://www.corninfo.com/environ.shtml Purpose of Use 4: Information on corn growth

Description 4: Students can find information on growing corn.

Title 5: Corn Connection - Crop Management

URL 5: http://www.corninfo.com/gen3.shtml Purpose of Use 5: Information about corn growth

Description 5: Students can find information on growing corn.

Title 6: Climate

 URL 6: http://www.usatoday.com/weather/climate/usa/wusaclim.htm

Purpose of Use 6: Choose city, find rainfall and temperature

Description 6: Choose city, find rainfall and temperature