Algebra Institute Summer 2001
Planning Guide
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Faculty Name: Ms. Miskia Meeks
School: Ruleville Central High School
Grade level: Ninth Grade Pre-Algebra
MS Framework competencies: 6a: Given a set of ordered pairs, draw a coordinate system using an appropriate scale.
* This lesson only deals with first quadrant.
1Purpose of Lesson Plan
Describe the purpose of lesson and the anticipated student outcomes.
Students will be able to identify and graph ordered pair in first quadrant only. Students will also learn the relationship between independent and dependent variables.
2Instructional Activities
Describe completely the class activities for your lesson.
Teacher will begin by giving each student a map of the city that uses letter-number combinations to locate points. Teacher will explain how a letter-number combination is used to locate places on the map. Teacher will emphasize that there must be a letter and a number used to locate a particular place. Teacher will then give letter-number combinations that describe particular locations, such as the school and library. Teacher will then ask students to give the letter-number combination of the street that they live on. Teacher will explain that these letter-number combinations are similar to ordered pair. Teacher will then use a transparency of the map and a transparency of a coordinate system. Teacher will place the origin at the bottom corner of the map, so that the map is in the first quadrant of the coordinate system. Teacher will then use ordered pair to find the same locations as before (school, library, and a few student’s streets). Teacher will show students that they must go across first and then go up. Teacher will instruct students that the across direction is the x-axis, while the upward direction is the y-axis. Teacher will then ask students to find the ordered pair of other locations, like SuperValu, and the bank. Teacher will listen to ensure that all students have grasped the concept of using the x-axis before using the y-axis. Teacher will show students how to write ordered pair using parentheses and comas to separate the two axes. Teacher will reemphasize the point that two numbers are used in an ordered pair, and that you go across and up. (Teacher is using only one quadrant.)
Teacher will then give students a graph that only consists of the first quadrant. Teacher will have several points plotted on the grid. Teacher will allow students a few minutes to find the ordered pair for the points plotted. Teacher will then go over the graph orally with students. Teacher will watch for students who are mixing up the ordered pair. Teacher will pair those students with another student who has a strong grasp on the concept. Teacher will then pass students out another sheet like the first, but with different points plotted. Teacher will call out an ordered pair, and the first student or student pair to find the letter that coordinates with the ordered pair will stand. Teacher will call on student. If they answer correct, student or student pair will receive a point, if the answer is incorrect, they must sit down and the next fastest person or persons will stand. The student or student pair with the highest score will win a no-homework pass.
Teacher will then explain that while both axes of the coordinate graphs in the map represented distances, coordinate graphs can also be used to represent situations involving other quantities. Teacher will tell students that it is common for the horizontal axis to represent time while the vertical axis sometimes represents distance. Students will be given the following example:
A car starts 10 miles away from home and continues to travel away from home at a constant speed of 30 miles per hour for 5 hours.
Teacher will model the following example with students. Teacher will first ask students what can they do to show this in a graph. Teacher will listen to student responses. Teacher will then ask a student how far away will the car be from home in an hour. If student answers correctly, teacher will still show other students how the student may have gotten the correct answer. Teacher will remind students that the car is traveling 30 miles per hour, which means after every hour, the car has traveled 30 miles. So after an hour the car will have traveled 30 miles away from where he started which was 10 miles away from home, so after an hour the car is 40 miles away from home. Teacher will ask another student how far has the car gone in an hour and a half. Teacher will remind students that if the car is going 30 miles in an hour, then in half an hour the car has gone 15 miles because half of 30 are 15. Teacher will continue asking these questions until she reaches 5 hours. Teacher will then put findings into a chart as follows:
1 hour40 miles
1.5 hr.55 miles
2 hour70 miles
2.5 hr.85 miles
3 hr.100 miles
3.5 hr.115 miles
4 hr.130 miles
4.5 hr.145 miles
5 hr.160 miles
Teacher will put students in groups of four and hand out graphs of the first quadrant. Teacher will ask students to write the following findings in forms of ordered pair. Teacher will ask students which they think should be on the x-axis and which should be on the y-axis. Teacher will then introduce independent and dependent variables. Teacher will define independent variable as the variable whose change is not related to the other variable. The dependent variable, on the other hand, changes due to the independent variable. For example, teacher will ask students if the change in time is related to the amount of miles the car has driven. Teacher will then ask students if the change in the cars mileage is due to the amount of time passed. Teacher will then ask students to distinguish between the dependent and independent variable. Students should be able to determine the time as being the independent variable and the mileage as being the dependent variable. Teacher will tell students that the x-axis is always the independent variable and the y-axis is always the dependent. Teacher will then allow students time to plot the previous points on their axes. Teacher will illustrate to students on the transparency how to label the axes and how much the increments should be. Teacher will advise students to make the x-axis in increments of thirty minutes and the y-axis in increments of 15 miles. Teacher will ask students why they think she chose these increments. Some answers should include because the time is always thirty minutes apart and the miles are always fifteen miles apart. Teacher will ask students if she could have chosen other increments. Teacher will advise students to choose increments that go along with your you must use 15 between the next two and so on. However, teacher will advise students that you do not have to use the same increments for x as for y, as shown on the transparency. Teacher will then allow students time to work on graph.
Assessment:
Teacher will listen to student responses to ensure that they are on the right track. Teacher will also pick up all graphs done by students and grade them.
Materials:
- Map
- Pencil
- Paper
- Transparency
- Transparency sheets
- Graph paper
Reference:
Merrill Pre-Algebra Book
Navigating through Algebra (though I didn’t use the activity, I used a lot of the ideas on independent and dependent variable. I wouldn’t have had time to do the actual activity on tennis balls.)
Ideas from institute
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