Background
Students will already be able to:
- sketch the graph of a linear equation in one variable
- write an equation of a vertical or horizontal line
- sketch the graph of a linear equation in two variables
1) using a table of values
2) using intercepts
3) using a point and a slope
- find the slope of a line using two points on that line
- plug in points to check if they are solutions
- interpret slope as rate of change
- create scatter plots and recognize linear patterns
The standards that we are going to be focusing on are as follows:
*For the MCCSC Standards of Mathematical Problem Solving:
1.1, 2.2, 2.3, 2.7, 3.2, 4.1, 6.2, 7.5, 7.6
*For the MCCSC Standards for Algebra 1-2:
4.2, 5.1, 5.3, 5.4, 5.7
*For the Indiana Standards for Algebra 1 under Standard 4:
A1.4.1, A1.4.2, A1.4.3, A1.4.4
*For the NCTM Standards under the Algebra Standards for grades 9-12:
-Understand patterns, relations, and functions.
-Use mathematical models to represent and understand quantitative relationships.
-Analyze change in various contexts
Goals and objectives
By the end of our three day lesson, we would like for students to be able to:
- write equations in slope-intercept form using
1) a graph
2) a slope and a y-intercept
3) two points
4) slope and any give point
- recognize what parallel lines have in common
- recognize the relationship between perpendicular lines
- fitting a line to data that is not "exactly" linear, then
writing the equation for that line
Materials and organization
Day One:
*Checkerboards
*Math chips
*Activity Worksheet and Chart
*Graph Paper
The students will be arranged in the groups in which their desks are arranged (6 groups of 4).
Day Two:
*Popsickle Sticks (6 x 40)
*Pennies
*Elmer's Glue
*Graph Paper
*Activity Directions
*Raft Worksheet
*Dixie Cups (6 x 5)
*Large Bucket
*12 Liters of Water
The students will be arranged in the groups in which their desks are arranged (6 groups of 4)
Day Three:
*Floor Markers (Tape)
*Large Room
*Lamenated Pieces of Paper
*String
*Dry Erase Markers
We will be in a larger room where the kids can move around so they can perform the activities. The class will be working in small groups (6 groups of 4).
Day One Task Description
Checkerboard Activity:
1. Introduce Lesson with Checkerboard activity and worksheet. The Checkerboard activity will allow students to manipulate a linear equation with math chips (circles) on a checkerboard (squares). Students will find the slope of the equation by noticing the number of squares that enclose a certain number of circles. (See activity worksheet)
2. After groups have answered all of the questions on the worksheet, help them tie everything together. Ask them questions to lead to the fact that the number in front of x is the slope and the number that is alone is the y-intercept. You will have to point out that in the general form b is used for y-intercept. Give them some practice problems to ensure that they understand all of the parts of the equation.
3. Assign a practice worksheet for homework.
Day Two Task Description
Raft Activity:
In this activity, we would like students to create their own linear equation by graphing how much weight it will take to sink different sizes of rafts (constructed with popsicle sticks). Each group will be given about 40 popsicle sticks, 20+ pennies, 5 dixie cups and a glue gun. With these materials, the students will need to build five rafts. The students will be given:
--a set of directions on how to build the rafts
--a worksheet with questions to answer regarding their observations
--a chart to fill out, plotting the amount of weights used (y) to sink the number of popsicle sticks (x)
--graph paper to plot their (x, y) coordinates
This activity will take the entire class period.
Day Three Task Description
Large Coordinate Plane with Human Lines Activity:
1. Review Day 1 and 2's activities.
2. Have the students graph the equation of the line of the Checkerboard activity using all of the students as points on the line. The students put their points of the line on the laminated paper (this serves as an erasable sign) and hang the sign around their neck using string.
3. Next, the students break into groups of 3 or 4 (6 groups in all), and each group is given an equation. With this equation, the students find the points that make up this equation, and write these points on the laminated paper. Each group, one at a time, builds their equation on the large coordinate plane, then the other groups physically examine the line to determine the equation that the group is representing. The other groups task is to determine the equation of the line being presented in slope intercept form, as well as the y-intercept. Then the papers from each group are collected at the end of the period.
The last 15 minutes of the class will be spent obtaining student assessments of the activities of the past three days.
Lesson outline with time indicators
Three 53 min periods
Day One:
1. Checkerboard Activity and Worksheet 9:00-9:40
2. Discussion on finding the equation for slope-intercept form 9:40-9:53
Day Two:
1. Raft project 9:00-9:45
2. Wrap up/Clean up 9:45-9:53
Day Three:
1. The entire period is going to be used to do Large Coordinate Plane with Human Lines activity 9:00-9:45.
2. Student Assessment 9:45-9:53
Assessment process and why
The students were given worksheets for Day 1 and Day 2 containing problems evaluating the data they collected in the experiments along with other similar problems dealing with slope-intercept form equations. On Day 3, the students were expected to determine the line that the groups of students were representing as a Human line on the large coordinate plane.
The lesson study group will evaluate the planned curriculum in order to determine if the lesson and activities are consistent with the objectives. After each day of the lesson the Lesson Study Group will evaluate the enacted curriculum to determine how the planned curriculum changed and why.
At the end of the three days the students will evaluate the experienced curriculum. This will help the Lesson Study Group determine how effective the lesson was in meeting the lesson objectives, and where changes might needed to be made in the lesson plans.
Notes to Teachers
Quick Notes:
*During the Raft Activity, make sure the water level is high enough in the large buckets so that the rafts are able to sink.
*If using glue guns, unplug the guns after each class.
*Make sure there are enough supplies for the students to
build and sink the rafts (glue, pennies, popsicle sticks,
dixie cups).