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# Slope

## Slope

1. Fourth Grade Assessment III - This is a written assessment where children will be asked to interpret graphs and to interpret and determine the truth or falsehood of equations and statements that describe comparisons between quantities.
2. Graphing Halves and Doubles - Children work on a problem about distance and time and compare two rates: half a meter per second and two meters per second.
3. Graphing Thirds and Triples - Children work on a problem about distance and time and compare two rates: one third of a meter per second and three meters per second.
4. The Better Paying Job I - Children work on a problem about rate of pay per hour of work. They compare ratios (dollars earned per hour of work) and discuss and plot points in a Cartesian plane.
5. The Better Paying Job II - Children work on a problem about rate of pay per hour of work. They compare ratios (dollars earned per hour of work) and discuss and plot points in a Cartesian plane.
6. Varying Speed - Children are asked to tell a story about a trip depicted through a graph that has varying slopes/speeds.
7. Varying Velocity - Children are asked to tell a story about a trip depicted through a graph that has varying slopes/velocities.
1. Varying Rates of Change - Students will compare three functions, two of which are nonlinear, that tell the story of three cousins who all save \$1,000 in one year. One saves a lot the first day and less and less each day as time goes on; one saves very little the first day and more and more each day throughout the year; the last cousin saves the same amount each day. Students will be asked to predict the shape of the graph for each function and, later, to look at and describe graphs of all three cousins' savings.
###### Middle School Lessons
1. Candy Experiment - Students will create their own data to construct a graph and equation of negative and fractional slope.
2. Compare and Contrast - Students will identify the y-intercept and slope using equations and then use that data to create corresponding tables and graphs.
3. Race Car Activity - Students will look at four different graphs to determine which two describe the scenario proposed by the teacher displaying parallel lines and the correct y-intercepts.
4. Relating Graphs and Equations - Linear and Quadratic Functions - Students will generate graphs from given equations and equations from given graphs.
5. Who Shares My Function? - Linear with Graphs and Stories - Students will make groups by finding other students who have the same quadratic or linear function in different representations.
6. Can We Predict Differences? - Students will predict, produce, and compare linear and non-linear function graphs used to represent the number of punches on a balloon.
7. Contrasting Equations - Students write equations for three graphs and examine their slopes by comparing and contrasting the graphs. Students also look at the same functions graphed on differently scaled coordinate planes.
8. Function Challenges - 20 Questions - Students will compete in a game to generate equations for functions that meet certain criteria, as given by the instructor.
9. Graphing Equations - Students will practice moving between graphs and equations of functions, as well as identifying the y-intercept and slope.
10. Who Shares My Function? - Linear with Negative and Fractional Slope - Students will find other functions that are the same as theirs, starting from a table, a graph, or an equation. Once they have identified the same function represented in a different way, they will create a story that describes all of the different representations of the same function.
11. Wind-Up Car - Students will produce an equation from a graph, based on an engineering-context.
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