6-8, 9-12
This lesson allows students to explore linear equations and the effects of changing the slope and
y-intercept on a line. It gives students exposure to
y =
mx +
b,
and can be used as an introduction to the topic. Using graphing
calculators, students are challenged to overlap lines onto the sides of
polygons. To achieve this goal, students change slopes and
y-intercepts of lines, noting observations about behavior as they work. As students change the
y-intercept
of a line, they see it raise or lower the line. As students change the
slope, they see it affect the steepness of the line.
6-8, 9-12
A common problem when students learn about the slope-intercept equation
y =
mx +
b is that they mechanically substitute for
m and
b without understanding their meaning. This lesson is intended to provide students with a method for understanding that
m is a rate of change and
b is the value when
x = 0. This kinesthetic activity allows students to form a physical interpretation of slope and
y-intercept
by running across a football field. Students will be able to verbalize
the meaning of the equation to reinforce understanding and discover
that slope (or rate of movement) is the same for all sets of points
given a set of data with a linear relationship.
6-8
In this lesson, students will design a playground using manipulatives and multiple representations. Maximum area with a given perimeter will be explored using tickets. The playground will include equipment with given dimensions, which decreases the maximum area that can be created. This is an interesting demonstration of how a real-world context can change a purely mathematical result. Finally, scale models will be created on graph paper and a presentation will be made to a playground planning committee for approval.
6-8, 9-12
This lesson offers students a method for finding the slope of a line from its graph. The skills from this lesson can be applied as a tool to real-world examples of rate of change and slope.
9-12
In this grades 9–12 activity, students write and solve a system of
linear equations in a real-world setting. Students should be familiar
with finding linear equations from 2 points or from the slope and
y-intercept.
Graphing calculators are not necessary for this activity, but could be
used to extend the ideas found on the second activity sheet. Parts of
this lesson plan were adapted from the October 1991 edition of
Mathematics Teacher.
6-8
In this lesson, students take on the role of a villager in a
third-world country trying to feed her village. While listening to you
read aloud the book
One Grain of Rice by Demi, students work
collaboratively to come up with a bargaining plan to trick the raja
into feeding the village using algebra, exponential growth, and
estimation.
9-12
In this lesson, students consider the costs of owning a car and ways to lessen those costs. In particular, highway and city mileage are considered, and optimal mileage is calculated using fuel consumption versus speed data.
9-12
Students discover the algorithm for solving linear programming problems and gain conceptual understanding by solving a real-world problem and using graphing calculator applications.
3-5
In this lesson, students will view several websites and determine what mathematical ideas and concepts are involved in scuba diving. The emphasis is on using technology to help students gain an understanding of how math is used outside of a school setting.
9-12
This lesson allows students to apply their knowledge of linear equations and graphs in an authentic situation. Students plot data points corresponding to the cost of DVD rentals and interpret the results.
