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
Students will use a clinometer (a measuring device built from a protractor) and isosceles right triangles to find the height of a building. The class will compare measurements, talk about the variation in their results, and select the best measure of central tendency to report the most accurate height.
6-8
In this lesson, students draw various polygons and investigate their interior angles. The investigation is done using both an interactive tool and paper and pencil to foster an understanding of how different patterns can lead to the same solution. After comparing results with a partner, students develop a formula showing the relationship between the number of sides of a polygon and the sum of the interior angles.
9-12
We are confronted with problems on a regular basis. Some of these are easy to solve, while others leave us puzzled. In this lesson, students use problem-solving skills to find the solution to a multi-variable problem that is solved by manipulating linear equations. The problem has one solution, but there are multiple variations in how to reach that solution.
9-12
In this lesson, students explore properties of polygons by trying to place the minimum number of security cameras in a room such that the full area can be monitored. From these polygons, students discover the formula for the maximum number of cameras needed. Students then use their discoveries to analyze the floor plan of a museum as a culminating activity.
6-8, 9-12
This investigation uses a motion detector to help students understand graphs and equations. Students experience constant and variable rates of change and are challenged to consider graphs where no movements are possible to create them. Multiple representations are used throughout the lesson to allow students to build their fluency with in how graphs, tables, equations, and physical modeling are connected. The lesson also allows students to investigate multiple function types, including linear, exponential, quadratic, and piecewise.
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.
9-12
In this lesson, students use remote-controlled cars to create a system of equations. The solution of the system corresponds to the cars crashing. Multiple representations are woven together throughout the lesson, using graphs, scatter plots, equations, tables, and technological tools. Students calculate the time and place of the crash mathematically, and then test the results by crashing the cars into each other.
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
Students explore two different methods for dividing the area of a circle in half, one of which uses concentric circles. The first assumption that many students make is that half of the radius will yield a circle with half the area. This is not true, and it surprises students. In this lesson, students investigate the optimal radius length to divide the area of a circle evenly between an inner circle and an outer ring.
