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, 9-12
In this lesson, students compare different costs associated with two
cell phone plans. They write equations with 2 variables and graph to
find the solution of the system of equations. They then analyze the
meaning of the graph and discuss other factors involved in choosing a
cell phone plan.
9-12
In this lesson, students use uncooked spaghetti to transfer lengths from the unit circle to a function graph on large butcher paper. In the process, they discover the key features of sine and cosine graphs. The activity is presented for students working in degrees, but another version of the handouts is provided for students working in radians.
9-12
Students explore and discover conic sections by cutting a cone with a plane. Circles, ellipses, parabolas, and hyperbolas are examined using the Conic Section Explorer tool. Physical manipulatives such as dough can optionally be used as well.
9-12
In this lesson, students explore polynomials by solving puzzlers. To solve the puzzlers, students factor polynomials and multiply monomials and binomials. The lesson includes ideas on how this format can be applied to other mathematical concepts.
9-12
This lesson helps students clarify the relationship between the shape of a graph and the movement of an object. Students explore their own movement and plot it onto a displacement vs. time graph. From this original graph, students create a velocity vs. time graph, and from there create an acceleration vs. time graph. The movement present and how to interpret each type of graph is emphasized through the lesson, which serve as an excellent introduction to building blocks of calculus.
9-12
In this lesson, students learn Polya's four-step problem solving heuristic and how to use metacognition. They practice these on simple word problems and equations, then apply the techniques to games and more complex problems. The problem solving heuristic can be applied to problems outside of mathematics and used for cross-curricular activities.
9-12
Before there were electronic calculators, there were logarithm tables and slide rules. In this lesson, students make and use slide rules to discover the properties of logarithms. The technique, analogous to number-line addition, reinforces the hierarchy among the operations of addition, multiplication, and exponentiation.
9-12
Students sometimes have difficulty using the order of operations when
evaluating expressions. By converting these expressions into binary
expression trees before evaluating them, students gain a better
understanding of the order of operations. In addition, students learn
to represent algebraic expressions using prefix notation, which is
often called "Polish Notation," because of the nationality of its
inventor, Polish logician Jan Łukasiewicz.
