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.
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.
3-5, 6-8
In this lesson students will review plotting points and labeling axis. Students generate a set of random points all located within the first quadrant. Students will plot and connect the points and then create a short story that could describe the graph. Students must ensure that the graph is labeled correctly and that someone could recreate their graph from their story.
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.
6-8
Students will plot points on a coordinate grid to represent ships
before playing a graphing equations game with a partner. Points along
the
y-axis represent cannons and slopes are chosen randomly to
determine the line and equation of attacks. Students will use their
math skills and strategy to sink their opponent's ships and win the
game. After the game, an algebraic approach to the game is
investigated.
6-8
In this lesson, students explore linear equations with manipulatives
and discover various steps used in solving equation problems. Students
use blocks and counters as tactile representations to help them solve
for unknown values of
x.
6-8
Students use equations to determine eBay profit on new technology. EBay is an online auction agency. For a limited time after a “new” product’s street release date, it is possible to track the profit that sellers make for auctioning them on eBay. Students use previous data of selling prices to derive a linear equation for the “closing bid price” on a product.
3-5, 6-8
The rules of Krypto are amazingly simple — combine five numbers using
the standard arithmetic operations to create a target number. Finding a
solution to one of the more than 3 million possible combinations can be
quite a challenge, but students love it. And you’ll love that the game
helps to develop number sense, computational skill, and an
understanding of the order of operations.
6-8
In this lesson, students determine the time it takes for a roller coaster to reach the bottom of its tallest drop. They use tables and graphs to analyze the falls of different roller coasters. Students conclude the study by creating their own roller coaster and providing an analysis of its fall.
