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.
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.
6-8
In this lesson, students learn about the mechanics of the Electoral College and use data on population and electoral votes for each state. Students calculate the percentage of the Electoral College vote allocated to each state, and use mathematics to reflect on the differences. Several questions are provided to strengthen understanding of measures of central tendency and fluency with decimals and percents.
6-8
This problem-solving lesson challenges students to generate election
results using number sense and other mathematical skills. Students are
also given the opportunity to explore the mathematical questions in a
politically challenging context. Calculations can be made using online
or desktop tools or using the data gathered on the Lesson 1 activity
sheet, Why California? Additional resources are introduced to extend
the primary activity.
6-8
A political map of the United States after the 2000 election is largely red, representing the Republican candidate, George W. Bush. However, the presidential race was nearly tied. Using a grid overlay, students estimate the area of the country that voted for the Republican candidate and the area that voted for the Democratic candidate. Students then compare the areas to the electoral and popular vote election results. Ratios of electoral votes to area are used to make generalizations about the population distribution of the United States.
6-8, 9-12
We often hear that there are measurements in the body that can be used to predict a person’s height. By graphing different body measurements versus height and comparing their correlation coefficient, students decide which body measurement is the best predictor.
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
Students begin by breaking down a typical summer day into a variety of activities and the amount of time they spend on each. They then translate their activity times into a simplified fraction, a decimal, and a percent. Students create a pie chart for this information that is unique to them. Students who struggle with the calculations will have the opportunity to practice these conversions by playing a game that can easily be differentiated for various levels of learners.
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.
