9-12
A surprising result occurs when two line segments are drawn through a point on the diagonal of a parallelogram and parallel to the sides. From this construction, students are able to make various conjectures, and the basis of this lesson is considering strategies for proving (or disproving) one of those conjectures.
9-12
By calculating the areas of regular polygons inscribed and circumscribed about a unit circle, students create an algorithm that generates the never-ending digits of π, a common curiosity among high school students.
6-8, 9-12
By using sampling from a large collection of beans, students get a
sense of equivalent fractions, which leads to a better understanding of
proportions. Equivalent fractions are used to develop an understanding
of proportions.
This lesson can be adapted for lower-skilled students by using a
more common fraction, such as 2/3. It can be adapted for upper grades
or higher-skilled students by using ratios that are less instinctual,
such as 12/42 (which reduces to 2/7).
Scaffold the level of difficulty in this lesson by going from a simple
ratio such as 2/3 to more complicated ratios such as 2/7 or 5/9.
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.
9-12
To determine the function of best fit for a set of data, students
should recognize which category of function bests fit the data and know
how to use technology to obtain a function. This lesson teaches these
skills and prepares students for the subsequent lesson(s), in which
they will collect their own data.
9-12
There is a leap to be made from understanding postulates and theorems in geometry to writing proofs using them. This lesson offers an intermediate step, in which students put together the statements and reasons to build a formal proof.
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
This lesson offers examples of inverse variation. Students collect data and generate graphs before finding specific equations for inverse variation relationships and examining their graphs.
9-12
Students will represent quadratic functions as a table, with a graph, and with an equation. They will compare data and move between representations.
6-8, 9-12
In this lesson, students will use Cuisenaire Rods to build trains of different lengths and investigate patterns. Students will use tables to create graphs, define recursive functions, and approximate exponential formulas to describe the patterns.
