In this lesson, students will extend the Pythagorean theorem by investigating the relationship between the areas generated by the lengths of the sides of a right triangle, investigate whether the Pythagorean theorem still holds if the shapes are not squares, and investigate whether the Pythagorean theorem still holds if the shapes are not regular.
9-12
This lesson introduces students to the many factors that play a role in
creating a forest-fire danger rating index. They will be looking at how
we use a scale to quantify the abstract idea of forest fire danger.
Using the real-world situation, students examine the meaning of the
slope and intercepts of a line. To complete the activities related to
these indexes, students should be comfortable with linear, quadratic
and exponential functions and their graphs. Students’ facility with a
graphing calculator is assumed. Students also use summation notation to
do the activities relating to the Nesterov index. This lesson plan was
adapted from the article "Smokey the Bear Takes Algebra," which
appeared in the October 1999 issue of the
Mathematics Teacher.
6-8
In Parts I and II of this investigation, students learn about the notion of equivalence in concrete and numerical settings. As students begin to use symbolic representations they use variables as place holders or unknowns. This part of the i-Math investigation illustrates the continued transition from the concrete balance view of equivalence to a more abstract view.
6-8, 9-12
Use tiles to represent variables and constants, learn how to represent
and solve algebra problem. Solve equations, substitute in variable
expressions, and expand and factor.
3-5, 6-8
Using the online game Deep Sea Duel, students play a card game against Okta. The objective is to choose cards so that some subset of three cards within their hand has a particular sum. Students will play several variations of the game, attempt to identify a winning strategy, and compare the game to other games that they know.
6-8
Students will balance shapes on the pan balance applet to study equality, essential to understanding algebra. Equivalent relationships will be recognized when the pans balance, demonstrating the properties of equality.
Pre-K-2
Through
the course of the lessons, students are exposed to algebra, measurement, and data
analysis concepts.Pre-K-2
Problems such as those in this activity help develop what students already know in preparation for writing equations and learning ways to solve for variables. Students use mathematical models to explore quantitative relationships. When presented with pictures of pan balances with one or more objects in each pan, they communicate relationships between the weights of the objects by comparing the balanced and unbalanced pans.
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, expressions representing area of a rectangle are used to enhance understanding of the distributive property. The concept of area of a rectangle can provide a visual tool for students to factor monomials from expressions.
