6-8
This activity uses a series of related arithmetic experiences to prompt
students to generalize into more abstract ideas. In particular,
students explore arithmetic statements leading to a result that is the
factoring pattern for the difference of two squares. A geometric
interpretation of the familiar formula is also included. This lesson
plan was adapted from an article by David Slavit, which appeared in the
February 2001 edition of
Mathematics Teaching in the Middle School.
9-12
As you review student work in this unit, it is important to remember
the mathematical objectives/expectations of this Unit Plan that are
stated in
Principles and Standards for School Mathematics.
Pre-K-2
Students review this unit by creating, decomposing, and comparing sets of zero to 10 objects and by writing the cardinal number for each set.
6-8
Students experiment with units of liquid measure used in the customary system of measurement. They practice making volume conversions in the customary system.
3-5
This lesson allows students to apply what they have learned in previous lessons by designing their own art. Students use Kandinsky’s style of art and their own creativity to make paintings that reflect their understanding of geometry.
6-8
Students typically learn about the concepts of identity, inverse,
commutativity, and associativity by exploring the four basic operations
(+, –, ×, and ÷) with integers. In this lesson, students investigate
these concepts using a geometric model. Moves are performed with a
rectangle, and the results of an operation that combines two moves are
analyzed. Students determine if the operation is commutative or
associative; if an identity element exists; or if there are inverses
for any of the moves.
3-5, 6-8
This lesson uses a real-world situation to help develop students' spatial visualization skills and geometric understanding. Emma, a new employee at a box factory, is supposed to make cube‑shaped jewelry boxes. Students help Emma determine how many different nets are possible and then analyze the resulting cubes.
6-8
Students will measure the length and width of a rectangle using both standard and non-standard units of measure. In addition to providing measurement practice, this lesson allows students to discover that the ratio of length to width of a rectangle is constant, in spite of the units. For many middle school students, this discovery is surprising.
6-8
Using a circle that has been divided into congruent sectors, students will discover the area formula by using their knowledge of parallelograms. Students will then calculate the area of various flat circular objects that they have brought to school. Finally, students will investigate various strategies for estimating the area of circles.
6-8
In this lesson, students develop the area formula for a triangle. Students find the area of rectangles and squares, and compare them to the areas of triangles derived from the original shape.
