6-8
Students use real-world examples to solve problems involving scale as they examine maps of their home states and calculate distances between cities.
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
In this lesson, students will compare the price of a toll to the distance traveled. Students will investigate data numerically and graphically to determine the per-mile charge, and they will predict the cost if a new tollbooth were added along the route.
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
Students measure the circumference and diameter of circular objects. They calculate the ratio of circumference to diameter for each object in an attempt to identify the value of pi and the circumference formula.
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.
6-8
Students will use their knowledge of rectangles to discover the area formula for parallelograms.
