6-8
Students learn about ratios, including the “Golden Ratio”, a ratio of length to width that can be found in art, architecture, and nature. Students examine different ratios to determine whether the Golden Ratio can be found in the human body.
6-8
Students extend their knowledge of proportions to solving problems dealing with similarity. They measure the heights and shadows of familiar objects and use indirect measurement to find the heights of things that are much bigger in size, such as a flagpole, a school building, or a tree.
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.
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
Students will estimate the areas of highly irregular shapes and will use a process of decomposition to calculate the areas of irregular polygons.
6-8
Students will measure the dimensions of a common object, multiply each dimension by a scale factor, and examine a model using the multiplied dimensions. Students will then compare the surface area and volume of the original object and the enlarged model.
