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Recursive and Exponential Rules

6-8, 9-12

In this lesson make connections between exponential functions and recursive rules. Students will use tables to create graphs, define recursive rules and find exponential formulas.

Dividing a Town into Pizza Delivery Regions

9-12

Students will construct perpendicular bisectors, find circumcenters, calculate area, and use proportions to explore the following problem:

You are the owner of five pizzerias in the town of Squaresville. To ensure minimal delivery times, you devise a system in which customers call a central phone number and get transferred to the pizzeria that is closest to them. How should you divide the town into five regions so that every house receives delivery from the closest pizzeria? Also, how many people should staff each location based on coverage area?

How Much Is a Million?

6-8

This lesson focuses students on the concept of 1,000,000. It allows students to see first hand the sheer size of 1 million while at the same time providing them with an introduction to sampling and its use in mathematics. Students will use grains of rice and a balance to figure out the approximate volume and weight of 1,000,000 grains of rice.

Fish Food, More or Less

Pre-K-2

Students are introduced to the concepts of greater than, less than and equal to by observing quantities and making comparisons. Using various instructional materials such as modeling clay, buttons, beans, and cotton balls, students create amounts to compare using the open-mouthed fish. Depending which fish is chosen, the fish cut-out (with its mouth open) represents either greater than or less than. For equivalent amounts, a clam cut-out represents equal to.

This introductory lesson can be assessed through visual observation and verbal questioning. A group size of 3 – 6 students per group is optimal.

Fibonacci Trains

6-8

In this lesson, students use Cuisenaire Rods to build trains of different lengths and investigate patterns. Students make algebraic connections by writing rules and representing data in tables and graphs.

One Grain of Rice

6-8

In this lesson, students take on the role of a villager in a third-world country trying to feed her village. While listening to you read aloud the book One Grain of Rice by Demi, students work collaboratively to come up with a bargaining plan to trick the raja into feeding the village using algebra, exponential growth, and estimation.

Constructing a Three-Dimensional Model

3-5

In this lesson, students build a three‑dimensional model from their two‑dimensional blueprint. In addition, they solve problems related to constructing and decorating their clubhouse.

Tetrahedral Kites

6-8, 9-12

Each student constructs a tetrahedron and describes the linear, area and volume measurements using non‑traditional units of measure. Four tetrahedra are combined to form a similar tetrahedron whose linear dimensions are twice the original tetrahedron. The area and volume relationships between the first and second tetrahedra are explored, and generalizations for the relationships are developed.

Stacking Squares

9-12

This lesson prompts students to explore ways of arranging squares to represent equivalences involving square- and cube-roots. Students’ explanations and representations (with their various ways of finding these roots) form the basis for further work with radicals.

Are They Possible?

6-8

Students examine some isometric drawings that seem to be impossible and investigate one way Escher used to create these "impossible" figures.

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