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### Geometry of Circles

6-8

Using a MIRA^{TM}geometry tool, students determine the relationships between radius, diameter, circumference and area of a circle.

### Armstrong Numbers

6-8, 9-12

An Armstrong number is an *n*-digit number that is equal to the sum of the

*n*

^{th}powers of its digits. In this lesson, students will explore Armstrong numbers, identify all Armstrong numbers less than 1000, and investigate a recursive sequence that uses a similar process. Throughout the lesson, students will use spreadsheets or other technology.

### Golden Ratio

6-8

Students explore the Fibonacci sequence, examine how the ratio of two consecutive Fibonacci numbers creates the Golden Ratio, and identify real-life examples of the Golden Ratio.### Bagel Algebra

6-8

A real-life example—taken from a bagel shop, of all places—is used to get students to think about solving a problem symbolically. Students must decipher a series of equations and interpret results to understand the point that the bagel shop’s owner is trying to make.### Arithme-Tic-Toc

6-8, 9-12

Students will be introduced to modular arithmetic by first examining a five-hour analog clock and its mathematical properties. Then students will investigate patterns and relationships that exist in 12-hour addition and multiplication clock tables. ### Walk the Plank

6-8, 9-12

When one end of a wooden board is placed on a bathroom scale and the
other end is suspended on a textbook, students can "walk the plank" and
record the weight measurement as their distance from the scale changes.
The results are unexpected— the relationship between the weight and
distance is linear, and all lines have the same *x*‑intercept. This investigation leads to a real world occurrence of negative slope, examples of which are often hard to find.

### Squares, Diagonals, and Square Roots

6-8

Students explore the relationship between the lengths of the sides and diagonals of a square. Students will use their discoveries to predict the diagonal length of any square. ### Square Circles

6-8

This lesson allows students to use a variety of units when measuring
the side length and perimeter of squares and the diameter and
circumference of circles. From these measurements, students will
discover the constant ratio of 1:4 for all squares and the ratio of
approximately 1:3.14 for all circles.### Space Shuttle

6-8

Students consider the amount of time that space travelers must spend on their journey. Students improve their concept of time and distance, while at the same time learn more about the solar system.### How Much Time Do We Need?

6-8

Students consider the amount of time that space travelers need to travel to the four terrestrial planets. Students also think about what kinds of events might occur on Earth while the space travelers are on their journey.