## Need to rent some chaise lounges

Brian is in Crete and he took a picture of this sign. What do you suppose he's going to ask next?

Yep.  "How much will 6 lounges and 2 umbrellas cost?"  And more ...

Systems begin.

rent-beach-stuff.pdf

## Olympic Skateboarding + more

Huston Nyjah

We are very excited to see skateboarding as an event in the Tokyo Olympics.  Skateboarding is athletic, artistic and difficult to master.  Why has it taken so long to become an Olympic sport?  What events will you be able to watch?  How are skateboard runs and tricks judged? Is there a possibility of bias in the judging? ... and who is well-known that we should make sure to  watch?

The activity: Skateboarding.pdf

## Beautiful mathematics

 Pythagorean triples are not only handy for students to recognize but produce some interesting and lovely patterns. We've combined a little coloring with our Pythagorean Triple pattern investigation to let your students relax while they color, view the beauty, and recognize the progression. Simply coloring our Fibonacci patterns might allow students to ponder the Fibonacci sequence (while they learn more about its beauty) and just relax while creating a pretty image. We've given you colorless patterns that students can shade in their own way (for a simple coloring project) or you can use our Fibonacci Project document to allow students to create these patterns themselves. Students explore the patterns of perfect squares and Pythagorean Triples as they analyze our piece of art and decide why the resulting construction looks like spiraling squares. For a finale they color their own spiraling triple. First ask students to color in our Golden Spiral by giving them the hexadecimal codes of the colors that we want them to use. Then help them begin to understand which number weights between 00 and FF have the strongest values and how they blend. As students begin working with the Pythagorean theorem let them create a little art project that help them actually see a segment of length square root of 2. Drawing this irrational number spiral is beautiful and motivating. Students use polar graph paper and calculate the size of each increasing round of squares. They consider what sort of spiral this makes and find spirals within spirals. Students investigate Pascal's triangle and the many useful patterns that it contains. The triangle is explored for patterns, coloring, and motivation to learn more about modular arithmetic (clock math). Students watch this tree grow and explore its fractal nature. They get a taste of Python computer language as they decipher the repeats and scaling of a drawing program. Students physically build an ellipse by choosing two foci and sketching the ensuing figure through a loop of string. While stitching this elliptical string design, they puzzle about the effect of varying the foci spread and the string length. They are intuitively introduced to the measurement of eccentricity. How do you find the area of a heart? Get your students to calculate how many sequins you'll need to order to create this mother's day class project. Use our hexagonal grid paper to create a lovely Pascal triangle and investigate where Pascal's triangle can help you with binomial expansions. Explore parametric equations in the construction of this heart. Students figure the coordinates of this figure using trigonometric unit triangles. They simplify and accelerate this task with either a graphing calculator or online software like Desmos or GraphSketch.com. Students explore 4 different ways of creating this cardioid ... Using our polar graph paper, with magnetic disks, on their graphing calculators, or with polar graph paper and a compass. Students measure and create whole number ratios for the official U.S. flag. They decide how their artistic flags will be different from the official flag and make stars from regular pentagons. They finally create their own flag. This time use Pascal's triangle to explore probability. We used coin tosses. When the combinations get too complicated to list, students use the numbers in Pascal's Triangle to ease their work. Students can learn to make cardstock polyhedra and assemble their nets and creations. This is from Leslie's old site on building polyhedra. Drawing and coloring a Fibonacci patterns might allow students to ponder the Fibonacci sequence (while they learn more about its beauty) and just relax while creating a pretty image. We've given you colorless patterns that students can shade in their own way (for a simple coloring project) or you can use our Fibonacci Project document to allow students to create these patterns themselves. Students can learn to make cardstock polyhedra and assemble their nets and creations. This is from Leslie's old site on building polyhedra.

## Ranked Choice Voting in NYC

New York City is still tallying its election results for a new Mayor.  This year they tried Ranked Choice Voting.  What does that mean? How does that work?  What are the ramifications of this sort of voting? Do you think that this will be a fairer and more positive way of electing a Mayor?

Students experiment with the technique of tallying the votes using our flow chart and make some observations and decisions about the process.

## Betsy Ross’s 5-pointed star + 4th of July activities

Flag of the United States from 1777 to 1795.

Click on the image above to see it larger in a new window.

In honor of Independence Day we thought it would be fun to look at one story about the first American Flag.

The rough design of the flag was drawn by a committee of George Washington, Robert Morris, and George Ross in 1776.  When approached by the committee, George Ross's niece, a respected seamstress, Betsy Ross, suggested some important changes.  One change was to use a 5-pointed star to represent each of the 13 colonies. The committee objected that a pentagram would be too hard to make. Betsy demonstrated that she could create the desired star by simply folding fabric and making just one scissors cut.  So, the design was changed.

How did she do that fold and cut?

## How much is a trillion dollars?

U.S. Congress is now debating how much money to approve on spending for infrastructure.  The numbers are between 1 and 3 trillion dollars. I can't even fathom that amount of money.  Is there a way to imagine it in proportion to something else?

In this activity students wrestle with comparisons to understand a trillion of anything.

Imagining-a-trillion.pdf