Is this thing rational?

180 Days of Ideas for Discussion in Math Class. (as of 9July2014, we're in overtime!)

## Thursday, July 31, 2014

## Wednesday, July 30, 2014

### 202: What is the area?

What combinations of addition or subtraction of figures could you use to find the area of the white?

## Tuesday, July 29, 2014

### 201: Circles and Pentagon

Two circles, radius 1 (each does not pass through the others center).

All seven regions are of equal area.

What is the area of the pentagon?

All seven regions are of equal area.

What is the area of the pentagon?

## Monday, July 28, 2014

## Sunday, July 27, 2014

## Saturday, July 26, 2014

### 198: Packing tires

Given the following information, what's the best packing method for those tires in one of these containers? You might want to Desmos-Draw the floorplan to be sure.

.

Overall diameter is 25", BTW.

.

Overall diameter is 25", BTW.

## Friday, July 25, 2014

### 197: Polar Figures 6

Can you recreate these figures? Note: Unlike the previous figures, these are all "incomplete" so you will have to do two things ... (a) figure out the form of the full figure (how many pedals, etc.) and (b) restrict the domain appropriately. In Desmos, domain restriction is done this way:

Here we go ....

Here we go ....

## Thursday, July 24, 2014

## Wednesday, July 23, 2014

## Tuesday, July 22, 2014

### 194: Polar Figures 3

Can you recreate these figures?

Single function.

In Desmos or Plot.ly, Create this Family of functions.

Single function.

In Desmos or Plot.ly, Create this Family of functions.

## Monday, July 21, 2014

## Sunday, July 20, 2014

## Saturday, July 19, 2014

### 191: Walking the Labyrinth

In this labyrinth, there are no false turns or dead ends. You walk the line around the outside, then follow it to the middle. Assume unit distance between lines and ends of turns except for that horizontal entry line. That seems to be half a unit apart from the other lines.

What are some different ways to measure the distance walked?

What are some different ways to measure the distance walked?

## Friday, July 18, 2014

### 190: Force Table

If the weights are all equal masses, is this in equilibrium?

If not, how would you change it?

Can this arrangement work with two equal masses?

If not, how would you change it?

Can this arrangement work with two equal masses?

## Thursday, July 17, 2014

### 189: Strasbourg Cathedral

Find the visual fractions.

Discuss the geometrical constructions the builder would have employed if he were limited to the following tools: a straight iron rod of 16.5 feet, string and a piece of chalk.

Discuss the geometrical constructions the builder would have employed if he were limited to the following tools: a straight iron rod of 16.5 feet, string and a piece of chalk.

## Wednesday, July 16, 2014

## Tuesday, July 15, 2014

### 187: Spiral

If we kept going, would any of the sides in this figure be parallel?

UPDATE: Asking a bad question is my fault. Of course, any polygon that has an even number of sides has n/2 pairs of parallel sides. What I was originally after, but didn't ask properly, was whether there a side of one polygon that was parallel to a side in another ... other than the pair in the triangle and square.

UPDATE: Asking a bad question is my fault. Of course, any polygon that has an even number of sides has n/2 pairs of parallel sides. What I was originally after, but didn't ask properly, was whether there a side of one polygon that was parallel to a side in another ... other than the pair in the triangle and square.

## Monday, July 14, 2014

## Sunday, July 13, 2014

### 185: Four is Cosmic

8 is 5; 5 is 4 ... and 4 is cosmic.

9 is 4 ... and 4 is cosmic.

10 is 3, 3 is 5, 5 is 4 ... and 4 is cosmic.

17 is 9, 9 is 4 ... and 4 is cosmic.

37 is 11, 11 is 6, 6 is 3, 3 is 5, 5 is 4 ... and 4 is cosmic.

What is going on?

Does everything lead to four?

9 is 4 ... and 4 is cosmic.

10 is 3, 3 is 5, 5 is 4 ... and 4 is cosmic.

17 is 9, 9 is 4 ... and 4 is cosmic.

37 is 11, 11 is 6, 6 is 3, 3 is 5, 5 is 4 ... and 4 is cosmic.

What is going on?

Does everything lead to four?

## Saturday, July 12, 2014

### 184: Is Eight Magic?

What is the pattern if we do this for other two-digit numbers?

Can we get other results? Are there results that we CAN'T get?

Challenge:

What is the longest string?

Can we get other results? Are there results that we CAN'T get?

Challenge:

What is the longest string?

## Friday, July 11, 2014

### 183: Italian Roulette

Could this work? What might go wrong with this plan?

If you divided the pizza into EIGHT pieces, what would be your chances of having to pay?

If you divided the pizza into EIGHT pieces, what would be your chances of having to pay?

## Thursday, July 10, 2014

## Wednesday, July 9, 2014

### 181: Inscribed Pyramid 2

## Tuesday, July 8, 2014

### 180: Inscribed Pyramid 1

## Monday, July 7, 2014

### 179: How Far to Bill's House?

Which distance is shorter?

Challenge:

Which two houses are the furthest apart when traveling by road?

Challenge:

Which two houses are the furthest apart when traveling by road?

## Sunday, July 6, 2014

### 178: Hexagonal Densepack

## Saturday, July 5, 2014

### 177: Parabola and friends

Is it possible to choose four points on the graph of y = x² that are the vertices of a trapezoid?

A parallelogram?

An equilateral triangle?

Here's y = x² to help you think.

A parallelogram?

An equilateral triangle?

Here's y = x² to help you think.

```
Is it possible to choose four pts on the graph of y = x² that are the vertices of a trapezoid? A parallelogram? An equilateral triangle?
```

— James Tanton (@jamestanton)

## Friday, July 4, 2014

### 176: Reported Ages

Sayeth Mr Honner:

What other questions did you have?

What would the graph look like if we asked people for the ages of their parents?

Here’s a fun little data set from a statistics textbook I’m reading.What do you think his two questions are?

These are the distributions oflast digitsof ages reported on the 1880 and 1970 US Censuses. At least two interesting questions come to mind, one with a seemingly easy answer.

What other questions did you have?

What would the graph look like if we asked people for the ages of their parents?

## Thursday, July 3, 2014

## Wednesday, July 2, 2014

### 174: Factors and Multiples

Least Common Multiple and Greatest Common Factor

A, B, and C are positive integers.

Greatest Common Factor of A and B is 5

Greatest Common Factor of B and C is 2

Greatest Common Factor of C and A is 3

Least Common Multiple of A and B is 900

Least Common Multiple of B and C is 2100

Least Common Multiple of C and A is 630

What is A?

A, B, and C are positive integers.

Greatest Common Factor of A and B is 5

Greatest Common Factor of B and C is 2

Greatest Common Factor of C and A is 3

Least Common Multiple of A and B is 900

Least Common Multiple of B and C is 2100

Least Common Multiple of C and A is 630

What is A?

## Tuesday, July 1, 2014

### 173: Bathtubs

Math is not always as easy for journalists as it is for you. Help this one with some of his calculations and assumptions.

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