Prove that anywhere on Pascal's triangle, products of numbers in yellow and in orange are equal.— ⋁△ ᴹᴬᵀᴴcafé ☕ (@Five_Triangles) August 18, 2016

Via @HopeHana pic.twitter.com/zgs3d0wenJ

# Math Arguments

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

## Thursday, August 18, 2016

### 515: Pascal Proof

An interesting Question ... is an algebraic method the only way to do this?

## Thursday, June 16, 2016

### 514: Probability Game

Temporary return! A quick probability question ...

Player A's score is determined by taking the highest of 3 dice.

Player B's is determined by taking second-highest of 8.

Who wins more games?

Player A's score is determined by taking the highest of 3 dice.

Player B's is determined by taking second-highest of 8.

Who wins more games?

Player A's score is determined by taking the highest of 3 dice.— Ben Orlin (@benorlin) June 16, 2016

Player B's is determined by taking second-highest of 8.

Who wins more games?

## Thursday, December 17, 2015

## Wednesday, December 16, 2015

### 512: Factory Ratios 3

We started with this:

If the ugly-sweater party was held in that factory with the minimum number of workers possible and the ratio of red to green ugly sweaters was 7:13, how likely is it that a left-handed man wore a red ugly sweater?

Source:

In a factory, the ratio of men to women is 2:3. The ratio of right-handed men to left-handed men is 7:3. The ratio of right-handed women to left-handed women is 11:1. What fraction of the factory workforce is right-handed?

And then we extended with: What is the fewest number of employees possible in this building?

And then we extended with: What is the fewest number of employees possible in this building?

If the ugly-sweater party was held in that factory with the minimum number of workers possible and the ratio of red to green ugly sweaters was 7:13, how likely is it that a left-handed man wore a red ugly sweater?

Source:

```
New GCSE Maths question:
Ratio and proportion is the buzz thing!
How are your students going to tackle it? pic.twitter.com/RyPsmc9z4m
— m4ths.com (@m4thsdotcom) December 16, 2015
```

### 511: Factory Ratios 2

We started with this:

Source:

In a factory, the ratio of men to women is 2:3.

The ratio of right-handed men to left-handed men is 7:3

The ratio of right-handed women to left-handed women is 11:1

What fraction of the factory workforce is right-handed?

But let's extend things a bit.The ratio of right-handed men to left-handed men is 7:3

The ratio of right-handed women to left-handed women is 11:1

What fraction of the factory workforce is right-handed?

**What is the fewest number of employees possible in this building?**Source:

```
New GCSE Maths question:
Ratio and proportion is the buzz thing!
How are your students going to tackle it? pic.twitter.com/RyPsmc9z4m
— m4ths.com (@m4thsdotcom) December 16, 2015
```

### 510: Factory Ratios 1

In a factory, the ratio of men to women is 2:3.

The ratio of right-handed men to left-handed men is 7:3

The ratio of right-handed women to left-handed women is 11:1

What fraction of the factory workforce is right-handed?

Source:

The ratio of right-handed men to left-handed men is 7:3

The ratio of right-handed women to left-handed women is 11:1

What fraction of the factory workforce is right-handed?

Source:

```
New GCSE Maths question:
Ratio and proportion is the buzz thing!
How are your students going to tackle it? pic.twitter.com/RyPsmc9z4m
— m4ths.com (@m4thsdotcom) December 16, 2015
```

## Saturday, November 28, 2015

### 509: Circles 2

Several days ago, I posted a slightly different question about tangential circles and the spaces in between. Compare this question, from the 2004 SAT Practice Test to that question from Emma Bell.

source: ETS, 2004

- Which question seems harder? What are the difficult aspects of each?
- Do we have to specify the angle APB?
- How are these two questions different in terms of the knowledge they require for solving?
- Is this question made harder by the "how many times" part? Does that phrasing make the question unnatural?

source: ETS, 2004

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