Can you come up with other, better, divisions?

source.

# MathArguments180.com

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

## 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

## Sunday, November 22, 2015

### 507: Orderly Probability

Scenario 1: Which winning number group is more likely to occur?

Scenario 2: Which winning number group is more likely to occur if the numbers are drawn in any order and THEN put into ascending order by the presenter?

In which of the above two scenarios is getting the winning numbers more likely?

source: Jeff Suzuki

1-2-3-4-5-6 OR 4-8-15-16-23-42

Scenario 2: Which winning number group is more likely to occur if the numbers are drawn in any order and THEN put into ascending order by the presenter?

1-2-3-4-5-6 OR 4-8-15-16-23-42

In which of the above two scenarios is getting the winning numbers more likely?

source: Jeff Suzuki

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