# Six Math Class Activities

## Inconsistent Highway Signs

You are driving along a highway and see this sign:

Nearville 150 miles

Farville 160 miles

Then, surprisingly, an hour later you see this sign on the same highway:

Nearville 100 miles

Farville 109 miles

While appearing inconsistent, the signs are both correct! How can this be possible?

## Secret Salaries

A group of 7 employees are out to lunch, sitting around a table, and the topic of salary comes up. They all want to know the average salary of the group, without anyone revealing their own salary. Can you think of a way to do that? [Hint: This can be accomplished without anything being written down.]

## Eggsactly!

A basket (like, say, an Easter basket) has exactly six eggs in it. Six different people each take one egg. These are normal people and normal chicken eggs. After all 6 eggs have been taken, there is still one egg left in the basket. How could this be? (No one put their egg back in the basket.)

Our favorite teacher-suggestion: There was also a chicken in the basket that laid an egg.

## Adapted from a Car-Talk Puzzler

Three pieces of paper are face down, each with a different number written on them (say from minus infinity to plus infinity). Your job is to find the highest number by following these rules:

- You can pick up a slip at random and either choose that number, or discard the number and pick up a second slip.
- You can then choose or discard the second number.
- If you discard the second number, then you automatically choose the last number.

So the question is, can you think of a way to improve on a 1/3 chance of picking the highest number? [Hint: there is a way!]

## Missing Dollar Conundrum

Three travelers stop for the night in a hotel. They are charged $30 at the front desk and each contributes $10. Later, a bellhop comes to the room and says there was a mistake; the room price is only $25, so he refunds $5. The travelers each take $1 and give $2 to the bellhop. So, each traveler spent $9 ($27 total), and together they tipped $2, for a total of $29 paid. What happened to the other dollar?

## Making Sense of the Census

A census-taker knocks on a door, and asks the woman inside how many children she has and how old they are. "I have three daughters. Their ages are whole numbers, and the product of the ages is 36," says the mother.

- "That's not enough information," responds the census-taker.
- "I'd tell you the sum of their ages, but you'd still be stumped," says the mother.
- "I wish you would tell me something more."
- "Okay, my oldest daughter Annie likes dogs."

What are the ages of the three daughters?

## Learn More about Catchup Math

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