Today’s Problem: Mystery Set

A set of five numbers have the following properties:

The mode of the set is 0 and 4.
The median of the set is 4.
The mean of the set is 4.

What are the five numbers in the set?

Today’s Problem: Seychelles Flag

Seychelles Flag

Find the area of each section of the Seychelles flag.

The flag is x inches tall by 2x inches wide. The top edge is divided into 3 equal lengths. The right edge is divided into 3 equal lengths.

Today’s Problem: Beans, Beans The Musical Fruit

There is a jar of jellybeans on Mr. Wallace’s Desk. He asked some students to guess the number of jellybeans in the jar.

Annie guessed 206, Bert guessed 197, Estella guessed 212 and Feliciano guessed 221.

Mr. Wallace told the students “No guesses were correct, but one guess was off by 4 jellybeans, one was off by 13 jellybeans, one was off by 11 jellybeans, and one was off by 2 jellybeans. I will give you extra credit if you can figure out the number of jellybeans now.”

What is the correct number of jellybeans?

Today’s Problem: Greener Pastures

Materials needed: Paper and pencil.

Randomly place between 8 and 16 dots on a piece of paper. These will be your “fence posts.”

Next, draw “fences” between your fence posts to make several “pastures.” Make sure you use every fence post and that have lots of open space for your livestock. Also, make sure your fences don’t cross.

Count the number of fences and pastures.

Add the number of fence posts to the number of pastures and subtract the number of fences. Your answer should be the same as your classmates, even if they used a different number of fenceposts, drew a different number of fences and had a different number of pastures.

Using this fact (related to something called the Euler Characteristic), how many fences will a farmer need if he wants 5 pastures and uses 51 fence posts?

Today’s Problem: In the Shade

Given segment x is 3 times the length of segment y and segment j is 2 times the length of segment k.

What fraction of the given rectangle is shaded?

Today’s Problem: Candy Costs

Kimo, Lena, and Alfons go to the candy store after school.

Kimo buys 10 Fireballs, 8 Bazookas, and 2 Root Beer Barrels for $1.34

Lena buys 5 Fireballs, 6 Bazookas, and 8 Root Beer Barrels for $1.26

Alfons buys 6 Fireballs and 6 Root Beer Barrels for 90¢

How much does the store charge for each piece?