What is the sum of the counting numbers from 1 to 1000? Explain how you know in a paragraph, showing all work.

Six bippities equal 3 bops, and six bops equal two boos. How many boos are there in one bippity, one bop, and one boo?

There are some bunnies and hutches. If one bunny is placed in each hutch, then one bunny will be left without a hutch. If two bunnies are placed in each hutch, then one hutch will have only one bunny in it. How many bunnies and hutchs are there? Explain how you know in a paragraph and at least one diagram.

Giles's numbers are multiples of 1, 2, 3, 4, 5, 6, 7, 8, and 9. What is the smallest of Giles's numbers? Explain in a paragraph how you found it. Be specific. Include numbers in your explanation. Diagrams might be helpful

The product of a set of consecutive integers is 720. If the mean is 3.5, what is the sum of the integers? Describe your process for finding the answer using a 4-step plan.

If A[flower]B means (A+B)/2, then what is the value of (3 [flower]5)[flower]8? Explain in detail!

Magic Square:
? 18 1 14 ?
11 24 7 ? 3
17 5 ? 21 9
23 6 ? 2 15
? 12 25 ? ?

Each row, column and diagonal (of 5) has the same sum. Fill in the missing numbers and EXPLAIN in a paragraph how you found them. Be SPECIFIC.

Note - due to the formating on this web page, you may need to re-copy the numbers on to a 5 x 5 grid in order to see the columns and diagonals properly.

In the diagram, how many C balls would it take to balance one A ball? How do you know? Explain in words, numbers and pictures.

Stan told Nan "I'm five times as old as you." Nan said, "So, what? Only 3 years ago, you were seven times as old as me." How old are Stan and Nan? Explain in a paragraph and show ALL work.

I have 4 pets: an iguana, a cat, a bird, and a large ape. Today I loaned all the pets to friends who enjoy the company of pets. The iguana is returned every 6 days. The cat comes home every 4 days. The bird, every 3, and the ape, every 7. Every time they come home, I loan them right back out again. How long until all of my pets will come home on the same day? Explain in a paragrah and show ALL your work. A diagram might help.

At the dog park, little Callie Counter counted 70 heads and 200 feet. How many humans were at the dog park? Explain in a paragraph and show your work.

Farmer John has many sacks of wheat and 8 gluttonous cats to protect them. In his granary, there is a crowd of voracious mice. Every night each mouse eats 1/4 of a sack of wheat. But they are smart and always eat a whole sack before starting the next one. Every morning each cat eats mouse. Last night there were 40 mice in the granary. When all of the mice have been eaten (assuming there are no new ones arriving) how many sacks of wheat will have been eaten? Explain how you know in a PARAGRAPH. Show all work. A table or diagram may help.

Write a numerical expression and draw a diagram (think time-line) to represent:

3 days before 2 weeks and 6 days from the day before yesterday.

Let x = today.
Then rewrite your expression in simplest form and explain your reasoning in a paragraph.