Sum of Odd #s is the Squares 1

1. What does picture A have to do with picture B?
2. Continue both A and B for two more steps.
3. Find the totals in A. What kind of numbers are they?
4. Does B tell you why these numbers are what they are? Explain.
5. What is 1 + 3 + 5 + 7 + . . . + 99?

Bowling Ball

After the earthquake, Junior found that the bowling alley slanted upwards, so that he had to roll the ball upward toward the pins. The slant was gentle enough so that the pins would not fall over, but just barely. He found that when he rolled the ball it went with a velocity of 12 – 4t feet per second (where t is the number of elapsed seconds.) (a) How fast was the ball going after 1 second? (b) How fast was the ball going after 3 seconds? (c) How fast was it going after 4 seconds? (d) What does this mean? (e) How fast does Junior roll the ball on a flat lane?

Chinese Restaurant Party

At a large party in a Chinese restaurant (Wok Around the Clock), every three guests used a bowl of rice among them, every four guests used a bowl of soup among them, and every pair of guests used a bowl of fish between them. There were 65 bowls of these three things altogether. How many guests were at the party?

Dorothy Eggs

Dorothy and Toto were carefully driving their small veggie-oil-powered truck containing three baskets of eggs to market, when a car going at full speed collided with the truck. Dorothy was unhurt, but Toto got a broken leg. The eggs were destroyed. The car’s driver admitted his responsibility and offered to pay for the eggs. Dorothy said he must pay Toto’s vet bill too. The driver, aghast, asked, “Toto too?” Dorothy compromised and said she’d pay half the vet bill if the driver could answer a simple problem for her:

The number of eggs was somewhere between 50 and 100. If they were counted out 2 at a time or 3 at a time, none would remain at the end. But if they were counted out 5 at a time, there would be 3 left over.

The driver was required to say how many eggs there had been in the baskets. What answer would get him off the hook for the full vet bill?

Integer Less than 9 Million

What is the largest integer less than 9,000,000 whose smallest prime divisor is 3163?

Marble Piles

Jasper had his marbles out on the floor the other day. His little sister Pearl was putting them in equal piles, or trying to. When she tried to put them in two equal piles, she had one marble left over. When she tried to make three equal piles she had two marbles left over. When she tried to make four equal piles, she had three marbles left over. Then she got mad and threw all of the marbles under the piano. Jasper pulled them all out (he didn’t lose any, and he kept his temper) and put them into seven equal piles, with no marbles left over. How many marbles does he have?

Cows and Oxen Cost

John spent \$1705 on cows and oxen. Cows cost \$40 and oxen cost \$75 each. He bought twice as many cows as oxen. How many of each did he buy?

Eggs to Carry

Your task is to carry 150 eggs from the car to the farm stand. You will be paid two cents for every one that arrives intact; you must pay back five cents for each one that you break. If you want to buy those swim goggles that cost \$2.98 (including tax), how many eggs can you break and still have enough money?