MTH420_IN-CLASS

IN-CLASS //These include non-text situations motivated, explored, or mentioned in class // __//(Green is one we definitely looked at in class...Yellow is pending) //__

Cider Problem A bottle of cider costs 86 cents. The cider costs 60 cents more than the bottle. How much does the just the bottle cost?

Hotel Madness Three men registered at a hotel. They were charged 30$ for their room.  The clerk realized later that he’d over-charged them by 5$, so he sent the bellboy up with the refund.

The bellboy knew it would be hard to split the 5$ evenly among the three men, so he kept a 2$ “tip” for himself and only gave the men 3$. So, each man had originally paid 10$, but was given back 1$.

The room therefore cost each man 9$, and together they paid 27$. This amount, plus the 2$ “tip” kept by the bellboy, adds to 29$.

But there were 30$ at the beginning. So, if 29$ have been accounted for, then what happened to the missing dollar?

Chain Links Given 4 pieces of chain consisting of 3 links each, explain how all 12 links can be joined into a single circular chain by cutting and rejoining only 3 links.

RBG Boxes You have three boxes: a red box, a blue box, and a green box. Inside each box is a single ball of the same colour as the box. Someone takes each ball out and puts it in a different box. You open the red box and discover a green ball. Is this enough information to tell what color ball is in the blue box? (If so, tell me the color; if not, explain or show why not).

Mrs. Hoffman’s Class Two-thirds of Mrs. Hoffman’s fifth-grade students are boys. To make the number of boys and girls equal, 4 boys go to the other fifth-grade class, and 4 girls come from that class into Mrs. Hoffman’s class. Now one-half of her students are boys. How many students are in Mrs. Hoffman’s class?

Folding Paper Show how to measure exactly 3 inches using only a sheet of paper that measures 8.5 inches by 11 inches.

Krazy Kids  [Version A] You knew that Mr. Jones has 2 kids, but that’s all you knew.  Then one day, you see Mr. Jones, and with him is his son. What <span style="font-family: Arial,sans-serif; font-size: 11pt;"> are the chances that Mr. Jones’ other kid is a girl? <span style="font-family: Arial,sans-serif; font-size: 11pt;"> [Version B] You knew that Mr. Jones has 2 kids, but that’s all you knew. <span style="font-family: Arial,sans-serif; font-size: 11pt;"> Then one day, you see Mr. Jones, and with him is his son. Mr. <span style="font-family: Arial,sans-serif; font-size: 11pt;"> Jones introduces his son, saying “This is my eldest, Jimmy.” What <span style="font-family: Arial,sans-serif; font-size: 11pt;"> are the chances that Mr. Jones’ other kid is a girl?

<span style="font-family: Arial,sans-serif; font-size: 11pt;"> My question: Are Versions A and B the same or different?

Cake Cutting <span style="font-family: Arial,sans-serif; font-size: 11pt;">Into how many different pieces, not necessarily the same size, can a <span style="font-family: Arial,sans-serif; font-size: 11pt;">circular cake be cut using only 15 straight vertical cuts?

Condo Conundrum <span style="font-family: Arial,sans-serif; font-size: 11pt;">In a certain Condo Complex, 2/3 of the men. Are married to 3/5 of the Women. <span style="font-family: Arial,sans-serif; font-size: 11pt;">What fraction of the people in the Condo Complex are married?

The Pool Problem:
Jenny’s old water pump could only fill 1 swimming pool in 5 hours. Her new water pump was able to fill 1 swimming pool in 3 hours. How long will it take Jenny to fill 1 swimming pool if she uses both pumps at the same time?

Average Speed

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 15.243800163269px;">What was my average speed for the entire round-trip?
Farmer Math

A farmer, when asked what number of animals she had, replied: “All but 9 are Cats, all but 8 are Birds, all but 10 are Dogs, and all but 6 are Fish. How many animals had she?

Our Pumpkin
<span style="font-family: Arial,sans-serif; font-size: 11pt;">Originally, our pumpkin was 99% water! Then, as it sat in the

<span style="font-family: Arial,sans-serif; font-size: 11pt;">sun, it began to lose weight. It lost weight only due to water

<span style="font-family: Arial,sans-serif; font-size: 11pt;">evaporation. Now, our pumpkin is only half of its original weight.

<span style="font-family: Arial,sans-serif; font-size: 11pt;">What percentage of our pumpkin is water now?

Always Tell The Truth

Bill could never tell the truth. Tom could never tell a lie. One of them said:

“The other one said he is Bill!” Which one said that?

Garage Sale <span style="font-family: Arial,sans-serif; font-size: 11pt;">Before going to a garage sale, Elise counted the money she was taking along. <span style="font-family: Arial,sans-serif; font-size: 11pt;">After an hour, she counted again and found that she had spent exactly half of it. <span style="font-family: Arial,sans-serif; font-size: 11pt;">The number of cents she now had equaled the number of dollars she started with; <span style="font-family: Arial,sans-serif; font-size: 11pt;">the number of dollars she now had was half the number of cents she started with. <span style="font-family: Arial,sans-serif; font-size: 11pt;">How much money did she spend?

Train Speed <span style="font-family: Arial,sans-serif; font-size: 11pt;">It took a train 45 seconds to pass through a 1320-foot tunnel. At the same speed, it <span style="font-family: Arial,sans-serif; font-size: 11pt;">took 15 seconds for the train to pass a telephone pole. How long was the train, and <span style="font-family: Arial,sans-serif; font-size: 11pt;">what was its speed (in feet per second) ?

Walnuts for You <span style="font-family: Arial,sans-serif; font-size: 11pt;">If Joe gives Pepe 10 walnuts and Mia gives Pepe 15 walnuts, then Pepe has as many <span style="font-family: Arial,sans-serif; font-size: 11pt;">as Joe and Mia together. But if instead Joe gives Mia 15 walnuts and Pepe gives her <span style="font-family: Arial,sans-serif; font-size: 11pt;">8 more, then Mia has as many as Joe and Pepe together. What is the smallest number <span style="font-family: Arial,sans-serif; font-size: 11pt;">of walnuts that each person could have?

Family Reunion <span style="font-family: Arial,sans-serif; font-size: 11pt;">At one family reunion, every nephew was a cousin. Half of all <span style="font-family: Arial,sans-serif; font-size: 11pt;">uncles were cousins. Half of all cousins were nephews. There <span style="font-family: Arial,sans-serif; font-size: 11pt;">were 30 uncles and 20 nephews. No uncle was a nephew. How <span style="font-family: Arial,sans-serif; font-size: 11pt;">many cousins were neither nephews nor uncles?