A “conjecture” is an educated guess. I noticed something when I divided a whole number and a fraction so I’m making a “conjecture”. Your job is to see if my conjecture is always true, sometimes true, or never true. You will do this by checking my work and then positing your own 3 examples. If you cannot find an example that disproves my conjecture you should assume it is always true. If you can find even one example that disproves my conjecture you would conclude that my conjecture is sometimes true. In this example, we know that “never true” isn’t an option because my examples are true! Here we go:

I took 60 and divided it by 1/2 (not 2) and my calculator said the answer was 120.

60 ÷ (0.5) = 120

I took 10 and divided it by 1/4 (not 4) and my calculator said the answer was 40.

10 ÷ (0.25) = 40

I took 75 and divided it by 1/10 (not 10) and my calculator said the answer was 750.

75 ÷ (0.1) = 750

My conjecture: When you divide a whole number by a fraction the answer is more than you started with. Is this always true or sometimes true? In order to pick “sometimes true” you have to come up with an example that disproves my conjecture.

Your heart pumps about 5 quarts of blood through its chambers every 60 seconds. A swimming pool (20ft x 60ft) will hold about 65,000 gallons of water.

How many weeks would it take your heart to pump that much blood?

You can find a conversion table HERE!

A canoe rental store on Lake Louis, Canada has 30 canoes that it rents on a daily basis during the summer season. If canoes rent for $15 per day, how much can the store collect for canoe rentals during the month of July?

In Reno, Netflix earned $5,393.25 in subscriptions during July. January subscriptions are expected to double that amount. If a Netflix subscription is $7.99, how many subscriptions are expected in January?

Remember that you will need to SHOW and EXPLAIN how you solved your problem. DO NOT just type an answer in!!

What is the smallest three digit palindrome that is divisible by 18? Explain how you found your answer.

This week you will visit the Get the Math website and discover how math is used in the fashion industry. The link below will start you at the Introduction to this activity. After you watch the introduction, follow the links to the right of the video to Take the Challenge, See how the teams solved the challenge, and finally, Try other fashion challenges. 

Tell me what garment you chose to take the other fashion challenge with and how you solved the challenge! 

http://www.thirteen.org/get-the-math/the-challenges/math-in-fashion/introduction/12/

For Mother’s Day you gave your mom 1 rose, 1 daisy, 1 lily, and 1 carnation one flower at a time. How many different ways can you hand those flowers to your mom? Explain how you came up with your solution!

Can you find 4 consecutive prime numbers that add up to 220?

It takes a lot of work to keep Disneyland’s two parks looking top notch. Some of that work is making sure that all the equipment is freshly painted and looking its best. When it comes time to paint the Ferris Wheel, Disneyland maintenance crews need to use a little math to get the job done. The diameter of the Ferris Wheel is 160 feet. They need to paint both of the outside rails of wheel red. How many feet total of red paint will they be painting? Explain how you found your solution.

It was Easter in Easter village and all the Easter bunnies are joyful. The annual Easter egg hunt was just finished. The Easter egg hunt is where four Easter bunnies search for any of the four colored eggs and then cross the finish line. Can you figure out which Easter bunny found which egg and what place they finished?

Easter bunnies- Mr Hops, Jumper, Long Ears, and Mrs. Littlenose

Easter Eggs- blue, red, green, and yellow

Clues:

1. Long Ears did not finish in 2nd place.

2. Jumper did not finish in 1st

3. Long Ears found the red Easter egg.

4. The bunny that finished in 2nd did not find the green egg.

5. Mr. Hops did not find the blue egg.

6. Littlenose did not finish in 2nd.

7. The bunny that found the blue egg did not finish in 1st or 2nd.

8. Hops finished in 4th.

Recently on Facebook the math problem below has been bouncing around. 

It has been very interesting to see the different comments and see the passion behind the answers given. The debate is heated and each person believes that they are correct and waste no time in defending their reasoning and every defense has to do with PEMDAS.

There is a correct answer. Which one is it? Defend why you believe your answer is the correct answer? 

After our Hour of Power last Friday I had 157 comments to sort through on our blog. On a normal week, I would have about 80 comments. What is the percent of increase in comments this last week? How did you find your solution?

While at the math conference in Las Vegas last week we did a scale activity. We started by building the small dog and then we were told to scale the dog by a certain amount to create a larger version.  I took pictures of our creation to share with you. 🙂

How many times bigger is our large dog than our small dog? How do you know?

Those of you who would like some extra credit, tell me the volume of the little dog and the volume of the large dog and write the volume in a ratio of little:large. Explain how you found your ratio too!

 ***Click on the picture to see a larger version.***

While I was waiting for Roni to finish rehearsals today, I stopped by a nearby Starbucks. I needed to buy a new travel coffee mug and they had many to choose from.  I finally narrowed the search down the two cups pictured above. The larger cup holds 12 ounces of yummy coffee and the smaller cup holds 8 ounces of yummy coffee. Please help me decide which coffee cup to buy by giving me one really great mathematical statement! Your statement should justify the reason you want me to buy the cup you choose. 🙂 

***MAKE SURE YOUR ANSWER IS UNIQUE!***