PROBLEM SOLVING TASKS
Grandpa’s Farm
Fred and Patti go to Grandpa’s farm. In the barnyard there are ducks and sheep. Fredand Patti see 9 animals all together. The animals have a total of 26 legs. How manyducks and how many sheep are there in the barnyard?
Cooper’s Dog Pen
Mrs. Callahan is building a new dog pen for her dog, Cooper. She has 24 feet of fencing to build the dog pen. The pen needs to be a rectangle. What are the lengths and widths of the different sizes of pens that she can make with that amount of fencing? Which pen will give Cooper the largest area to run around in?
Three Chips
We have three chips. A one-digit positive whole number is written on each side of each chip. The six numbers used on the chips are consecutive.
Tossing the chips once, we get 6, 7 and 8, for a sum of 21. Then we shake and toss them a few more times and get the sums of 16, 17, 20 and 23.
Which number is on the opposite side of number 6? number 7? number 8?
Two Pails
How can you bring up from the river exactly six quarts of water when you have only two containers, a 4-quart pail and a 9-quart pail, to measure with? (There are no markings on the pail, so the only way to fill up these pails is to fill them all the way up to the rim.)
Yokes on You!
If three hens lay four eggs in five days, how many days will it take a dozen hens to lay four dozen eggs?
Jason’s Piggy Bank
Jason emptied his piggy bank and counted out exactly $10 in nickels, dimes and quarters. There were twice as many dimes as nickels. There were twice as many quarters as dimes. How many nickels did he have?
Filling the Tub
It takes three minutes to fill a tub to the top and five minutes to drain the full tub. If the faucet and drain are both open, how long will it take to fill the tub?
Ration Ratios
At a recent math conference, lunch was provided for the participants. To be sure that there was enough food for everyone, the kitchen staff made more lunches than there were people attending. In fact, the ratio of prepared lunches to people was 7:5.
Because they anticipated a large number of vegetarians at the conference, the staff made 2 vegetarian lunches for every 3 non-vegetarian lunches.
It turned out that the ratio of non-vegetarians to vegetarians at the conference was 3:4.
What was the ratio of vegetarian lunches to vegetarians?
All Wet
A rectangular lawn has an area of 667 square meters. Surrounding the lawn is a flower border 4 meters wide. The border alone has an area of 548 square meters.
A circular sprinkler is installed in the middle of the lawn.
- What is the spraying radius of the sprinkler if it covers the entire yard, including the flower border? (Answers may be given to the nearest hundredth.)
- What percentage of water is wasted (i.e. water that lands outside the lawn and garden)?
Sums of Consecutive Integers
This is the sum of the first three positive consecutive integers:
1 + 2 + 3 = 6
What is the sum of the first four positive consecutive integers? The first seven positive consecutive integers? The first 100 positive consecutive integers?
Find a formula for adding the first n positive integers.
The Proof is in the Pudding(from Dr. Mike Shaughnessy’s class Visual Math for Middle School Teachers, 1995)
The host at a party turned to a guest and said, “I have three daughters and I will tell you how old they are. The product of their ages is 36. The sum of their ages is my house number. How old is each?”
The guest rushed to the door, looked at the house number, and informed the host that he needed more information. The host then added, “The oldest likes strawberry pudding.” The guest then announced the ages of the girls.
What are the ages of the three daughters? (All ages are whole numbers. It is possible that there may be twins or triplets.)
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