Archives for category: Problems

Here is a problem I found in Jo Boaler’s book “What’s math got to do with it?” She credits it to Ruth Parker:


A woman is on a diet and goes into a shop to buy some turkey slices.  She buys 3 slices which together weigh 1/3 of a pound, but her diet says that she is only allowed to eat 1/4 of a pound.  How much of the 3 slices she bought can she eat while staying true to her diet?

My friend, Ellen and I brainstormed this one at coffee the other day, as an opening day activity.

Hand each member of the group an envelope with 3 to 4 post its, each with a different number on them.  Have the group combine their post its, and place them on a generic number line (not labeled) posted on the wall in the classroom.  Once all groups are finished have them check the work of another group (each group will have their own set of numbers), or do a gallery walk, looking at all the number lines in the class. 

The numbers should include decimals, fractions, integers, square roots, pi,simple cube roots, etc.  NO CALCULATORS allowed.



Here’s a real life problem I gave my students.  It was a lot easier to explain, than to write here as a problem. :).  My students were highly motivated, as I was going to make my decision that morning, based on their findings.   It was great having the students share their solutions with the class, as there were many different methods of solving:


Yesterday I had someone paint the spare room in my house.  When I came home I was dismayed that the color I chose was much darker than I had anticipated.  I went back to the paint store to try again.  Since I liked the color I asked for a lighter version.  The clerk made a “batch” which had a color strength of 25%.  It was too light.  He informed me that he was only able to mix in increments of 25%, so he made a batch of 50%.  It seemed a bit dark.  He suggested I take this 50% strength gallon home along with a quart of white paint, and a large pail for mixing.  I painted a swatch of the 50% on the wall and checked it in the morning.  I was still undecided.  Since my painter was coming back that morning, I needed to make a decision as to whether to mix the gallon of 50% and the quart of white.  The question posed to my students was:  What would the color strength (%) of the mixture be, in relationship to the original paint. 


Note:  most of my students came up with the same wrong answer to begin with, but when I prompted them to try again, they were able to determine the correct percent.