Good Problems

Brown Eyes, Blonde Hair browneyesblondehair.png
Grade(s): 8
Strand(s): Number Sense (Fractions)
Problem:
In a particular class, each student has blonde hair or brown eyes; 1/4 of students with blonde hair have brown eyes and 1/3 of the students with brown eyes have blonde hair.

What fraction of the class in total have brown eyes?
What is the minimum number of students in the class?
What fraction of the class have both brown eyes and blonde hair?
PDF.jpg.pdf download link here
Source: http://mathschallenge.net/full/blonde_hair_brown_eyes
Submitted by: Mark Ross, Norseman JMS

Bat Wings BatWings.jpg
Grade(s): 6,7,8
Strands(s): Number Sense

Problem:
Three students had collected some data for a project about bats. Each had collected a different set of readings for the wingspan of some bats. Unfortunately, each student had lost one measurement.
Two of the students had already added up their data and worked out their individual means and the overall mean was also known. The known information is summarized below: (see .pdf)
Using the above information, can you complete the missing data?

PDF.jpg.pdf download link here

Source: Intermediate Math ABQ Package – Summer 2009 (Compiled by Trevor Brown)
Submitted by: Mark Ross, Norseman JMS


Ben’s Game Ben's_Game.png
Grade(s): 7 & 8
Strand(s): Number Sense
Problem:
Ben, Jack and Emma were playing a game with a box of 40 counters – they were not using all of them. They each had a small pile of counters in front of them.
All at the same time, Ben passed a third of his counters to Jack, Jack passed a quarter of his counters to Emma and Emma passed a fifth of her counters to Ben.
They all passed on more than one counter.
After this they all had the same number of counters.
How many could each of them have started with?

PDF.jpg.pdf download link here

Source: Intermediate Math ABQ Package – Summer 2009 (Compiled by Trevor Brown)
Submitted by: Mark Ross, Norseman JMS