Standard Three – Foundation Level Problems
Prompt: A fifth number, n, becomes a member of the set of numbers {3, 6, 9, 10} to
make the mean of the five numbers equal to their median. What are the possible
numbers for n?
Answer: 2, 7, 27
Mathematics Teacher April 1992 V85 N4
Prompt: In how many different ways can a panel of four on-off switches be set if no two
adjacent switches can be off?
Answer: 8
Mathematics Teacher September 1992 V85 N6
Prompt: Three digits are randomly selected without replacement from one 1, two 9s,
and one 6. What is the probability that the three digits form a three-digit number that is
a multiple of 3?
Answer: ¼
Mathematics Teacher April 1996 V89 N4
Prompt: If you meet any two of the Jones sisters, the chance is 50-50 that they will
both be blue-eyed. What is the likeliest number of blue-eyed Jones sisters?
Answer: 3 blue-eyed sisters, 4 total sisters (could also unrealistically be 15 blue-eyed
and 21 totoal).
Mathematics Teacher April 2000 V93 N4
Prompt: Rewrite the problem in your own words, discuss different methods of solving
this problem, and solve for the number of paths. Be sure to justify your steps.
Answer: Pascal’s Triangle
D.C. Heath and Company, Teacher Resource Materials: Alternative Assessment