Example Problems
Below, find some example problems that could serve as jump-off points for discussions and explorations of mathematical concepts. They are split into those for older and younger students.
Each problem is accompanied by a hint -- simply click on the text.
For older students
Grid Walking
We have a grid of 3 columns and 4 rows. How many different paths can we draw from the bottom left to the top right (following the grid lines), with only 7 moves?
Sum of Consecutive Integers
Suppose you are a farmer, planting one flower the first day, two the second, three the third, and so on. How many flowers in total will you have by the nth day? Can you prove a general formula for the sum 1 + 2 + 3 + ... + (n-1) + n?
For younger students
Scaling Shapes
If we have a rectangular pool and we decide to make a new one whose side lengths are twice longer, what will happen to the area of the pool? Will it double? Why or why not?
Venn Diagrams
Let's create our own venn diagram based on characteristics we come up with. How do we define the sets of objects? Are there sets that don't have any objects in common? If we know the number of objects in each set and know the number of total objects, can we figure out how many are in both?
Fractional Pies
Would you rather have half of five pies, or five halves of pie? Is there a difference? How can we show there is or isn't?