Nrich is a great site that has plenty of activities that encourage children to think. The site is just one of the pieces that make up the Millennium Mathematics Project from the University of Cambridge. There are games, problems, and articles geared towards four grade groupings that represent the lower and upper primary grades and the lower and upper secondary grades.
Below is an example problem from the Being a Good Thinker - Upper Primary collection. The collection is broken into four important mathematical habits: curiosity, thoughtfulness, collaboration, and determination. This puzzle specifically is from “Being Determined.” In Nrich’s own words:
“Here are some problems that may require some determination. The solutions may not be immediately obvious, so you will need to persevere. Success can be sweeter after a struggle!”
Use the lines on this figure to show how the pattern of triangles can be used to divide the square into two halves, three thirds, six sixths and nine ninths.
More lines are needed to divide it into four quarters.
What is the least amount of line needed to do this if the quarters are in one piece and all the same shape?
How many ways can you divide it into halves using just the lines given?
If you really want to find interesting problems or to find different ways of approaching old standard problems, look at this site. Sign up for the newsletter and you will love everything you read!