This problem explores the concept of "squareness". It reinforces the understanding that a square has 4 equal sides and 4 right angles. The students need to recognise that a square is not always
but may be
How many squares can you find that have dots from this array as their corners?
- Introduce the problem as a "treasure hunt". How many squares can be made on this board (or grid)? Let the search begin!
- Ask the students, in pairs, to make a square on the geoboard with a rubberband (or draw one on the dot paper). It can be any size and in any location.
- Share the squares found by the class. Notice whether the squares displayed are different by size, location or both.
- Pose the problem: How many squares do you think that you can find?
- As the students work ask:
How do you know when something is a square?
What did you find out during this activity?
Are you organising your search for the squares? How?
- Share answers. If there are different answers look at why this is so. Get the students to share the ways that they organised their search.
Squares in a 5x5 geoboard or copymaster 5 x 5 dot paper
Other contexts for the problem
Solution to extension
|Size of square||Number|
|tilted (one dot enclosed)||4|
|tilted (4 dots enclosed)||2|
Some students may notice that there is a pattern in the number of the non-tilted squares (1, 22, 32)