I just hosted my sixth fabulous Family Math Night event of the school year and with it came another new What Do You Notice? poster. Here are the deets:
Title: Fractions on the Geoboard
K-2: shapes, counting, area
3-5: congruency, area, fractions, equivalent fractions
Background Information: This is similar to the Squares and More Squares poster. Like that one, this was designed around fractions but at a higher level. The dots for each square represent the dots on a regular geoboard. Each square is made up of 5 by 5 dots. If lines were drawn connecting each of the dots, the larger square would show 16 small squares (4 x 4 small squares). Each of these small squares represents one square unit.
I divided each of the large squares into fourths. The third and fifth squares on the poster are the easiest representations of fourths. It is also easy to see equivalent fractions such as ½ = 2/4.
Upper elementary students can figure out the area of the sections by counting the square units. Just like in the Squares and More Squares poster, I deliberately made different shapes with the same area because sometime students will think that because the shape is different, the area must be different, as well.
Some students may notice congruency. For example, in the first square, two of the sections are identical (congruent) even though the orientations are different.
Here’s what it looked like at the event: