Making equal parts

For this post, we're back to fractions....
The third grade classes are beginning to explore fractions.  To introduce the idea of equal parts (an essential foundation for fractions), we worked on equal parts situations on-line using ST Math.

Students had to figure out which object to choose and then we discussed why our choice was correct.  (If you choose correctly, the penguin is able to walk across the screen.)  After conversation about what made the parts equal, students were given geoboards so they could explore equal parts with a partner.

These girls created parts that were not equal.  They shared with me that the parts were not equal because they did not cover the same area.  To find the area, the girls counted the "squares" between the pegs.  (The third grade classes had just finished a study of area - so this was a great connection!)

These boys created parts that were equal.  They described the parts as being the "same".  The boys in this group are learning English as a second language and this activity gave them a great opportunity to explore examples and nonexamples of equal parts.

After having time to explore with their partner, we came back together as a whole group.  Students were asked to share one of their representations and explain whether the parts were equal or not - and how they knew.  This group described knowing the parts were equal because they divided the square into four equal parts (smaller squares).  Then they divided each square in half.  Such great conversation and thinking from these third grade students!

As a challenge to the class, I left them with three representations on geoboards.  Each geoboard was divided into fourths - one with squares, one with rectangles, and one with triangles.  Students agreed that each of the geoboards was divided into equal parts.  I then asked whether the triangle was equal to the square - or if the rectangle was equal to the square.  Students were intrigued by this idea - intuitively they thought yes but they weren't certain.  I left the problem as an open question and asked them to think about it further.  I can't wait to hear their ideas!