Understanding Fractions - Group 7

Today I asked Group 7 (Yr 5/6) to show me fractions in more than one way (multiple representations). This group of students are lacking understanding of the key idea that fractions is about parts of a whole. They are learning that the whole could be five, the whole could be 100, the whole could be a set of objects (discrete), just repeated numbers added together, or even a shape (continuous) but they can all show the same fractional number related to the whole.

In the photos below I asked the students to show me four quarters, this is only the beginning of these lessons so as they progress we will use other materials as well so that they get experience of fractions in many forms.

• The multi-link cubes stuck together are fractions of a shape 
• the groups are fractions in sets 
• The numbers represent equal sharing creating a whole using numbers

Group 7 Problem Solving

Today my group (7) began working on a problem solving task (about workers packing cherries into boxes and cartons) near the end of their session. This group is very enthusiastic about mathematics so we have a lot of cooks in the kitchen as the saying goes. I'm sharing this video to show what is working well and what needs improvement with this group dynamic. 

As you'll see the girls take over quite a bit so we are working on listening to each other more and taking turns with sharing ideas. Jarome tries to share his thinking - that they can use their basic facts to help work out larger numbers when he says, "8 + 4 is 12" in reference to the problem where they are trying to work out 80 + 40, though he is talked over. It also shows how important it is for us as teachers to listen to what our students are muttering or saying within a group especially the quiet ones, as they usually know more than they let on. 

They are very engaged in this task. However, as we continue the task in the next session I will need to go over the expectations of working in a group and also the importance of reading the problem. They have come a long way with their communication in mathematics and they will surely continue to improve :-)