Math Problem Solving

During math we are beginning to work on complements of 10 and other numbers. Complements of 10 would include 1 and 9, 2 and 8, 3 and 7, 6 and 4, 5 and 5. We work on learning/remembering these in many different ways. One day last week we worked on finding complements of or ways to make 8. We used dot cards that had 2, 3, 4 or 5 dots on them to help us. We spread out all over the room to work. This activity was something that all of us were comfortable working on and the room became very quiet as we worked. As some students needed more challenge, Ms. Wendy and I would either challenge them to find more ways to make 8 (if this was true for them and they like to "complete" problems) or we would give them another number to work on. After working on this for a while, we came back together as a whole group to debrief our solutions, how we found them and what we noticed about the numbers as we worked.

Some students showed their thinking by drawing the dot cards that they put together to make 8 while others wrote out equations to show their thinking: 5+3=8, 4+4=8. As they worked all of the students began to realize that you could use more than 2 numbers to make 8: 4+2+2=8 and some even used 4 numbers: 2+2+2+2=8. This is an example of a low floor/high ceiling activity. Low floor/high ceiling means that all children can do the activity at a basic level and some will continue to take the activity to higher levels of thought.

In math, it is important to me that we have whole group lessons and activities that we can all work on although at different levels. I want us to have common experiences, language and background in math content. After we work on a whole group lesson or activity, we will often but not always break up into small groups based on abilities to work on concepts that we need more help on or to try some more challenging math. This way, all of our crew is exposed to new math concepts and deep discussions and also given remediation or enrichment if needed. I believe that all children can learn math at high levels if given open ended activities and time to play with and discuss math concepts.