Combinations, Day 2

Using the new adaptation of the Start At/Stop At routine, that was introduced three days ago, have the students play a few rounds of the activity.  Continue to play as time allows.

The focus of this conversation is on looking at the relationship of combination of numbers up to 9 and how to prove that they found all of the possible combinations.  

I start by calling all of the kids back to the carpet and ask them to sit in a circle.  I want this to be more of a class "discussion" and I want them to be able to see each other as they are speaking.  I will also have an easel and poster available to record combinations on (later in the discussion).

"I want to know what are different strategies that you used to create combinations of 9.  Who would like to tell us who they did it?"

Examples of strategies might look like:

• Use one tower of 10, break off 1 and record the combination.  Then do the same with 2, 3, 4, …).  
• Use cubes to make a tower for each combination and leave them together
• Use mental math to make an organized list with pencil and paper.
• Flip facts with any of the strategies.  In other words I found 8 rocks and 1 ball, so I could do 1 rock and 8 balls.

Once all of the strategies have been exhausted, model one of the strategies with cubes.  Then create a list of combinations to 9 using the cube combinations you just built.

I will end the discussion with the following:

"Do you believe we have found all of the combinations of rocks and balls?"  You want to make sure they look at the cube models to help them with their thinking.  

*Note: At this point, you will have a variety of beliefs about this.  Some will think that you could keep looking and eventually find more.  Others will know that you have but won't be able to explain it, and a few will be able to defend why they think all of the combinations have been found.