April 26th - Compare - Difference Unknown

So the three of us decided to go into the 2/3/4 class and observe the following "Quick Think":

Tomorrow is the Floor Hockey tournament and there is going to be 357 boys here and 279 girls.  How many more boys than girls will there be?

Even though the numbers were small here we were looking to see if they could represent the problem in some way.

We stopped the students after 2 minutes and asked for them to describe their representation.  Some students had 357 - 279 written and a few had 357 + 279 written, but again there were not "mathematical graphics" to illustrated what it might look like.
A quick congress to talk about what a 'math graphic' could look like elicited some of the following:

So we decided to pull the grade 1 students and lower the numbers a bit to see what they would come up with.  We changed the numbers to be 37 boys and 19 girls; and allowed them a minute...and...they actually solved it each demonstrating a 'counting on' strategy on a number line, however, when we changed the numbers to be ones to big to count on from the students response was that they couldn't do it with those numbers.....

Still a Lingering Question??

I'm still struggling with what to do with the kids who can go right to a correct number sentence but can't create a 'thumbnail sketch' to prove it would work?....I'm hoping that by having them articulate where the numbers came from and then modeling what that might look like in a 'sketch' will help them to realize that it doesn't have to be this great picture but just something that would work to help them explain to others where the numbers came from.

JK/SK/Grade 1 Problem

Used with JK/SK's

Used with some SK's and Grade 1's

Grade 2 - 4 Problem

Carpentar Problem charts

Children's "Mathematical Graphics"

If you get a chance, read the site linked to below,
Children's Mathematical Graphics
I like the way it refers to their thinking as 'mathematical graphics'.  The section on 'mathematical disconnects' was also interesting and I can see how by introducing these symbols can lead to them writing them but not understanding what they mean.