Professional+Development

=Summer Session June 3, 2008 Notes=

We discussed the number system and how it develops across the K-2 grade span. We discussed how kids should be let in on the development of this system - that it MAKES SENSE, and that knowledge of how the system developed actually helps us to understand it!

In second grade, we venture deeper into the whole numbers, taking children into the base-10 system. So, a good activity to get things going would be to look back at kindergarten, and the types of things we counted. Fish in a fish tank, fingers on a hand, pockets on our clothes, brothers and sisters, etc. Then, in first grade, we looked at some of these numbers we counted to and at the combinations of other quantities that they were made of. For example, 10 is made of 6 and 4, and 7 and 3, and 8 and 2...

"Now, in second grade, we are going to be counting to ENORMOUS numbers! We will need a system to allow us to write those numbers!"

From this day forward, we should not hear discussion about carrying and borrowing in 2nd grade, because the strategies we are guiding our students toward do not use them. The two addition strategies we will focus on:

1. Adding in parts 2. Adding 10s and 1s

The two subtraction strategies we will focus on are:

1. subtracting in parts 2. counting up

Number Lines
The number lines supplied with Investigations are too small! We also have trouble finding a place to put them in the classroom so that everyone can access them easily. Number lines are critical to the strategy of counting up to solve subtraction problems.

Kathy Richardson
We looked at a Kathy Richardson activity, "Build It Fast," pg. 73 of Book 3 - Place Value, Multiplication, and Division that leads students to quickly construct numbers in the base-10 system, and guided them efficiently toward the strategy of "Adding 10s and 1s." We didn't see as quickly how this could lead to subtraction strategies.

A subtraction strategy was shown which built upon students' experience with comparing two trains of cubes to determine which was bigger. But this strategy used base-10 blocks, and many found it to be an interesting strategy. Chris was asked to write it down and get it to everyone. Maybe video tape its use.