As I do every year, I start off with really trying to wrap my head around where my students are with their understanding of "number". We start by talking about composing and decomposing small numbers, we make sure we understand the concept of "equal", and a number of other foundation concepts that are critical for later learning.
Not much later, I dig into my number line studies with numbers up to 1,000--and am always shocked at how difficult some of this work is for my students. I put them in situations where they have to work with all sorts of number lines...lines that start with 0...lines that don't. Lines that ask them to place a number in the right spot. Lines where I show them a point and ask THEM to name the number. I'm always amazed that many of them struggle knowing the concept of "half"...so if the number line starts at 0 and has a 300 on it, many have a hard time knowing that the halfway point between 0 and 300 is 150. It is not easy going, but we work hard to develop these concepts.
So, months later, it's time to revisit number lines with larger numbers. We have had a few GREAT days of exploration, discussion, and debate! Check out a few pics below.
|We continue to work hard on explaining our thinking-both verbally and in writing. We are trying to show our thinking on diagrams and then translate that into sentences that others would understand.|
|Sometimes I need to do some coaching..."What do you know about the halfway point on this number line?" That's all it took to get her started.|
|I threw a few of our problems under the document camera and we worked hard to use "precise math language".|
|We even looked at a few different problems and tried to find how they were similar and how they were different.|
We are going to do a few more days of work with some tougher numbers--and a few tougher situations (like where the number line doesn't start at 0...my FAVORITES!), but I already see so much improvement in their ability to "justify" (word of the week) their ideas and improve their accuracy.
Interested in seeing more? Here are the two resources I use. The maroon one uses bigger numbers (up to 1,000,000) and the purple one uses numbers up to 1,000.