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.

## Number lines and place value thinking

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.

Students seem to need a lot of coaching on the idea of making “jumps” of equal distance on a number line…that if your number line goes from 300 to 500, you can make “jumps” of 100 to find 200 and 400 and 600…and then can split those jumps in half to make 50’s and so on. It takes practice and LOTS of math talk and sharing!

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. |

## Justify thinking and critique the reasoning of others with number lines

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. It is so important to find ways for students to share their thinking and math talk. Sharing in partners. Having partners with different answers talk to each other and try to “prove” their thinking–and edit and revise when needed. Sharing under a document camera. Using “misconceptions” and errors to ask students to try to use their brains differently to explain how the number line could be fixed to be more accurate. All of these are great ways to get students thinking deeply!

Many teachers asked me for more help with number lines, so I have added a series of number line resources to my store to help you…each is low ink and has LOTS of number line options for you to use! The image below will take you to the “original” set that works with numbers to 1,000 and a similar set that goes to 1,000,000. NOTE: If students have very little experience with this kind of deep thinking, I highly recommend starting “low” before working with numbers so large that they are hard to visualize.

I also bundled these two with my fraction and decimal number lines if you are interested in all three at a reduced rate.