Vertical Number Lines
My school district has adopted a new math series, called Eureka Math, to support our elementary curriculum. I have mentioned this in passing a few times, but I thought now would be as good a time as any to write more specifically about what this is (and what it is not).
Eureka Math started out a few years ago as EngageNY. It was started with a grant and was a cooperative process intended to align math materials taught in the classroom with the Common Core State Standards. (Illinois has adopted these standards but is also adopting new social studies and science standards, which is why you will sometimes see them referred to as the New Illinois Learning Standards, instead.) A not-for-profit organisation, Great Minds, was formed to take over EngageNY and develop it further, which they did under the name of Eureka Math. It has been built from the ground up by teachers and for teachers.
What Eureka Math is not is a prescriptive curriculum intended to force teachers to read a script with the vain hope that students will respond exactly as expected. There are sample dialogues included in each lesson to give an idea of how a class discussion might go, but anyone who has spent 30 seconds in an elementary classroom knows that students rarely follow the script, especially when they don’t even know it exists!
Even though I have only been teaching with Eureka Math for a couple of weeks, and even though we just finished Lesson 8 today, I am already very impressed with what I have seen. The first few lessons were very challenging, as students were asked to do more with and think more deeply about numbers than they were used to. One of the most common words to describe the “new” math standards is rigour, and boy howdy is this rigourous math! (I put “new” in quotation marks because, honestly, the math hasn’t changed; what has changed is how we think about it and how we expect students to think about it.) Coming off of a textbook series that had third grade, fourth grade, fifth grade, and sometimes even sixth grade work all wrapped into one, it is relieving to have a set of materials that is focused on just fourth grade standards!
One challenge is that Eureka Math is designed to be cumulative. Students build on their knowledge from year to year. Of course, this is the first year for any of us in our building (except for those students’ whose teachers field tested parts of Eureka Math last year), so my fourth graders are coming into it with no prior experience. That just means that I have to pre-teach some concepts and spend more time explaining ideas, words, phrases, and tools that, in four or five years, will be completely familiar to them.
Which finally brings me to the actual topic of this post. (Hey, only four hundred words or so to get to it!) One of the tools we have been using for rounding multi-digit whole numbers is called a vertical number line. It is exactly what it sounds like: a number line that is oriented top to bottom instead of left to right. In case you are a person like me who does not visualise things, here is an actual picture:
Because we are using the vertical number line to round, the students first identify the endpoints, then they find the midpoint. For example, if you were to round 4,105 to the nearest thousand, this is what your vertical number line would look like:
The bottom endpoint is 4,000, the top endpoint is 5,000, and the midpoint is 4,500. The students then write the original number (4,105) on the number line. A quick glance shows that, because 4,105 is less than the midpoint (4,500), it is closer to 4,000 than 5,000, therefore 4,105 rounded to the nearest thousand is 4,000.
Simple. Clear. Brilliant.
I am sure that other people have used vertical number lines before, but I had honestly never seen nor heard of them before this. It makes so much sense, though! We talk about rounding up and rounding down. Now students can actually see how to do it.
The challenge for tomorrow is to try to round without using the vertical number line. But, honestly, if my students need to quickly jot down a vertical line with arrows, mark the endpoints and midpoints, and then label the original number in order to determine how to round, I am 100% okay with that! The one thing I have always emphasised in my classroom when it comes to math is this: if the tool you are using allows you to quickly and accurately find the answer, then it is an efficient tool for you to use!