Understanding numbers requires some understanding of number relationships. For little people, there are several relationships that can be explored that will lead to a richer understanding of the number system.

Today we will talk about the **“one more/one less”** relationship which can later be extended to the **“two more/two less”** relationship.

The relationship is exactly as it sounds. We want children to easily identity for any given number which number is one more that the original number and which number is one less than the original number. Thus, when considering the number 4, we want a child to know that 5 is one more and 3 is one less.

It is great to make sets of things to explore this. If there is a pile of 5 blocks, ask the child to make a pile that has one more or one less (or fewer). Expect the idea of less/fewer to be trickier at first. From the time children are little “more” is in their vocabulary. We ask them if they want more water. They tell us they want more candy. They have built an understanding of “more”! We do not use “less” and “fewer” as frequently when speaking to them and often it is a less known concept. But as with any vocabulary, as we use words in context, children learn them. It applies here as well.

It is important to have a visual reference for this concept, and I often talk to children about all of the numbers holding hands in a line. In general, a **number line** is a great aid and one I use in a multitude of ways with students exploring math at many levels. This is an early use of such a number line.

You might have magnetic numbers placed in order on your fridge or onto a cookie sheet. You might print out numbers from your computer and tape together a large number line. Or you might want to take the time to cut out a string of paper dolls holding hands and write numbers on them. A ruler is a ready-made number line, but at this level the numbers tend to be too small and thus the ruler is not a good representation to use at this point. We just want the children to begin to recognize the numbers and understand the “beside each other” relationship. The question then becomes, who does 4 “hold hands with” in the line of whole numbers?

This topic certainly ties into the counting exercises we have been talking about in recent posts, for the “one more” number is the next counting number higher and the “one less” number is the next number counted “down” or “backwards”. (Although the backwards idea can be a tricky one. I once asked a young boy to count backwards for me and he promptly turned around, with his back facing me, and counted, “One, two, three, …” Clearly he was counting backwards!)

The extension of this relationship is the “two more, two less” one, which again, is exactly what it sounds like. Thus for the number 4, 6 is two more while 2 is two less. We are looking for the number two away on the number line, not the immediate “hand holder” but the number we find when we skip the hand holder and identify the one on the other side of the hand holder. Obviously the extension is more difficult for young learners, with practice it will come.

I want to point out here that all of the relationships that we will talk about are not just for young learners. In fact,** these relationships extend to all number in different positions of the place value system.**

For example, we want students to know other one more/ one less relationships and be able to think fluidly about them:

- one ten more and one ten less of a number (e.g., 50 is one ten more than 40; 30 is one ten less than 40; 53 is one ten more than 43; 33 is one ten less)
- one 100 more or one 100 less
- one 1000 more or one 1000 less
- one 1/10 more or one 1/10 less (in the case of decimal place values)
- the same with all place value amounts

Of course all of the above can and should be extended to the two more/two less relationships.

We are endeavoring to build a foundation for understanding numbers. What they learn about numbers in an early context is to be built upon as they encounter numbers of greater and smaller magnitutude.

In closing, don’t just talk about the more/less quantities. Build them. Compare them in rows to show the relationship. Make it a game. Keep it fun!

Mathematically yours,

Carollee