Anchoring Numbers

Think about this. As quickly as you can, tell the answer to 8 + 5 = ?
What about 13 x 5 = ?

I don't know about you, but I come from a math era that made these kinds of problems...errmm...difficult. At least, I had to always visualize carrying the one, or count on with my fingers....or just TRY to think but I couldn't.  And I was embarrassed!  That is, until I started teaching it and found out about all these different strategies to help students become mental math thinkers.  Anchoring to ten is one of these concepts. 
If we look back at 8 + 5, what if...
                           we made the 8 a 10
                           Now to keep it equal, that is 2 more from 8, so i'll take 2 away from the 5
                           That leaves 3 more to add 
                           Now my problem is 10 + 3 =
                           How much simpler, quicker, and easier is that???

How about 13 x 5....
                           break the 13 into 10 and 3
                           we'll have 10 x 5  and 3 x 5
                           that makes 50 and 15
                           I'll have to add those together (remember that multiplying is really just faster addition)
                           I'll break the 15 into 10 and 5
                           Now I have 50 + 10 + 5
                           Think you can do that without paper??? 

If that brought you a whole new lens on math, I know. I had no idea how easy it could be mentally. My husband and dad are these kinds of thinkers. My mom also taught me how to find the sale of an item by finding ten percent...then if it is 40% off, add it together four times. I realized a few years ago that I can be that kind of mental math solver too! That is the point of the Common Core of the USA (in my humble opinion) and even if you think not, the teachers are trying to get kids to think more mathematically, to break it into easier chunks. 

One more example of anchoring to easy numbers. Think about our dollar bills. They come in 1, 2 (ha!), 5, 10, 20, 50, 100, 500....do you see a pattern here?!? These numbers are easy to count in big groups. Even clocks go by 5s with the minute hand. The world around us is filled with numbers grouped a certain way. You won't usually come across something that's grouped by 7s. 

This is why it is essential that we help our children understand the quantity/concept/set of five and ten. This is where the ten frame comes in. It is just a mathematical tool that we use a lot in elementary. 

 Notice there are two rows, 5 on top and 5 on the bottom. So while working with a ten frame, you are also anchoring the concept of 5. Double win!

There are a lot of activities and games you can play with the ten frame.  Fill in the ten frame with circle markers. You can start by filling up the top row, then move to the bottom row. Once they are getting the idea of the quantity, you can fill up the frame any way you want and start noticing different dot patterns that can appear with a particular number. You can also talk about how many boxes are empty to help with understanding of making a ten, how many left, as well as greater than and less than number concepts. 

I made a simple- and I mean simple- game last year for my firsties. They LOVED it, the entire year long! I jazzed it up a bit and placed it in my store. You can grab it here! 

Here is a great website for online ten frame play. Kids love it because they can manipulate it however they want, AND it talks to them. Another win! Click here. 

TTYL ;)