The links below will take you to some handouts that you can use for more practice with your student!!
Today’s lesson is on NUMBER BONDS … and we will be addressing the two most important questions. What is it? … and Why do we use it?
Before we can get into WHAT a number bond is … we need to define the word decomposition. To decompose a number literally means to “take apart”, or “break down”, a number into parts or pieces.
You may be asking, “Why is this so important?” Well, down the road we will be using really, really big numbers … where being able to break down, or decompose, those numbers will allow us to work with smaller, easier numbers that we are familiar with.
So, for today, let’s start with learning how to decompose smaller numbers. Let’s take the number 5 as an example. If we wanted to show the number visually, we could draw 5 pictures, 5 shapes, or even 5 dots. I am going to use 5 dots. (Pause 2, 3, 4, 5)
In order to decompose the number 5, we need to find two numbers … inside of our 5 … that will make up the number 5 when put together.
Let’s just draw a line in between two of these dots. Ok … we just broke down the number 5 into two parts, or pieces. On this side, we have 2 dots … and on this side there are 3.
So these 2 dots with these 3 dots altogether make up the original 5 dots … or … we can say that the number 2 and the number 3 make the number 5.
Alright, what about a larger number? Let’s decompose the number 9.
Now remember … to decompose means to take apart or break down. So we will be taking apart the number 9.
So let’s start with a visual representation. (Pause 2, 3, 4, 5, 6, 7, 8, 9)
Here, we have 9 d0ts … and I am going to just draw a line somewhere to break it up into two parts.
How many dots do you see over here? … 1, 2, 3, 4, 5, 6, 7, 8 … So 8 dots.
And how many dots do you see over here? … 1
So … our 9 dots decomposed into 8 dots and 1 dot … or … another we can say this … the number 9 is the number 8 and the number 1.
Great! So how does this apply to Number Bonds?
Well … let’s start with a definition. A number bond is a mental picture, or a model, that shows the relationship between a number and the parts that combine to make that number.
Ok … so adding on to our last example … where we decomposed the number 9 into the numbers 8 and 1 … we will take this decomposition and illustrate it using a number bond.
A number bond consists of 1 large box, representing the total or whole … connected … by branches to other boxes, (pause 1, 2) which represent the parts (pause 1, 2) that make up the total.
Since there are 9 dots altogether … we will write a 9 here.
And because we broke up the 9 into two parts consisting of 8 dots and 1 dot … we will write 8 here … and 1 here.
So we just built a number bond … where we are able to see a number like 9 break down into two other number 8 and 1 … or see that these two numbers can combine to make this one.
Ok … so now the big question … why are number bonds so important? They may seem a bit tedious or like pointless activities for your student … aka “busy-work”. But, I can assure you that they will help your student later on … when they come across more difficult numbers.
These mental pictures are the key to helping your student do mental arithmetic. Although this concept is very simple … right now … it is an extremely important foundation for understanding how numbers work.
Not only, do number bonds allow us to see the relationship between addition and subtraction, and assist in that transition … but they also help us to break down a number like 42, into 40 and 2 … which are much easier to work with than the number 42.
So, if I asked you to multiply 42 by 6 in your head … you could do it the way we were taught … and try to visualize 42 over a 6 … multiply by the 2 first and don’t forget to carry the 1 … and then a couple more steps … but by then … we will already forget the first number that we came up with … for the ones place.
What if I told you that multiplying 42 by 6 is the same as multiplying 40 by 6 … and then multiplying 2 by 6 … and just putting those numbers together … or adding them … so 240 plus 12 is 252. Done! 42 times 6 is 252.
Thanks for watching!
Danielle the tutor