Adding in Any Order
In this video, we going to learn
how to find sums up to 20 by adding in any order. Here are two ten frames. These two robots have been
programmed to paint the ten frames, five blobs of orange and nine blobs of pink. Let’s start with the orange robot
first. One, two, three, four, five. Now, we need to add nine more. We know that a row of a ten frame
is worth five. So we can count the blobs from
five. Six, seven, eight, nine. We found the sum of two numbers
Remember, sum means total. It’s what we get when we add two
numbers together. We started with five, and then we
added on another nine. What’s the sum? Well, we know that a full ten frame
is always worth 10. So we can just count on from
10. 11, 12, 13, 14. Five plus nine equals 14.
But what if we programmed the pink
robot to go first? We’ll use the same numbers, but
we’re going to add them in a different order. So we’ll start off with nine pink
blobs. We can do this quickly because we
know it’s one less than a full ten frame. And now we just need to paint our
five orange blobs. One, two, three, four, five.
The two robots were programmed to
paint in a different order this time. So the addition that this shows is
nine plus five. We’re adding the same two numbers
together, but they’ve just been swapped around. What do you notice about the
Once again, we have a full ten
frame and then four more. The robots have painted 14 blobs
again. Both additions give the same
answer. And these two robots have taught us
something very important about adding numbers. It doesn’t matter which way around
we add numbers together. Seven and two is exactly the same
as two and seven. Five more than 15 makes 20. And if we swap the numbers around
and find 15 more than five, we get exactly the same answer. Whether we find the answer to five
plus 13 or 13 plus five, the total of a sum will stay the same.
Let’s have a go at answering some
questions now where we have to put into practice what we’ve learned. And remember what we’ve learned, it
doesn’t matter which way around we add numbers together.
Do these sums have the same
Under the question, we can see two
lines of cubes. And they both represent different
additions or sums. When we find the sum of something,
we find the total. And in our first addition, we’re
finding the sum or the total of 10 and seven. We know this because there are 10
yellow cubes, and then another seven blue cubes are added onto it.
Let’s have a look at our second
addition. What’s the same and what’s
different? Well, what’s the same is that the
addition contains the numbers 10 and seven again. Only this time they’re added
together in a different order. This time, we start with seven and
we add 10 more. So our question is asking us, is 10
plus seven the same as seven plus 10?
Can you think of a way to answer
this question without doing any adding. We could just look at the picture
and say to ourselves that the two lines of cubes are exactly the same length. So it looks like the total of the
cubes whether we add 10 and then seven or seven and then 10 is the same. But as well as looking at the
picture, it’s probably a good idea to work out the answer.
To begin with, let’s count on seven
more than 10. 10, 11, 12, 13, 14, 15, 16, 17. The sum of 10 and seven is 17. Now, let’s start with seven and
count on another 10. Seven, eight, nine, 10, 11, 12, 13,
14, 15, 16, 17. Just like we thought, both sums
have the same answer. It doesn’t matter which way around
we add two numbers together. They’ll always give the same
total. Do the sums 10 plus seven and seven
plus 10 have the same answer? Yes, they do.
On Monday, Isabella got two
stickers for her reward chart. And on Tuesday, she got three
stickers. On Monday, Mason got three stickers
for his reward chart. And on Tuesday, he added two
more. Who has more stickers?
This question is about two reward
charts for two different children, Isabella and Mason. Let’s look at Isabella’s reward
chart first. We’re told that on Monday, she got
two stickers for her chart. And if we look at the row for
Monday on Isabella’s chart, we can see those two stickers that she got. We’re then told that on Tuesday,
she got three stickers. And again, we can look on her chart
and we can see those three stickers.
Now, the question that we’re asked
at the very end of this is, who has more stickers? So let’s think about how we might
find the total of Isabella’s stickers. She started off with two on Monday
and then was given another three. So we’re going to need to find the
answer to two plus three. But before we do that, let’s have a
look at Mason’s reward chart. On Monday, he got three stickers
for his chart. And then we’re told that on
Tuesday, he added two more. So which two numbers are we going
to need to add together to find the total of Mason’s stickers?
He starts off with three and then
adds two more. Can you see something interesting
about these two additions? They both contain the same
numbers. They’re just added in a different
order, two plus three and then three plus two. Now, what do we know about numbers
if they’re added in a different order?
Well, they give the same total. It doesn’t matter which order we
add two numbers. Two plus three is the same as three
plus two. So if Isabella starts with two and
then counts on three, four, five, this is exactly the same as if Mason starts with
three and counts on another four, five. They both have five stickers. And so who has more stickers? They have the same number.
Find the missing number. Nine plus seven equals what plus
You know we can find the answer to
this question without doing any adding at all. But to do this, we need to look
very carefully at what the question tells us. We’re given two additions here with
an equal sign in between. This shows that they’re worth the
same. Nine plus seven is the same as
something add nine. Now, if we look at these two
additions, we can see something very similar. They both contain the number
nine. Now, in the first addition, the
number that’s added to nine is seven. In the second addition, nine is
added on to a number. But we don’t know what that number
is. And so nine and seven make exactly
the same number as nine and seven. This is the only answer that makes
sense. The additions are the same. It’s just the numbers have been
swapped around. And we know that if we add two
numbers in a different order, they make the same total.
If you have time, try working out
the answer in the two different ways. But we don’t need to actually do
this to answer the question. Nine plus seven gives exactly the
same answer as seven plus nine. The missing number is seven.
What have we learned in this
video? We’ve learned how to find sums up
to 20 by adding two numbers in any order. And we’ve also learned a really
important fact. We can add in any order, and it
makes no difference. The total will be the same.