WEBVTT
00:00:03.060 --> 00:00:05.210
Adding in Any Order
00:00:06.550 --> 00:00:12.470
In this video, we going to learn how to find sums up to 20 by adding in any order.
00:00:13.660 --> 00:00:15.940
Here are two ten frames.
00:00:16.780 --> 00:00:25.460
These two robots have been programmed to paint the ten frames, five blobs of orange and nine blobs of pink.
00:00:26.340 --> 00:00:28.680
Let’s start with the orange robot first.
00:00:29.560 --> 00:00:36.060
One, two, three, four, five.
00:00:36.810 --> 00:00:39.310
Now, we need to add nine more.
00:00:39.870 --> 00:00:42.730
We know that a row of a ten frame is worth five.
00:00:43.650 --> 00:00:45.650
So we can count the blobs from five.
00:00:46.640 --> 00:00:52.230
Six, seven, eight, nine.
00:00:53.220 --> 00:00:56.430
We found the sum of two numbers here.
00:00:56.940 --> 00:00:59.120
Remember, sum means total.
00:00:59.300 --> 00:01:01.450
It’s what we get when we add two numbers together.
00:01:02.280 --> 00:01:06.790
We started with five, and then we added on another nine.
00:01:08.040 --> 00:01:09.070
What’s the sum?
00:01:09.760 --> 00:01:13.680
Well, we know that a full ten frame is always worth 10.
00:01:14.380 --> 00:01:16.640
So we can just count on from 10.
00:01:17.480 --> 00:01:24.160
11, 12, 13, 14.
00:01:24.740 --> 00:01:28.260
Five plus nine equals 14.
00:01:29.300 --> 00:01:32.830
But what if we programmed the pink robot to go first?
00:01:33.560 --> 00:01:37.800
We’ll use the same numbers, but we’re going to add them in a different order.
00:01:38.640 --> 00:01:41.450
So we’ll start off with nine pink blobs.
00:01:42.220 --> 00:01:45.870
We can do this quickly because we know it’s one less than a full ten frame.
00:01:46.780 --> 00:01:49.790
And now we just need to paint our five orange blobs.
00:01:50.490 --> 00:01:56.990
One, two, three, four, five.
00:01:57.920 --> 00:02:01.730
The two robots were programmed to paint in a different order this time.
00:02:02.280 --> 00:02:07.450
So the addition that this shows is nine plus five.
00:02:08.370 --> 00:02:12.750
We’re adding the same two numbers together, but they’ve just been swapped around.
00:02:13.750 --> 00:02:15.680
What do you notice about the total?
00:02:16.690 --> 00:02:21.090
Once again, we have a full ten frame and then four more.
00:02:21.760 --> 00:02:24.360
The robots have painted 14 blobs again.
00:02:25.290 --> 00:02:28.290
Both additions give the same answer.
00:02:28.600 --> 00:02:32.860
And these two robots have taught us something very important about adding numbers.
00:02:33.630 --> 00:02:37.620
It doesn’t matter which way around we add numbers together.
00:02:38.530 --> 00:02:43.710
Seven and two is exactly the same as two and seven.
00:02:45.720 --> 00:02:49.090
Five more than 15 makes 20.
00:02:49.790 --> 00:02:57.340
And if we swap the numbers around and find 15 more than five, we get exactly the same answer.
00:02:58.260 --> 00:03:08.010
Whether we find the answer to five plus 13 or 13 plus five, the total of a sum will stay the same.
00:03:08.760 --> 00:03:12.680
Let’s have a go at answering some questions now where we have to put into practice what we’ve learned.
00:03:13.220 --> 00:03:18.150
And remember what we’ve learned, it doesn’t matter which way around we add numbers together.
00:03:20.900 --> 00:03:23.230
Do these sums have the same answer?
00:03:24.320 --> 00:03:27.900
Under the question, we can see two lines of cubes.
00:03:28.680 --> 00:03:32.480
And they both represent different additions or sums.
00:03:33.490 --> 00:03:36.560
When we find the sum of something, we find the total.
00:03:37.310 --> 00:03:43.260
And in our first addition, we’re finding the sum or the total of 10 and seven.
00:03:44.090 --> 00:03:50.730
We know this because there are 10 yellow cubes, and then another seven blue cubes are added onto it.
00:03:51.550 --> 00:03:53.500
Let’s have a look at our second addition.
00:03:54.240 --> 00:03:57.380
What’s the same and what’s different?
00:03:57.980 --> 00:04:03.660
Well, what’s the same is that the addition contains the numbers 10 and seven again.
00:04:04.320 --> 00:04:07.580
Only this time they’re added together in a different order.
00:04:08.050 --> 00:04:11.660
This time, we start with seven and we add 10 more.
00:04:12.670 --> 00:04:19.300
So our question is asking us, is 10 plus seven the same as seven plus 10?
00:04:20.530 --> 00:04:25.140
Can you think of a way to answer this question without doing any adding.
00:04:26.020 --> 00:04:33.260
We could just look at the picture and say to ourselves that the two lines of cubes are exactly the same length.
00:04:33.800 --> 00:04:41.450
So it looks like the total of the cubes whether we add 10 and then seven or seven and then 10 is the same.
00:04:42.110 --> 00:04:46.270
But as well as looking at the picture, it’s probably a good idea to work out the answer.
00:04:46.950 --> 00:04:50.390
To begin with, let’s count on seven more than 10.
00:04:50.920 --> 00:05:00.720
10, 11, 12, 13, 14, 15, 16, 17.
00:05:01.410 --> 00:05:04.470
The sum of 10 and seven is 17.
00:05:04.830 --> 00:05:08.030
Now, let’s start with seven and count on another 10.
00:05:08.480 --> 00:05:20.160
Seven, eight, nine, 10, 11, 12, 13, 14, 15, 16, 17.
00:05:20.610 --> 00:05:24.510
Just like we thought, both sums have the same answer.
00:05:24.890 --> 00:05:28.360
It doesn’t matter which way around we add two numbers together.
00:05:28.710 --> 00:05:30.730
They’ll always give the same total.
00:05:31.200 --> 00:05:35.840
Do the sums 10 plus seven and seven plus 10 have the same answer?
00:05:36.180 --> 00:05:37.240
Yes, they do.
00:05:41.640 --> 00:05:45.550
On Monday, Isabella got two stickers for her reward chart.
00:05:45.770 --> 00:05:48.380
And on Tuesday, she got three stickers.
00:05:49.020 --> 00:05:53.210
On Monday, Mason got three stickers for his reward chart.
00:05:53.480 --> 00:05:56.300
And on Tuesday, he added two more.
00:05:57.010 --> 00:05:58.750
Who has more stickers?
00:05:59.340 --> 00:06:05.000
This question is about two reward charts for two different children, Isabella and Mason.
00:06:05.660 --> 00:06:08.270
Let’s look at Isabella’s reward chart first.
00:06:08.590 --> 00:06:12.210
We’re told that on Monday, she got two stickers for her chart.
00:06:12.510 --> 00:06:17.530
And if we look at the row for Monday on Isabella’s chart, we can see those two stickers that she got.
00:06:17.890 --> 00:06:21.330
We’re then told that on Tuesday, she got three stickers.
00:06:21.600 --> 00:06:24.810
And again, we can look on her chart and we can see those three stickers.
00:06:25.310 --> 00:06:29.980
Now, the question that we’re asked at the very end of this is, who has more stickers?
00:06:30.420 --> 00:06:34.290
So let’s think about how we might find the total of Isabella’s stickers.
00:06:34.530 --> 00:06:38.900
She started off with two on Monday and then was given another three.
00:06:39.290 --> 00:06:42.700
So we’re going to need to find the answer to two plus three.
00:06:43.140 --> 00:06:46.810
But before we do that, let’s have a look at Mason’s reward chart.
00:06:47.210 --> 00:06:50.230
On Monday, he got three stickers for his chart.
00:06:50.730 --> 00:06:53.920
And then we’re told that on Tuesday, he added two more.
00:06:54.350 --> 00:06:59.040
So which two numbers are we going to need to add together to find the total of Mason’s stickers?
00:06:59.400 --> 00:07:02.670
He starts off with three and then adds two more.
00:07:03.210 --> 00:07:05.880
Can you see something interesting about these two additions?
00:07:06.210 --> 00:07:08.780
They both contain the same numbers.
00:07:09.410 --> 00:07:14.830
They’re just added in a different order, two plus three and then three plus two.
00:07:15.550 --> 00:07:19.940
Now, what do we know about numbers if they’re added in a different order?
00:07:20.880 --> 00:07:22.350
Well, they give the same total.
00:07:22.680 --> 00:07:25.220
It doesn’t matter which order we add two numbers.
00:07:25.860 --> 00:07:28.870
Two plus three is the same as three plus two.
00:07:29.640 --> 00:07:43.530
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.
00:07:44.360 --> 00:07:46.840
They both have five stickers.
00:07:47.560 --> 00:07:49.520
And so who has more stickers?
00:07:50.030 --> 00:07:52.070
They have the same number.
00:07:55.440 --> 00:07:56.730
Find the missing number.
00:07:57.580 --> 00:08:01.900
Nine plus seven equals what plus nine.
00:08:02.900 --> 00:08:07.100
You know we can find the answer to this question without doing any adding at all.
00:08:07.990 --> 00:08:13.020
But to do this, we need to look very carefully at what the question tells us.
00:08:13.790 --> 00:08:17.520
We’re given two additions here with an equal sign in between.
00:08:17.550 --> 00:08:19.470
This shows that they’re worth the same.
00:08:20.450 --> 00:08:25.480
Nine plus seven is the same as something add nine.
00:08:26.530 --> 00:08:31.780
Now, if we look at these two additions, we can see something very similar.
00:08:32.550 --> 00:08:35.060
They both contain the number nine.
00:08:35.980 --> 00:08:40.920
Now, in the first addition, the number that’s added to nine is seven.
00:08:41.910 --> 00:08:45.110
In the second addition, nine is added on to a number.
00:08:45.300 --> 00:08:46.790
But we don’t know what that number is.
00:08:47.370 --> 00:08:57.390
And so nine and seven make exactly the same number as nine and seven.
00:08:57.630 --> 00:09:00.240
This is the only answer that makes sense.
00:09:00.930 --> 00:09:02.400
The additions are the same.
00:09:02.720 --> 00:09:05.060
It’s just the numbers have been swapped around.
00:09:05.250 --> 00:09:10.940
And we know that if we add two numbers in a different order, they make the same total.
00:09:11.750 --> 00:09:15.010
If you have time, try working out the answer in the two different ways.
00:09:15.440 --> 00:09:18.430
But we don’t need to actually do this to answer the question.
00:09:19.130 --> 00:09:24.170
Nine plus seven gives exactly the same answer as seven plus nine.
00:09:24.760 --> 00:09:26.830
The missing number is seven.
00:09:29.960 --> 00:09:31.590
What have we learned in this video?
00:09:32.610 --> 00:09:38.380
We’ve learned how to find sums up to 20 by adding two numbers in any order.
00:09:39.170 --> 00:09:42.290
And we’ve also learned a really important fact.
00:09:43.000 --> 00:09:48.350
We can add in any order, and it makes no difference.
00:09:48.520 --> 00:09:51.150
The total will be the same.