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Hello, my name's Mr. Peters, and welcome to today's lesson where we are gonna be thinking about how we can use our understanding of place value to calculate with decimal numbers up to and bridging 1/10.
Hopefully by now, we're really confident with using our understanding of a bridging strategy, as well as what we mean by decimal numbers.
And today, we're gonna be thinking about how this links from what we already know to what we can do with decimal numbers as well.
If you're ready, let's get started.
So by the end of today's lesson, you should hopefully be able to say that you can use knowledge of place value to calculate with decimal numbers up to and bridging 1/10.
In this lesson today, we've got two key words that we're gonna be referring to.
I'll have a go at saying them first, and then you can repeat them afterwards.
Ready? Number facts.
Bridging.
Simple calculations using two numbers are known as number facts.
For example, two plus four is equal to six.
And bridging is a mental strategy that we should be familiar with already, and it uses addition or subtraction to cross a number boundary.
Today, the number boundary we're gonna be thinking about is the tenths boundary.
So in this lesson, we are breaking it down into three cycles.
The first cycle is to use facts to add and subtract within 1/10.
The second cycle is to use facts to calculate complements to 1/10.
And finally, the third fact is to use facts to calculate when bridging 1/10.
If you're ready, let's get started on the first cycle.
Throughout this session today, you're also gonna meet Lucas and Laura.
They're here to share their questions and share their thinking, and to help us with our learning along the way.
So to start our learning off today, we're gonna be thinking about how we can use what we already know and apply that to decimal numbers, including hundredths.
Here, we've got a part, part, whole model, and in one of the parts, we've got two, and then the other part, we've got four.
And Lucas is saying that, "I know that two ones plus four ones is equal to six ones." Laura is saying, "Well, how will I use this "to help me with my understanding "when adding decimal numbers?" Well, let's have a look.
What do you notice this time? That's right, the counters have changed, haven't they? They were red counters with a value of one each, whereas now they are green counters with a value of 1/100 each.
Lucas is saying that, "I know that four plus two is equal to six.
"So 4/100 plus 2/100 is equal to 6/100." We can write this as 0.
02 plus 0.
04 is equal to 0.
06.
Or we could write it as 0.
04 plus 0.
02 is equal to 0.
06.
Laura is then thinking, well, can this be applied to subtraction as well? Well, let's have a look.
Here, we can see we've got a tens frame with some ones in it.
We've got six ones here.
And Lucas is saying that he knows that if he has six ones and he minuses two ones, that he'll be left with four ones.
Now look at what's happened to the counters.
Again, the counters have changed from ones, and they've become 1/100 of the size, haven't they? They've become 100 times smaller and they've turned into hundredths, haven't they? So now, using that understanding, I know that six minus two is equal to four.
We can say 6/100 minus 2/100 is equal to 4/100.
And again, this can be written as an equation.
0.
06 minus 0.
02 is equal to 0.
04.
Okay, check for understanding here.
4/100 plus 3/100 is equal to what? A, B or C.
Take a moment to have a think.
That's right, it's B, isn't it? 4/100 plus 3/100 is equal to 7/100.
Laura's saying that, "As long as we keep the unit the same when we're adding, "we can always use our number bonds within 10 to help us." Here's another check.
Match each expression with a known fact that would help us to solve it.
Take a moment to have a think.
Okay, so the first one, 0.
06 plus 0.
02.
Well, for that one, we could use two plus six is equal to eight, couldn't we? Because it doesn't matter which order the add ends come, does it? We could have six plus two is equal to eight or two plus six is equal to eight, and that will help us.
The second one, 0.
05 minus 0.
03, or we could use five minus three is equal to two to help us with that, couldn't we, yep.
And then finally, 0.
08 minus 0.
07.
Well, we could use seven plus one is equal to eight because we also know that we can convert this into eight minus one is equal to seven, so therefore 8/100 minus 7/100 would be equal to 1/100.
Well done if you got that.
Okay, your first task for today, can you choose a relevant number fact to help fill in the missing numbers on these equations here? Once you've done that, I'd like you to fill in the missing numbers on these equations as well.
You might like to think about drawing a part, whole model to help you represent what's missing, whether it's a part or a whole.
And should you manage that okay, then I'd like you to think about choosing your own number fact within 10 and write as many decimal equations as you can for that number fact.
Good luck with that, and I'll see you back here shortly.
Okay, welcome back.
Here are the answers to the first part there.
5/100 plus 2/100 is equal to 7/100.
So 0.
05 plus 0.
02 is equal to 0.
07.
4/100 plus 5/100 is equal to 9/100.
So again, 0.
04 plus 0.
05 would be equal to 0.
09.
8/100 minus 5/100 would be equal to 3/100.
So 0.
08 minus 0.
05 is equal to 0.
03.
And finally, 7/100 minus 2/100 is equal to 5/100.
0.
07 minus 0.
02 is equal to 0.
05.
For task two, fill in the missing numbers here.
Well, 0.
09 is equal to 0.
04 plus 0.
05.
So the whole was missing there.
Now we've got 0.
09 minus 0.
07.
So we've got a whole minus a part, which would leave us with a remaining part, which would be 0.
02.
The number fact that would help me with that would be nine minus seven is equal to two.
Now we've got 0.
08 minus something is equal to 0.
05.
So, hmm, I've got the whole, and I'm subtracting a part, which I don't know, and I've got the remaining part.
So we could use the fact of eight minus five is equal to three to help us solve that.
So we could say that 0.
08 minus 0.
03 is equal to 0.
05.
And then finally, the last one, 0.
08 is equal to something plus 0.
04.
So again, we're missing a part here.
Hmm, one of the parts is 4/100, and I'd also need another 4/100 with my four plus four is equal to eight, so 4/100 plus 4/100 is equal to 8/100.
Well done if you managed to get all of those.
Okay, onto cycle two of our lesson now, using facts to calculate complements to 1/10.
Before we get started with that, I think it's important that we practise counting up in multiples of 1/100 again.
And we're gonna do that all the way up to 1/10.
Are you ready? 1/100, 2/100 3/100, 4/100, 5/100, 6/100, 7/100, 8/100, 9/100, 10/100 or 1/10.
We know that 10/100 are equal to 1/10.
So we can use our understanding of number facts to 10 to help us add hundredths to make 1/10.
Have a look here.
I've got a tens frame.
And in my tens frame, I've got 7/100.
How many more hundredths do we need to make 1/10? Lucas is saying, "I know that seven plus three is equal to 10.
"So 7/100 plus 3/100 would be equal to 10/100, "which is equal to 1/10." And there we go.
There's the additional 3/100, which makes it 1/10.
Laura is saying, "We can also record this "as 0.
07 plus 0.
03 is equal to 1/10." Let's have a look how that links with our part, whole models then.
I know that seven plus three is equal to 10.
So 7/100 plus 3/100 is equal to 10/100.
And again, that can be written as a decimal number here.
0.
07 plus 0.
03 is equal to 0.
1.
Knowing that we can use on number facts to add hundredths to make 1/10, we can also think about subtracting hundredths from 1/10.
So again, here, I've got 10/100 in my tens frame, which is equivalent to 1/10.
If I were to subtract 4/100, how many hundredths would I be left with? Well, Laura is saying, "I know that 10 minus four is equal to six.
"So 10/100 minus 4/100 would be equal to 6/100.
So there'd be 6/100 remaining, as we can see here.
Again, we can record this as a subtraction equation.
0.
1 or 1/10 minus 0.
04 or 4/100 is equal to 0.
06, 6/100.
Let's look how that links to our part, whole models.
I know that 10 minus four is equal to six.
So 10/100 minus 4/100 is equal to 6/100.
And again, written here as a decimal number, 0.
1 or 10/100, 1/10, minus 0.
04, 4/100 is equal to 0.
06, 6/100.
Okay, time to check our understanding again.
Can you fill in the missing numbers? Eight plus two is equal to 10.
So 0.
08 plus something is equal to 0.
1.
That's right, it's B, isn't it, 0.
02.
0.
08 or 8/100 plus 2/100 is equal to 10/100 or 1/10.
Another check, which known fact can help me to solve 0.
1 minus 0.
03.
That's right, it's C, isn't it? I know that 10 minus three is equal to seven.
So 10/100 minus 3/100 is equal to 7/100.
You may have also used B.
You may have said one or 10/10 minus 3/10 is equal to 7/10.
That could also help us because if we make each one of those numbers 1/10 of the size, we'd also have the equation that we're trying to solve now.
10/100 minus 3/100 would be equal to 7/100.
So you could have used either of those equations.
But the bottom one is a known number fact that we should know off by heart by now.
Okay, onto our second task for today.
What I'd like you to do here is, again, use a relevant number fact to help you solve each one of these calculations.
And then for task two here, I'd like you to look at the numbers given, and I'd like you to think about which two numbers would sum to make 10, which two numbers would sum to make one and which two numbers would sum to make 0.
1.
You can then write a sentence to explain what is the same and what's different about each of these equations.
Good luck, and I'll see you back here again shortly.
Okay, welcome back.
Let's go through these then, shall we? 2/100 plus something is equal to 10/100.
Hmm, well, I know that two plus eight is equal to 10.
So 2/100 plus 8/100 would be equal to 10/100.
10/100 minus 5/100.
Well, I know that 10 minus five is equal to five.
So 10/100 minus 5/100 would be equal to 5/100.
Something plus 7/100 is equal to 10/100.
Well, I know that three plus seven is equal to 10.
So 3/100 plus 7/100 would be equal to 10/100.
Up onto D now.
10/100 minus something is equal to 2/100.
Again, I know that 10 minus eight is equal to two.
So 10/100 minus 8/100 would be equal to 2/100.
10/100 is equal to something plus 9/100.
So that must be, nine plus one is equal to 10, isn't it, so 9/100 plus 1/100 would be equal to 10/100.
And then finally, 1/100 is equal to 10/100 minus something.
Hmm, well, I know that 10 minus nine is equal to one.
So 10/100 minus would be equal to 1/100.
Well done if you got those.
Okay, which two numbers here sum to make 10? That's right, four plus six is equal to 10.
And which two numbers sum to make one? That's right, 4/10 plus 6/10 is equal to 10/10 or one.
And finally, which two numbers sum to make 1/10? That's right, 4/100 plus 6/100 is equal to 10/100 or 0.
1.
Hopefully, you were able to write a sentence to explain what you notice, what was the same, what was different about them? Laura said that, "All the calculations had the same digits in them, "but each number in the equation below "had 1/10 the size in the equation above of it each time." Right, onto the last section for today, then, using facts to calculate when bridging 1/10.
Okay, so we can see here, I've got 6/100 in my tens frame, and I've got an additional 7/100 here.
And Lucas is saying, "I have 6/100, "and this time, "I have seven more hundredths to add this time.
"How many hundredths will I have all together?" Laura is saying that, "I know that six plus seven is equal to 13.
"So 6/100 plus 7/100 will be equal to 13/100." We can now see that we've got 10/100 and 3/100, and we know that 10/100 is equal to 1/10.
So we can write this as 0.
13.
The zero represents zero wholes, the one represents 1/10, and the three represents three additional hundredths.
Or we could say that it represents 13/100 all together.
Again, we can write this as an equation, can't we? 0.
06 plus 0.
07 is equal to 0.
13.
When thinking about subtracting, we could use a bridging strategy if we wanted to as well.
And Jacob is saying, "Why don't we start by bridging 10 first of all, "and then apply that to bridging 1/10." Let's have a look here.
13 minus seven.
To do this, we could partition the seven into three and four.
We can find 13 on our number line, and then we can minus the three first of all, and then we can minus the four.
And that would leave us with six, wouldn't it? So 13 minus seven is equal to six.
Now let's apply that when looking to bridge 1/10.
We've now got 13/100 minus 7/100 is equal to something.
Well, we know that 7/100 can be partitioned into 3/100 and 4/100.
We can find 13/100 on our number line as 0.
13.
Then we can minus the 3/100.
Then we can minus the 4/100.
And that will leave us with the 6/100.
So 0.
13 minus 0.
07 is equal to 0.
06.
Have a look at the number lines now, then.
The first one was when we bridged 10, and the bottom one was when we bridged 1/10.
What do you notice? Jacob's noticed that the numbers on the top number line have become 1/100 the size on the bottom number line, or 100 times smaller.
So you can see how bridging 10 can help us with our understanding of bridging 1/10.
Good spot, Jacob.
Okay, true or false now.
0.
4 plus 0.
07 is equal to 0.
11.
Take a moment to have a think.
That's right, it's false, isn't it? And which justification helps us with this? It's B, isn't it? 4/10 plus 7/100 are equal to 47/100.
Hmm, the place values weren't the same here, were they? If they were the same place values, we'd be able to apply our known facts to help us here, but we can't because they're different place values.
So we need to be careful when adding that we're checking that we're adding the same units here.
Okay, and our next check, choose the equations that help to solve this, 0.
12 minus 0.
04.
Take a moment to have a think.
That's right, there are actually three different answers for this one.
The answer is 0.
08, and Lucas is asking whether we can explain why.
Well, the first one says 12 minus four is equal to eight.
I know that 12 minus four is equal to eight, so 12/100 minus 4/100 is equal to 8/100.
The second one shows 12 minus two minus two is equal to eight.
We know that minus two minus two is the same as saying minus four.
So again, 12/100 minus 4/100 would be equal to 8/100.
And finally, four plus eight is equal to 12.
Hmm, well, we know that if 12 is the whole and four and eight are parts, then if I subtract one of those parts from the whole, that will leave me with the remaining part.
The parts that we knew were 12 and four, so the missing part would be eight.
So 12/100 minus 4/100 would be equal 8/100.
Okay, onto our final task for today, then.
What I'd like you to do is fill in the missing numbers here on these equations.
And then for task two, what I'd like you to do is spot the incorrect equations here, and then you can correct them as well.
Good luck with that, and I'll see you back here shortly.
Okay, let's work through these together then.
7/100 plus 5/100 is equal to 12/100.
So 0.
07 plus 0.
05 is equal to 0.
12.
9/100 plus 4/100 is equal to 13/100.
So 0.
09 plus 0.
04 is equal to 0.
13.
16/100 minus 7/100 is equal to 9/100.
So 0.
16 minus 0.
07 is equal to 0.
09.
And finally, 13/100 minus 9/100 is equal to 4/100.
So 0.
13 minus 0.
09 is equal to 0.
04.
Well done if you got those.
Okay, and what were the incorrect equations that you might have spotted here? Well, the first one's incorrect because 4/100 plus 8/100 would be equal to 12/100, and we write 12/100 as 0.
12.
Okay, the third one, 16/100 minus seven is equal to 9/100.
We're not subtracting the correct place value here, are we? That seven should represent 7/100.
So it should be 16/100 minus 7/100 is equal to 9/100 to make that one correct.
1.
5 minus 0.
9 is equal to 0.
06.
Hmm, well, 1.
5 is one whole and 5/10, and 0.
9 is 9/10.
So actually, there's two ways we could have corrected this.
We could have either made 1.
5 and 0.
9 1/10 the size so it became 0.
15 minus 0.
09 is equal to 0.
06.
Or we could have made the 0.
06 10 times bigger so it became 0.
6.
The next equation was also wrong.
0.
05 plus 0.
9 is equal to 0.
14.
Hmm, what did you spot was wrong with that equation? That's right, the 0.
9 should represent 9/100 instead of 9/10, which would be 0.
09.
And finally, this equation here was also wrong.
0.
9 minus 0.
5, that's 9/10 minus 5/10.
Hmm, it's equal to 14/100.
That doesn't sound right, does it? I know that nine minus five is equal to four.
So 9/10 minus 5/10 would be equal to 4/10, wouldn't it? So it looks like not only are the place values slightly different here, but it's asking us to subtract, and by the looks of it, we've actually tried to add, haven't we? Because we know that nine plus five is 14, which is one of the reasons why maybe somebody thought it could be 14/100.
Well done if you managed to spot those and to correct them for yourself as well.
That's the end of our learning for today.
Hopefully, you're feeling a lot more confident about how you can use your known number facts to help you when calculating within 1/10 and bridging 1/10.
Let's just summarise some of our key points that we've learnt today.
Known number facts can be used when adding and subtracting using hundredths within 1/10.
Known number facts can also be used when adding and subtracting using hundredths to 1/10.
And finally, using known number facts and bridging strategies can help us when we're looking to bridge through or across 1/10.
That's all for today's learning.
Thank you for joining me, and hopefully you found that enjoyable and learnt something new from that as well.
Take care, and I'll see you again soon.
