All right, this is fifth-grade module three lesson 14 and the purpose of this lesson is to help you get confused for this kind of work
To solve addition problems and subtraction problems the idea being sometimes we don't have to follow
The official standard algorithm sometimes we can use logic to make the problem simpler
Let's do some examples so that you can see what I'm talking about
So this says rearrange the terms so that you can add or subtract mentally and then of course
Solve the problem so the idea being is we're going to look at this first problem
And we're gonna see if we can add something together mentally to make our life easy
And I can see a couple of examples I can see that one in 3/4 plus 1/4
I'm gonna add those two together, and I get 2
Similarly I could see that 1/2 plus 1/2 is
1
So I can add those together and I get 3 and there's I'm done
I just added that whole problem together mentally without using any standard
Algorithm in this case without using common you're getting common denominators
For all the fractions now for our our math purists. They're probably going to not like the way I did it, so let's let's
Be a little bit more official here
And what we're going to do is we're going to use the commutative property
To move the quarters next to each other and to move the halves next to each other and
Then we're going to use the associative property
To add these together so one in 3/4 plus 1/4. That's equal to 2 and
1/2 plus 1/2 that's equal to 1 and now we have 2 plus 1 and that equals 3 all right?
So that's a little bit more of an official way of doing it up here was a little bit
Informal no. That's all right
Similarly, let's do this one. So this says. We've got three and a sixth. We're going to subtract 3/4, and we're going to add
5/6 so let's use the commutative property
To get the sixths next to each other now
Here's the tricky thing and then we've got the 3/4 left over over there now. Here's the tricky thing
This says start with three six three and a six
This says take away 3/4, so that's over here and this has add
5/6 so a lot of students are gonna want to leave the minus sign and the plus sign stationary and
And then move just the numbers no no no no no no actually what's happening
And I'm gonna zoom in so that we can see this a little bit better
What's happening is?
Here this says we're going to take away 3/4, and this says we're going to add
5/6 so when we move them around you need to make sure that the new problem
Still is adding 5/6 and is still
subtracting
3/4 now that we've done this we can use the associative property right here and
3 and 1/6 plus 5/6 that equals 4
minus 3/4
And now we could do that in our head and that answer is 3 and
1/4
All right, and I'm gonna zoom back out so that we can see everything. We've done so far
There you go
Now let's do the next problem
All right so for this problem, we're adding three numbers that have a sum of 14
But we don't know what this third number is so one way to do it
They kind of the official way, maybe would be to start with 14 and then subtract each of these numbers
But we're gonna see if we can do a little bit of logic and a nice little shortcut
So I'm gonna write this problem out a little bit
Spread out here
There and
let's get our common denominator for just these two fractions and
A common denominator is 12 that we can use we don't have to use 12
But that's a good one so we're gonna change
The sixths into twelfths and we're gonna turn the fourths into twelfths
So the denominator how do you turn the denominator into 12 you do 6 times 2?
Which means the numerator is going to be multiplied by 2, and that gives us 10 and?
Similarly how do you turn the denominator of fourths?
Into a denominator of twelfths you multiply by 3
which means we multiply the numerator by 3, and so we get a
numerator of 3
So now I'm gonna see that
If well let's just add these together so 9 plus 1 is 10
That was this 9 Plus this one is 10 and then 10 12 plus 3 12
gives us 13 12
Plus a blank
equals 14 and
Really 10 and 13 12 set equals 11, and 1 12 plus what equals
14 right now here, I would use our nice little empty number line
And our empty number line is we're gonna start with 11 and 1 12
And we need to figure out what we have to add to it
What we have to add to it to get all the way up to 14 because that's what we're doing right here
Well first thing I'm gonna do is figure out what we can do to bump it up to the next whole number which is 12
Well that means we have to add
11 twelfths so that bumps us up to 12 and then 12
plus 2
gives us 14 so we could see our correct answer or missing value is 2
and 11 12
2 and 11 12 and
Our last problem, I chose this because it's a good opportunity to
Draw a tape diagram to help us understand. What's going on so
It says Laura bought
Eight and three tenths yards of ribbon
she used one and two fifths to tie a package and
two and a third to make a bow
and Joe later
gave her five and 3/5 yards
So how much does she have so actually I'm probably not going to draw
Well no no I think I might draw a number line on this one I think a number line might be pretty
So we might start here with eight and three tenths
Because that's what she started with and then she used one in two fifths so that means we're gonna go backwards
one in two fifths and
then she used two and a third so we're gonna go backwards two and a third and
then
Joe gave her four and three fifths so that means
It's gonna go forward
four and three
Fifths so that's going to help me understand all of this
Is going to help me?
Efficiently write the equation which is eight or the expression eight and three tenths?
subtract 1 and 2/5
subtract 2 and 1/3 and
add
4 and
3/5 right so there we go
so I
Think what I would do is I would say well, let's add our
Let's add well, let's use the commutative property
Because I want to put this guy
Next to this guy all right, so I'm gonna write eight and three tenths
plus
four and three-fifths
Let's do minus 1 and 2/5, and then minus 2 and 1/3
So I'm gonna scroll up a little bit, so there's our
Expression and now let's solve it now first thing I see is
Well, let's do
Let's subtract here, so
We have
We're gonna add in 4 and 3/5, but we're also gonna subtract out one in 2/5, so let's just
Use the associative property
c:
Right here and do that
practically in our head so 4 minus 1 is 3
3 fifths minus 2/5 is
1/5
So now we have 8 and 3 tenths
plus
3 and 1/5 minus 2 and 1/3
All right, so now
Let's get our common denominator in this case it's gonna be oh
Well if we wanted to we can get a big common denominator for all 3 of these numbers
our common denominator could be 30
Let's do that in fact
so our common denominator
Is gonna be 30 now teachers?
And parents you may have to pause the video and help the students. See why the common denominator is 30
So to turn the denominator of 10 into a denominator of 30, we're gonna multiply by 3
Which means we're going to multiply our numerator by 3, which is not
To turn our denominator of 5 into a denominator of 6. We're gonna multiply by 6
Which means we multiply our numerator by 6 and?
to turn our denominator of 3 into a denominator of 30
We're gonna multiply by 10, which means we're gonna multiply our numerator by 10
And now we are free to get going on this so I'm gonna scroll down
even further
So let's see we're gonna do and we could do this all in one step. We could do 8 plus 3 is 11
Minus 2 gives us 9
And then let's do the fractions
9 xxx
plus 6 xxx is 15 thirtieths and
then 15 thirtieths minus 10 thirtieths
gives us
5 xxx
So technically our answer is 9 and 5 xxx, but
We want students to be able to see that that could be simplified because both the numerator and the denominator
Can be divided by 5 so our
Fraction could be written as 9 and 1/6
But really either of these would have been correct
Woah, that was a big problem. I don't know if our strategy made that much simpler that was just a big old problem
And
that's
grade 5 module 3 lesson 14 the idea being
Occasionally we can use strategy to make the problem simpler