All right, this is
Fifth-grade module to lesson four and in this we're going to be using some
Visual strategies to help us understand some mental math here. Yeah
involving
multiplication
All right for example. So we have the problem 37 times 19
And there's a lot of ways that we can think of
37 times 19 1 we can think of it as 37
19's as in 19 Plus 19 plus 19 plus
Forever and ever and ever so we're being told to circle each expression that is not
Equivalent, so this guy he's equivalent, so I'm gonna cross him off
saying well he's he's cool, and
Now this one this next expression here
we have 37
19's all right
And we know that from right here 37 19 s well if we were to take
39 teens and
add it to
719
so if we have 30 times 19 and add
7 times 19 that would be cool because that would give us 37
19 but this guy is no good
that's it's nothing even close in fact I kind of think that 29 might even be a typo like it should be a
19 instead of A 29
So we're gonna definitely circle that second one because it is not equivalent
Going on to the third one
well if we had 37 times 19
So 37 times 19 well this guy is definitely
Equal to 37 times 19 because 20 minus 1 is 19
21 yeah 20 minus 1 is 19, so this guy is
Equivalent, so we're not going to circle him so just so that we don't get all confused on the crossing ah and then the last
one
We know that we want it to be equal to 37 times 19, but this right here is 38
Times 19, so this is also not equivalent
So the two ones that we're going to circle because they're not equivalent is the second one and the fourth one
Now here, we're going to be solving using mental math
But we're going to use a tape diagram to help us understand how to think about this mental math
for example
19 times 50 we're going to think of that as
1950s so that that would be like 50 plus 50 + 50 bla Bla Bla
19 times all right in fact that's what this tape model is right here
This is saying that you've got a bunch of 50s all lined up next to each other and that in fact
We even to make our mental math easy. We think of it as 20
50 s because 20 times 15 is way
easier 20 times 50 is way easier to do in our head then 19 times 50 and
Then so we've got 20 times 50 and then because we have we've multiplied
20 times 50 and really we only need 19. We're gonna have to subtract 1 times 50
We're Gonna Subtract an extra 50
Because we multiplied 20 times 50 instead of 19 times 50 now
We could do the math really easily in our head. This is a thousand and
then 1 times 50 is 50 and
then a thousand minus 50 is
950 all right let's try problem b. So 11 times 26. We can think of this as
11
26 s
Well 11 26 is there's a lot of different ways. We could think of our mental math, but they're kind of
Guiding you towards one way of doing it. Which is we could think of this as 10
26 --is plus one extra 26 and
!@#@!#!#$
13
Which is equal to?
286
Now folks if a student has a different way of thinking of this, maybe a student says hey
I really really understand 11 times 26 as being
526 is Plus
626's, and that's how the student wants to do it more power to her that's okay because the beauty of mental math is
There's a lot of different ways to do it
You don't all have to agree and do it the same way
BLAH BLAH BLAH
Draw the tape diagram, so let me go in here and draw in that tape diagram and that tape diagram
Would it says 11 times 26?
So really we have 11 26 s so really what they would want is a 26
And then another 26, and then another 26, and we'd keep going all the way until we have
11
26 --Is and
That's essentially what the tape diagram would look like now
Here is kind of more of the same. We're Gonna just
Without using the tape diagram without using that visual oh by the way, I think I forgot the visual on the other one
I'll see if I could go back and add that anyway on this one
29 times 12 so we're Gonna think of that as
29 12
so we're gonna be thinking of 12 plus 12 plus 12 plus 12 29 times and
a nice easy way of thinking of that would be
thinking about 30 12
minus 1 12
Because 30 is too much, so we're gonna take away one extra 12
so that would be 30 times 12 and
Then we're gonna take away 1 times 12, so 30 times 12 is
360 minus 12 gives us
348
All right, let's take a look at number be
11 times 31 so we're for some reason they've decided
For us to think of this as 31
11s
We could have thought of this as 11
30 ones, but they chose to kind of guide us towards 31 11s. Which can be thought of as 30
11s
Elevens Plus 111
So that would be 30 times 11 plus 1 times 11
So that's 330 plus oops not 33
330 Plus
11 and that gives us
341
last slide here
And on this last slide joy is helping her father to build a deck that measures
14 feet by 19 feet find the area of the deck using a mental strategy so the first thing you're supposed to remember
Is that if you have a deck that is 14 by 19?
And you're trying to find the area that means you're gonna do 14 times 19 all right
So my mental strategy and a lot of different ways to do this
I'm gonna do I'm gonna think of 14 times 19, and I'm gonna think of this as having
Nineteen
Fourteen
meaning 14 plus 14 plus 14 plus 14 blah blah blah blah
Well that's really the same thing as doing 20 times 14 and then taking away 1 times 14
Because really we're supposed to only add 19 of them so but we're gonna add 20 of them together
So we're gonna multiply by 20, and then we're gonna Subtract 1 because we multiplied by too much
so 20 times 14 that's
281 times 14 is 14 now 280 minus 14 is
266 and there is our answer and really we should do square feet
and
That is our
Lesson 4 for module 2 Fifth Grade Module 2