All right This IS fifth-grade module Two lesson One and in this lesson Students are going to be learning. How to
Multiply multi digit Whole Numbers and Multiples of Ten
Using Place value patterns okay so basically What Does this Mean This means the idea of we Know for Example
40 times 30
The Classic trick That Teachers Would teach is well you take The 4 you take The 3 you multiply you get 12 then you stick
On the 2 zeroes and That's Your Answer the point of This lesson is to
Explain The
Mathematical underpinnings of Why that Makes sense so that Math Is more Than Just a trick to
memorize but It has some meaning to it so let's Get started
Alright so
The Directions Up Here say fill in the blanks using your knowledge of Place value so the idea is this is going to guide us
Towards That Classic trick
of
Multiplication
But with an idea of well it's gonna make sense because we're gonna
Explain The Mathematics That's going on behind it so Let's start with a
It Says 43 Times 30 and They want us to think about this As 43 Ones Times three tens
So over Here Forty three copies so Forty three
Ones Is another Way of Saying Forty Three Copies of a One
Times Because It Says Times right Here and then three tens so that Means three copies of
Ten and That's Kind of The mathematical This is the mathematical Way of explaining
What is going on over here well Now we could use the commutative property and the associative property to rearrange this
To be forty three Times three Times
One Times ten so you see i just took these and used the commutative property and
regrouped and Rhea Rhea and regrouped them so Now 43 Times 3 That's
Pretty Straightforward That'S 129
Times and Then 1 Times 10 well That's Pretty straightforward That'S 10 and We Learned from the previous
Module That 129
Times 10 Is
1290 so there we Go so this Whole
Answer Goes right Heat Well i Mean This is all the Work to Explain What's going on That
Right Here 43 Ones Times 3 Tens That's right Here 129 10 so That'S 129
Tens Which Ends Up Equaling
1290
Let'S see let's Go let's skip down to problem C so we've got
830 Times 20 so
830
Times 20 well That's the same Thing as Saying well That's Eighty Three Copies of
Ten Eighty Three Tens
Times two Copies of tens are two tens and
So we can use our
associative and Our commutative properties to get that This Is Equal to 83 Times 2
Times 10 Times 10
so 83 Times 2 well 83 Times 2 Is Let's Say
166
Times and we Know that 10 Times 10 well That's a Hundred
And
So we end up with
166 with those two Extra Zeros so it's the idea is this Becomes
166 Times 100 Which from the previous module We Learned how to multiply by Powers of ten Ten Hundred Thousand
so this Ends Up equaling
Where am i oh right here one?
16600 Now we do want to fill in this Blank so when you have?
Eighty-Three tens Times two tens That's Equal to a Hundred and Sixty-six
Hundredths so we could write in the word
Hundreds
Right Here
Hundreds Yeah
All right so this slide is Really Just a bunch Of practice so we're gonna start with 80 times five and
we Know that 80 is eight Copies of ten
Times five Now five can Be Thought of as five copies of one
And so now using the associative and the commutative property
we can Regroup and rearrange and Get eight Times five Times ten Times one
Which Ends Up giving Us 40 times ten and
We Now know that you know from the previous module that 40 Times 10 is Equal to
400 so there is our answer right There
so Now let's take a look at 80 Times 50 well Eighty Times 50 well That's eight Copies of ten
Times five Copies of Ten
Using The commutative and the associative property we can Move Things Around and regroup them and
so you Get 8 Times 5 Times 10 Times 10
so that Equals 40 Times 100
Which is Equal to 4,000 the idea being we've Got 40 and we're gonna stick on those two extra Zeros
All right Let's squeeze in one last Example Let's Just do
8,000 Times 50
Now 8,000 Times 50 so 8,000 is 8 copies of
A Thousand Times and then 50 is
Five Copies of 10 so using the commutative property to rearrange everything and the associative property
to regroup We Have eight Times five
Times a Thousand Times ten and
so we know that 8 Times 5 Is 40 i
Then a
Thousand Times ten is
Ten
Thousand and so that We Know our answer is that Forty
With four Extra Zeros One Two three four we Know that from the previous module
So our answer here is four Hundred
Thousand and that is That One right There
Last Problem For This video It Says a concrete stepping stone Measures Twenty square inches so you've Got this
concrete stepping stone and They're Saying That
stepping Stone is Twenty square inches
But We Have Thirty of them so we've got another one and another One and another one
Dot And all The Way and
To that last one and we Have Thirty?
Copies
of that so that means we're gonna do Thirty Copies of
The Twenty Inches Squared
so
Temporarily we're gonna ignore that Inches Squared
Label
Right Here and we're Just going to focus on that Thirty Times Twenty so That's gonna be three
Times ten
Times two
Times ten and Then Using The commutative and the associative property that Gives us whoops sorry That Gives us three
Times two Times ten Times ten Which Gives us six times a Hundred
Which Gives Us six Hundred
square inches
so that Is the area of 30 of these stepping Stones
And
That wraps Up
fifth-grade module Two Lesson One the idea of Using
Mathematics to understand the trick of
Taking The four and the three multiplying them and Then Sticking on
Those Two Zeros