All right This Is Fourth-grade module five lesson two and in this lesson Students are going to be
decomposing Fractions As a Sum of unit Fractions and They're going to be modeling that using tape diagrams and number Bonds
And The idea of of This is you know we want students to be Able to visualize
3/4 for Example as
One-Fourth Plus one-Fourth Plus one-Fourth and sometimes it'S going to help them to think of It as a Number Bond
Sometimes it's going to help them to think of It as a Tape diagram
sometimes it's Just going to be helpful for them to think of It as a sum of
Three unit Fractions and
So That's What This lesson is about it's not Really leading Towards any particular
Standard Algorithm At This point at This point we're Just Really Building
Understanding of Fractions for our Students we don't want students to be thinking of Fractions As some sort of mysterious Thing to avoid
Instead We Want them to understand That Number Fractions are numbers and They make sense and
They're Kind of fun really so let's Get started on this
So the idea on this problem Is we are Supposed to do three things first we're gonna
Draw and Shade a tape diagram then we're going to record the decomposition as a sum of unit
Fractions and Then Record The decomposition
Position in two different Ways right so the first Thing is well what are unit
Fractions and Just As a Recap Unit Fractions are Fractions where the numerator
Is
A 1 so these are two Examples Up here of
Unit Fractions
For Example Here's 5/6 Here's a picture of 5/6 Here it is as a Sum of unit Fractions and Here is
5/6 in two
different Ways of
Decomposition
Without Using Necessarily all Unit Fractions so for one
7/10 so what Is 7/10 gonna look like well we're going to start with a bar of Any length and
We Know because the denominator is a 10 we're going to cut it up into
Equal-Sized Pieces Let's Label This entire Thing one and
Then we Want to shade in Seven of those Ten little Pieces so one two three
Four
five six
Seven and so there is our drawing so we've done step one
We've Drawn it Now the idea is record It as a Sum of unit Fractions so 7/10 is going to be
1/10 plus 1/10 plus 1/10 plus
1/10 oh My Goodness plus 1/10 plus 1/10
One Two three four five six plus one more tense so there's our Seven tenths As a
Sum of unit Fractions and Now our Job is to show it in two other Ways
Oh so i'm Just gonna Kind of Cheat Here i'm gonna Say okay how about three tenths plus four tenths and
Then Let's do oh
Two Tenths
Plus
four tenths Plus 1/10 so
There you go in fact there's a ton of different Ways That students can do It and for Your real High flying Kids a
Really Neat Lesson a Neat Activity Would Be Give them something with a small
Numerator some
Sort of Fraction with a small numerator oh?
Let's Say
3/7 it doesn't Really Matter as long as That Numerator is Pretty small and
Tell them come up with all of the different Ways That
you can Make
3/7 using nothing But Addition so there's i Mean There's going to be lots of Ways 2/7 plus
1/7 and then in in this case you might argue whether
1/7 plus 2/7 is something different and the idea IS come up with all the different Ways
To create That Fraction Keeping in Mind you Need to use a Fairly small
Numerator oh maybe something Seven or smaller
And Your High-Flying students are going to love this this this Math is called Combinatorics
Combinatorics and it's really Just Kind of fun
fun Way to make math
Engaging a Little Bit
So we're gonna do more of the same
Here we have to draw and Then Record The decomposition in three different Ways?
So we're going to begin By drawing. Our bar and i Just made it long for no particular reason and this Whole bar
Represents One
and Then we're gonna cut it into
12 Pieces so i'm going to begin by cutting it into four Pieces and
Because 4 Times 3 Is 12 i'm going to cut each One of Those
Into three Pieces so 4 times 3 Is 12 and now i know i have 12 Pieces and
The Numerator Is a 10 so i need to shade in 10 of
Those 12 Pieces Which means i'm not going to shade in to
There we Go and so there is our picture of
10 twelfths and Then There's a Whole ton of Ways That you can write decompose that As a
Sum of a Variety of different Fractions right so you could do five twelfths Plus
5/12
Let'S see 10 12 could be
3 12 oops Whoa 3 12 plus 3 12
Gee-Whiz Why do i keep putting a 10 here plus 3 12 plus
1/12 and you Get the idea there's Just a ton of
different options Parents and Teachers Feel free to differentiate this
By Allowing Your students to try and find all the possible Ways to
Create 10 12 it's a Really engaging problem some Beautiful patterns show up it during that hunt as
You're looking for all the possible Ways Rather Than Just 3 and
The Last slide for This video Just more The same Now the idea might Be Why are we going through This
Rigmarole Why are we Going through This hassle and the idea is because we want students to learn how to
Visualize
Fractions so when we're drawing six fifths we want students to visualize this as
Something That's going to be larger Than one
Because
Let'S see i'm gonna start by drawing
six Pieces
so there are our six Pieces Because the numerator Says six Now that five is the
Denominator Meaning One Whole Is
Going to be right Here after five Pieces so those five Pieces 1 2
3 4 5 Those 5 little unit Pieces
Represents The 1 Whole
Plus
We have that Extra 5th right Here so That's our 6
fifths 1 2 3 4 5 6 and we Want students to really
Not Just rote memorize oh if the numerator is bigger Than the
Denominator Then it's more Than one we Want students to have an Understanding of Why and That's What This is about and then
Once You've Drawn the picture six fifths can Be done a Whole Variety of Ways in
Most Importantly Probably One five five fifths Plus One fifth Because That tells us
That's Equal to 1 and 1/5
right so we're doing a Little Bit of Foreshadowing of how to turn an
Improper Fraction into a Mixed Number and
This is another Example right Here of Why that Makes sense so if we're going to draw One Whole and
1/4 the idea is well Here's one hole and
That hole must be cut into fourths Why is it cut into fourths Because This other Fraction Here Says so
So we now so this hole right Here is our picture now we need to draw 1/4
more Because That's What This
One Fourth Is so Here's Our one hole and Here's Our one fourth and there's our picture and we can See
That we Now have five
Fourths Because Another Way to think of This IS 1/4 plus 1/4 plus 1/4 plus 1/4 plus 1/4 in
Fact That Is one of our
Sums That we can decompose and write As a sum
There you go and then another 1 1 and 1/4 well we Could do
3/4 plus 2/4 and There's a ton of different options and
That Wraps Up less a
Fourth-Grade Module 5 lesson to where students are
visualizing Fractions Using tape diagrams and Then They're writing It in a Variety of decompositions