Transcript No Problem! - MathinScience

Count on
Chemistry
Presented by the MathScience
Innovation Center
Written by Theresa Meade
What is a polymer?
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It is a long, long molecule!
Polymers can occur in nature or they can be
made by humans.
This is a small
molecule. It is
not a polymer.
What kind of math is here?
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Long chains mean adding the same thing over
and over.
How does that relate to math?
Long chains can be hard to analyze. Sometimes
it’s easier to look at the parts.
How does that relate to math?
Today we will…
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Look at large pieces
Look at the smaller pieces “inside”
Think about changes
And have fun with math and science!
What is a polymer?
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A polymer has a repeating pattern inside it. That
pattern is made of a few atoms joined together
to make a monomer.
Many, many monomers join together to form
polymers. The number of parts determines what
the whole looks like! Ethane, butane, paraffin, and
polyethylene
Ethane
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First discovered in 1834
A component of natural gas
Butane
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Liquid form
Found in LPG bottles used in gas grills
Paraffin
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Waxy solid
Used in candles and has a low melting point
Polyethylene
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Solid
This is everyday plastic—milk jugs, detergent
bottles, or any plastic
Thinking…
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How can we create a model for the parts of a
whole?
We will start with some basic materials. Get
ready!
Let’s look at a model
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Label one end of a strip of paper 0.
Fold, then open.
What should we label the fold line?
What should we label the other
end?
0
1
2
1
Let’s look at a model
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Let’s look at another strip of paper.
Label one end with 0 again.
Fold.
Without unfolding, fold the paper one more time.
Unfold your strip.
How many pieces all together?
0
1
4
2
4
3
4
1
Let’s look at a model
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Do you remember the steps? What do we do first?
Fold your paper. Without out opening, fold it again.
Now fold one more time.
How many pieces do you predict there will be?
What should we label the end?
How many parts all together?
0
1
8
2
8
3
8
4
8
5
8
6
8
7
8
1
Let’s look at a model
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Let’s make one more fraction strip.
Remember the process?
Label the end with 0. Fold the strip. This time fold
it a total of 4 times without opening.
How many pieces do you predict there will be?
Open and look!
0
1 2 3 4 5 6 7 8 9 10
16 16 16 16 16 16 16 16 16 16
11 12 13 14 15
16 16 16 16 16
1
1
4
Guided Practice
Don’t answer any of the questions yet!
We’ll do these together in just a moment!
1
1
 So which one is larger, 4 or 2 ?
 How do you know?
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Guided Practice
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What are equivalent fractions?
Yes! They are two different ways to name the
same amount!
Write some of the equivalent fractions we talked
about on the lines in Part 1 of your Data Sheet.
What are some of the numbers you wrote?
Guided Practice
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What happens when you add
0
1
4
2
4
1
4
+
1
4
?
3
4
1
Guided Practice
1
3
4 - 4 =
0
1
4
2
4
3
4
1
Guided Practice
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Work with a partner to figure out problems 3
and 4.
Guided Practice
I have
1
2
0
I want to add
0
1
4
2
4
3
4
1
Guided Practice
I have
0
1
8
2
8
3
8
4
8
5
8
6
8
7
8
1
I want to add
0
1 2 3 4 5 6 7 8 9 10
16 16 16 16 16 16 16 16 16 16
11 12 13 14 15
16 16 16 16 16
1
Saving your work
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Use a glue stick to save all of your fraction
strips.
What if…
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…you didn’t have fraction bars?
Number lines can help you think about
fractions!
Number lines
0
1
8
2
8
3
8
4
8
5
8
6
8
6
8
1
8
7
8
1
When you add fractions with the same denominator, draw
one line. Find your starting point and decide how many
“hops” to take to get an answer.
6
8
+
1
8
Number Lines
Step 1: Draw two number lines since you are adding
numbers with two different denominators.
1+1 =
4 8
Number Lines
0
0
1
8
2
8
3
4
2
4
1
4
3
8
4
8
5
8
6
8
Step 2: Decide how to mark your number lines.
1+1 =
4 8
1
7
8
1
Number Lines
0
1
8
2
8
3
4
2
4
1
4
3
8
4
8
5
8
6
8
1
7
8
0
1
Step 3: Find an equivalent fraction to use for a starting
point.
1+1 =
4 8
Number Lines
0
0
1
8
2
8
3
4
2
4
1
4
3
8
4
8
5
8
Step 4: Add!
1+1 =
4 8
3
8
6
8
1
7
8
1
Time to work with your partner
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You and a neighbor will work together to
complete the rest of your data sheet.
There is a front and a back, but don’t worry if
you don’t have time to finish!
Remember to work like a mathematician—be
accurate, take your time, and talk to your
partner.
Answers?
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How did you do?
Why look at parts of the whole?
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Many scientists do exactly what you did!
Think about genetics! We look at part of the
DNA strand.
Think about creating synthetic vitamins. We
look at part of the molecule and recreate it!
Think about making better plants and crossbreeding to get new varieties of roses.
It’s all about the parts!
Now let’s look at polymers again
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What do those long strings of monomers do?
They have some very interesting properties!
It’s time for a demonstration!
Did you enjoy polymers?
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Chemical engineering uses math and the art of
putting things together to create and discover
new compounds.
Thank you!