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Join Benny in his school where he is investigating fractions on number lines. He gets some help from his friend Thania, and then shows his stuffed animal how to write 1/3 on the number line. While doing his homework later in the evening, Benny gets stuck on a problem about plotting a fraction on a number line that is greater than one, so he texts Thania to get some help.

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I asked my friend if she could help me find

where to write one-half on the number line.

She said, “First draw a line with two arrows.”

Then she sang a song; here’s how it goes:

Zero to one is the whole that we split apart.

The denominator tells us into how many parts.

Make a line that starts from zero to the first mark,

and one-half is what you’ll find when you get that far.

My stuffed animal can’t talk, but I thought I heard,

“Hey, Ben, on the number line, where’s one-third?”

I said, “First, draw a line with two arrows.

And hey! I know a cool tune; here’s how it goes.”

Zero to one is the whole that we split apart.

The denominator tells us into how many parts.

Make a line that starts from zero to the first mark,

and one-third is what you’ll find when you get that far.

Then I texted my friend, “What’s to be done

when the numerator isn’t one?”

She said, “Let’s try to find five over nine

on the number line in - like - no time.

Simply partition nine parts from zero to one.

Starting from zero, count five, and at five-ninths we arrive.”

Zero to one is the whole that we split apart.

The denominator tells us into how many parts.

Make a line that starts from zero to the fifth mark,

and five-ninths is what you’ll find when you get that far.

Let’s use the number line to describe this pie.

First, count the total pieces... there are five.

Five’s the denominator (all the parts), so five goes underneath the fraction bar.

This number line goes from zero to two,

but the fraction’s less than one, so here’s what to do:

Make five equal spaces from zero to one.

Now the final step before we’re done:

The numerator is the one piece that’s mine.

After the first space I’ll write one-fifth under the line.

Just remember this one tip in your minds:

Always count the spaces - never the lines.

Zero to one is the whole that we split apart.

The denominator tells us into how many parts.

Make a line that starts from zero to the first mark,

and one-fifth is what you’ll find when you get that far.

TEKS Readiness Standard

2.3B

The student is expected to explain that the more fractional parts used to make a whole, the smaller the part; and the fewer the fractional parts, the larger the part.

3.3A

The student is expected to represent fractions greater than zero and less than or equal to one with denominators of 2, 3, 4, 6, and 8 using concrete objects and pictorial models, including strip diagrams and number lines.

Common Core Standard ( CCSS )

This video addresses the following Common Core Standards:

3.NF.A.2

Understand a fraction as a number on the number line; represent fractions on a number line diagram.

3.NF.A.2.a

Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line.

3.NF.A.2.b

Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line.

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