Explore A - Lesson 5.9 Partitioning a Number Line

For this lesson you will need the Cuisenaire Rods app, Rulers, the open number line mat (found in the lesson materials), and 1 inch by 12 inch construction paper.

Cuisenaire Rods App Links to an external site.  (Click on Link)

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Part 1

Which piece of licorice is partitioned into three equal pieces?  Why?

• The second piece.  All are the same size.

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Look at this number line.  What do you notice?

Do you see that the first tick mark is 0?

Do you notice that each tick mark is the same distance apart?

Do you notice the arrows at each end?

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Do you see that the first tick mark is 0?

Do you notice the arrows at each end?

Is each tick mark the same distance apart?

• No

This is an example of what not to do.  When drawing a number line, all spaces must be the same size or equal sized pieces.

The order of the numbers must be sequential--from smallest to largest left to right.

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This number line is correct. 

• The tick marks are equally spaced.
• The numbers are in order from least to greatest, left to right

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What do you notice about this number line?

• Did you notice there are tick marks between 1 and 2?
• Did you notice how many tick marks are between 1 and 2?
• What would each of those tick marks represent?
  • one-third
• Where would the numbers 0, 3, 4, and 5 land?
• Each length between 1 and 2, 2 and 3, and so on is one unit--or one whole.

Part 2

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On your open number line, and using the ruler, measure and mark the length of an orange rod.  Make the left tick mark equal to 0 and the right end equal to 1.

The distance between 0 and 1 is the whole.

Which rod would partition the length of the whole into halves?

• yellow

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Line up the end of the yellow rod (using your ruler) with the 0 tick mark on the number line.  Make a tick mark at the end of the yellow rod.

What unit fraction would label this tick mark?

• $\frac{1}{2}$

What do you notice about the two partitions?

• They are both the same size.
• They are both the unit fraction $\frac{1}{2}$.

Can you find a tick mark on a ruler that is halfway between 0 and 1?

Part 3

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Let's create another number line.

This time use an orange rod and a red rod.

Partition the line into 4 equal parts.

How would you do this?

Which rod represents the the length of one-fourth section?

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Each section represents one-fourth of the whole.

This $\frac{1}{4}$refers to the section length.  

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Now let's add another section.  

Where would 2 be on this number line?

• It would be a "whole" length from 1.
• This is an orange rod and an orange rod end to end on the number line.

Does your number line look like this one?

Are your whole number tick marks labeled?

Are your tick marks equally spaced?

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