Explore A1 - Lesson 5.11 Partial Partitions: Number Lines

For this lesson you will the Partial Partitions recording sheet in the lesson materials.

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Part 1

Let's look at some possible answers.

a) $\frac{3}{5}$

• This response is incorrect.  This response was found by counting all of the tick marks to get a denominator of 5.  Then counting the third tick mark to get a numerator of 3.
• The space between the tick marks is the length, not the tick mark.

b) $\frac{2}{4}$

• This response is incorrect.  This was found by counting the number of spaces between zero and one to get a denominator of 4.  Then counting over two spaces from zero to get a numerator of 2.
• The spaces are not the same size.  They are not equal.  The denominator refers to equal sized pieces of the whole.  This number line does not show all of the tick marks.

c) $\frac{4}{6}$

• This response is correct.  The number line needs to be partitioned into equal size pieces.  The tick marks between 0 and 1 are not equally spaced.  The space between 0 and the first tick mark is not the same spacing as the rest of the number line.  This first space needs to be divided into smaller partitions.  This will give a total of 6 equally sized spaces.  The red mark being at 4 which clearly indicates a distance of $\frac{4}{6}$.

Record this on the Partial Partitions recording sheet.

Part 2

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What is the value of the tick mark at the red arrow?

Are the tick marks equally spaced?

• No.

Where do you need to add more tick marks to make them equally spaced?

• after the fourth tick mark and the fifth mark from the left.

What does this make the number line partitioned into?

• eighths

What is the label for the tick mark with the red arrow?

• $\frac{3}{8}$.
• The mark is at 3 one-eighths.

Record this on the Partial Partitions recording sheet.

Part 3

Look at Number line 3 on the Partial Partitions recording sheet.

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How would you adjust this number line to have the partitions be equally spaced?

• Place tick marks so that the number line has partitions of size one-fourth.

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