📊Math G3 L6.10 🤔Explore A - Numerator Comparison

For this lesson you will need your math journals, the fraction strips you created in lesson 6.4, and the Numerator Comparison recording sheet found in the lesson materials.

Play media comment.

Part 1

a)

What do the number lines represent in this scenario?

• A row of corn and a row of tomatoes from a garden.

How did you evenly partition the number lines?

• Paper folding or measuring device

How much of a row of corn was planted?

• $\frac{1}{4}$

How much of a row of tomatoes was planted?

• $\frac{1}{3}$

Which row is longer?

• The tomato row.

How do you know?

Play media comment.

b)

For this part you will need your folded paper strips.

Line up the zero marks from each number line that has fourths and thirds.  

Compare.  Which number is to the right? $\frac{1}{4}$or $\frac{1}{3}$?

(The number to the right is larger.  For example 5 is to the right of 2 on a number line, so 5 is larger.)

You can also fold the paper strips to compare the lengths of $\frac{1}{4}$and $\frac{1}{3}$.

Which is larger?

• $\frac{1}{3}$

Which row does this refer to?

• tomatoes

On your recording sheet:

• Fill in the number line for problem 1 with the corn and tomatoes.
• Place <, >, or = in the circle.
• $\frac{1}{4}$< $\frac{1}{3}$

Part 2

On your recording sheet, let's move to problem 2.

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This same garden has half a row of strawberries.  The garden also has one-eighth row of bell peppers.

Which row has more plants in it?

• On your recording sheet, mark the number line for the strawberries $\frac{1}{2}$and the bell peppers $\frac{1}{8}$.
• Which row is longer?
  • strawberries

How do you know?

• $\frac{1}{2}$is farther to the right on the number lines than $\frac{1}{8}$
• $\frac{1}{2}$is greater than $\frac{1}{8}$

Fill in the circle with the correct relationship symbol <, >, or =.

Part 3

Play media comment.

On your recording sheet, let's move to problem 3.

In this garden there is a $\frac{1}{6}$of beans.  There is also a $\frac{1}{4}$of carrots.

Which row of vegetables is longer?

• On your recording sheet, mark the number line for the beans $\frac{1}{6}$and the carrots $\frac{1}{4}$.
• Which row is longer?
  • carrots

How do you know?

• $\frac{1}{4}$is farther to the right on the number lines than $\frac{1}{6}$
• $\frac{1}{4}$is greater than $\frac{1}{6}$

Fill in the circle with the correct relationship symbol <, >, or =.

Part 4

Play media comment.

Which row is longer in each case?

• tomatoes, strawberries, and carrots

How do the fractional amounts relate to each other?

• For each fraction comparison, the numerator is one.  That means there is one piece of the equally sized partitions that is being considered.
• Each denominator is different.  That means that the number of equally sized partitions of the whole are different for each row.
• The larger the denominator, the more equally sized partitions the whole is broken into.  The more equally sized partitions, the smaller the size of the partition.

What pattern do you notice about the larger fractions?

• The larger fraction has the same numerator as the smaller fraction, and the smaller number in the denominator shows a longer section of the row of vegetables.

Part 4

Does the pattern work when the numerator is not 1?

Play media comment.

Let's look at problems 4, 5, 6 on your Numerator Comparison recording sheet.

4)

Use your fraction strips for $\frac{2}{4}$and $\frac{2}{3}$.

Line up the 0's.

Which fraction is farther to the right?

• $\frac{2}{3}$
• $\frac{2}{3}$is greater than $\frac{2}{4}$

The numerator is the same.

The larger the denominator the smaller the equally sized pieces of the whole.  Thirds are larger than fourths.  Two-thirds is larger than two-fourths.

5)

Use your fraction strips for $\frac{2}{2}$and $\frac{2}{8}$.

Line up the 0's.

Which fraction is farther to the right?

• $\frac{2}{2}$
• $\frac{2}{2}$is greater than $\frac{2}{8}$

The numerator is the same.

The larger the denominator the smaller the equally sized pieces of the whole.  Halves are larger than eighths.  Two-halves is larger than two-eighths.

6)

Use your fraction strips for $\frac{2}{6}$and $\frac{2}{4}$.

Line up the 0's.

Which fraction is farther to the right?

• $\frac{2}{4}$
• $\frac{2}{4}$is greater than $\frac{2}{6}$

The numerator is the same.

The larger the denominator the smaller the equally sized pieces of the whole.  Fourths are larger than sixths.  Two-fourths is larger than two-sixths.