Lesson 16 Application Problem
Hannah bought 1 yard of ribbon to wrap 4 small presents. She wants to cut the ribbon into equal parts.
Draw and label a number line from 0 yd. to 1 yd. to show where Hannah will cut the ribbon.
Label all the fractions including 0 fourths and 4 fourths. Label 0 yd. and 1 yd., also.
Lesson 16 Concept Development
Let’s draw a number line with the endpoints 1 and 2.
The last few days our left endpoint was 0.
Where has 0 gone? It didn’t disappear; it is to the left of the 1. The arrow on the number line tells us that there are more numbers, but we just didn’t show them. It’s as if we took a picture of a piece of the number line but those missing numbers still exist.
We are going to partition this whole into 4 equal lengths.
Our number line doesn’t start at 0 so we can’t start at 0 fourths.
How many fourths are in 1 whole? 4 fourths.
So we will label 4 fourths at whole number 1. Label the rest of the fractions up to 2.
Check to see if you have the same number line.
What are the whole number fractions, the fractions equal to 1 and 2? 4 fourths and 8 fourths.
4 fourths is the same point on the number line as 1. We call that equivalence.
How many fourths would be equivalent to, or at the same point as 2? 8 fourths.
What fraction is equivalent to 3? 12 fourths.
Draw a number line with the end points 2 and 4. What whole number is missing from this number line? The number 3.
Let’s place the number 3. It should be equally spaced between 2 and 4. Let’s draw that in.
We will partition this line into 3 equal lengths.
To label the number line that starts at 2, we have to know how many thirds are equivalent to 2 wholes.
3 thirds made 1 whole. So, 6 units of thirds makes 2 wholes. 6 thirds are equivalent to 2 wholes.
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