*The following post comes from Rafael Quintanilla, a Mathematics Instructional Coach for the Los Angeles Unified School District and a long-time teacher of number strings. *

About eight years ago, I was teaching fifth grade and I wanted students to begin to see relationships between halves, fourths and eighths, be able to decompose fractions into unit fractions, and have an understanding of scaling when multiplying. So I decided to write and try out some strings that focused on benchmark fractions as helpers and then go from there. I used a number line as a model because that is what we tended to use as a fraction model because the students were able to connect it to real life applications. I decided to use the context of a bicycle ride because students can relate to to riding bicycles and because they can picture a straight bicycle ride (I let them know I ride my bicycle on the riverbed next to my house), hence the number line.

Students are really engaged in this string because as the string develops, I tell a story of why we stopped at certain places. Some of the “look-fors” in the string is that students might just give you numbers instead of saying the numbers represent miles on a bicycle ride. Be careful because students will see the numeric patterns that exist but not make connections that these numbers represent fractional distances on the ride.

**Multiplying Fractions by a Whole Number**

*Model: Number Line*

*Context: On weekends, my friend and I enjoy riding our bicycles. Our goal is 24 miles. But sometimes, we stop for breaks.*

*Draw number and teacher labels 0 miles on left side and 24 miles on right side*

String:

1/2 of 24 (“tell the story, we stopped half way through the bike ride to get ice cream”)(take one or two strategies, helper problem)

1/4 of 24 (“Oh, I forgot, we also stopped one fourth of the way to drink some water”)(take one or two strategies, helper problem)

3/4 of 24(this is where the string begins to develop, allow more time, ask students to think-pair-share and then model their thinking whole class)

1/8 of 24(take one or two strategies, helper problem)

3/8 of 24(this is where the string continues to develop, allow more time, ask students to think-pair-share and then model their thinking whole class)

7/8 of 24(this is where the string continues to develop, allow more time, ask students to think-pair-share and then model their thinking whole class)

5/8 of 24(usually comes up during other problems or else you can use it as your last problem)

Two notes:

- Keep in mind that the goal of the string is to multiply fractions by a whole number. Therefore, the teacher puts the tick mark on the number and labels the fraction. The students are computing the number of miles and developing strategies.
- The goal of the lessons is to allow students to discuss the relationship between the fraction and the whole. The goal is
**not**to determine where the fraction is located on a line. That is why the teacher marks the location. Also do not worry about rushing into writing the expression or equation.

Thanks for sharing!

One correction on the bottom right:

1/4 of 24 = 6

Great problem

—