Why kids struggle with measuring with a ruler (and how coloring inches can help):

## Measuring with a ruler uses the area model for fractions.

1. Measuring in inches requires a different way of thinking about fractions. The most common way for kids to think about fractions is the area model. This is where a space is divided into equal parts, or areas. However, when measuring inches, we have to think about fractions as a point on a line. This is called the linear model. And the difference between the two models can be confusing to students.

It’s hard for kids to connect the idea of ½ of a cookie with a line on a ruler being ½ of an inch. Coloring inch measurements on rulers can help students make that connection between the area model and the linear model of fractions. When they color in half of an inch on a ruler, they can SEE why that line is the halfway mark for measuring inches.

## Students need to understand equivalent fractions first.

2. Students need a strong understanding of equivalent fractions to understand the lines on the ruler when measuring inches. The ruler lines count like this: whole number, 1/8, ¼, 3/8, ½, 5/8, ¾, 7/8, whole number. That’s very confusing for kids who are just starting to understand both measurement and fractions.

Coloring the inch measurements on a ruler can help students see the patterns. Once they see the patterns, they can begin to make sense of this confusing order of fractions. Color-coding the different fractions of an inch will help students see the progression from one fraction to the next. That understanding will help them internalize the sequence.

## It’s hard to see the patterns in all those lines.

3. There are SO MANY LINES to look at when measuring inches on a ruler! It can be really hard to know which one(s) to focus on and which ones mean which fractions. Coloring the measurement lines on a ruler will help students to make sense of all of those lines.

In order to color the ruler, students have to focus on the measurement lines, which will help them see the patterns. They will begin to notice that some measurement lines are longer. Then, they’ll see that the longer lines connect to the fractions with the smaller denominators (half inches and quarter inches). Then, they’ll be able to visually see that the bigger spaces/ bigger fractions have the longer measurement markings on the ruler, and the smaller spaces/ smaller fractions (eighths) have the smaller measurement markings on the ruler.

## Tips for Using Coloring to Teach Measuring on a Ruler:

-Give students printed rulers with only the lines on them. Have the students color in the measurements (whole, half, quarter, or eighth of an inch). Then, they can label the lines of the ruler with the correct measurements. (To align to the Common Core, second graders should work with whole inches. Third graders should work with halves and quarter inches, and fourth and fifth graders should work with eighths of an inch.)

-Start by using rulers marked with only whole inches. Then, add half inches and quarter inches. Eventually, add in eighths or even sixteenths of an inch.

-Differentiate by writing in some of the measurements for students who need support. You can challenge students with completely blank rulers.

-Give the students paper rulers with only whole inches marked. Have them draw the half lines and color each inch in halves. Or, have them divide each inch into fourths or eighths, mark each line, and color each fractional piece.

-Use color-coding to help kids see the patterns: Color all the spaces from the whole to ¼ inch blue, the spaces from ¼ to ½ yellow, from ½ to ¾ green, and from ¾ to the whole red. Students will begin to notice the pattern: whole, ¼, ½, ¾, whole, etc. The same can be done with ½ inches or eighths of an inch.

Happy Teaching (to the Nearest Quarter Inch)!

Christine Cadalzo

Pssssssst…

Here’s a ready-made math unit for teaching students to measure to the nearest quarter inch!