Ruler Fractions Script* to Be Used with the Ruler Fractions Grid

Ruler Fractions Script* …to be used with the “Ruler Fractions” grid.

*This script will sound stilted and artificial until you read it and practice it often enough to be comfortable with it. Certain word choices have been made on purpose, but other vocabulary is personal choice.


Turn your paper so that “0” is on the left and “1” is on the right and the blank for your name is at the bottom of the page.

We will be working from the bottom towards the top on this page. On the bottom horizontal line, mark the heavy line in the middle “1/2” (say ‘one half’). Notice how many spaces there are from the “0” to the line marked “1/2”. Count that number of spaces going to the right and mark the last vertical line as “2/2” (say ‘two halves’). “Two halves” is the same as “1”.

Now move up to the next horizontal line. There are two other vertical lines that are slightly heavier than the others. Start on the left; the heavier line that is half-way between “0” and “1/2” should be marked “1/4” (say ‘one fourth’). Just the same way as you did before, count the number of spaces between “0” and “1/4” and then starting at the “1/4” count that number of spaces going to the right and mark the heavy line “2/4” (two fourths). Again, count that number of spaces going to the right and mark the heavy line “3/4” (say three fourths). One more time, you should count going to the right and mark the last line “4/4” (four fourths). “Four fourths” is the same as “1”.

Move up to the next horizontal line. Now we need to find the half-way mark between 0 and ¼. Count the spaces between “0” and “1/4” and find where half will be. (You can do this by placing one finger on the “0” line and one on the “1/4” line and moving each finger in toward the center.) Double check that you have found the line half-way between “0” and “1/4” and mark it “1/8” (say ‘one eighth’). You need to mark each of the ‘eighths’ between “0” and” 1”; “2/8” (same as ‘1/4’), “3/8”, “4/8” (same as ‘2/4’ and ‘1/2’), “5/8”, “6/8”, “7/8”, and the last one will be “8/8”. “Eight eighths” is the same as “1”

The next step is to fill in the next horizontal line up with the sixteenths. “1/16” is half-way between “0” and “1/8”. Fill in all the ‘sixteenths’ all the way across the line.

[Give students time to do this and monitor that they are doing this correctly!]

Page 2 Ruler Fraction Script

This step is very important. As you look at some of the vertical lines, you will see several different fractions. For example, look at the very heavy middle line. It should have 5 labels: “1/2” “2/4” “4/8” “8/16” “16/32”. The only one we will use in the “lowest” one…”1/2”.

On each vertical line, starting on the left, circle or highlight the lowest fraction on that line. On the first line, “1/32” is the lowest. The next vertical line to the right has “2/32” and “1/16” sooooo…the “1/16” is ‘lower’…now circle “1/16”. “3/32” is the only fraction on its vertical line…circle it. “4/32” is not the lowest on that vertical line, “2/16” is not the lowest…circle “1/8”.

[Try to get a student to explain that the fractions that we are circling or highlighting are only the ones that have an odd numerator. Perhaps several can do this on an individual basis as you cruise around the room checking the work in progress.]

[Once all the proper fractions are circled or highlighted, the top horizontal line needs every fraction written in lowest terms. This top line is the crowning jewel!]

To finish our ruler, start on the top horizontal line at the “0” and ‘drag’ (trace with your finger) up from the lowest to the highest and write the lowest fractions on each of the lines. Every numerator should be an odd number. ‘Every other’ fraction should have a denominator of ‘32’.

End script

To the Teacher: continue this activity in several different ways.

1. Have students use a calculator and give the decimal equivalent of each fraction. This will help some of them understand better the size of the fraction. If they thought that 1/32 was larger than 1/8, the decimal may help them see that 1/8 is 4 times larger than 1/32. DO NOT dwell on this activity, as some students will become dependent on the decimal form and the benefit of this lesson will be lost!

2. Make a set of cards with the ruler fractions on them (one per card). Randomly select three or four fractions and assign them to students. Have the students go stand in a line, in ruler order. Practice this several times with different students and different fractions. They need to see the sequential order of the fractions they will be using even if they are taken out of context. Example: should “7/8” be to the left or the right of “7/32”? Which one is closer to “0” or “1”?

3. Draw a line and mark the beginning and the end with “0” and “1”. Choose a random point and have 3 students ‘guess’ what fraction measures that point. Repeat several times with points larger than “1/2” and smaller than “1/2”. Ask questions that provoke their thought process, such as, “Out of these 3 fractions, __, __, and __, which one is closest to “1/2”? or “ which one of these 3 fractions, __, __, and __, is closest to “3/4”?