Using a blank number line, I mark the points of zero at the left end and one on the far right end. I make a point of eyeing the line I've created carefully, before I mark 1/2 on it. What does this line that I drew, here in the middle, mean? What have I done with this distance, between 0 and 1?
Using a new number line of the same length, I choose a different color and mark it into fourths making a point of creating the half first, and then dividing each half into halves. Then I go back to label - thinking aloud - "One, two, three, four. I have 4 pieces here. So this one is our first piece, I label it 1/4, this is the second piece - 2/4, and here is the third piece - 3/4. Can anyone tell me why we use this four (pointing to the denominator) here?" I discuss how each part of the number line now shows fourths. I ask, "Which two fractions are the same?" Because the number line is large, it is easy for the students to determine the equivalent fractions.
I choose a new color and mark the eighth sections on another new number line the same length as the other two. All three number lines are viewable at the same time for visual comparisons. I begin at zero and say that each of these is now for eighths and write the eighth fractions in order asking the students to count as I write.
Because the Common Core standards require students compare equivalent fractions, I explain they will be making fraction strips to use throughout the fraction unit to put fractions in order and to find equivalent fractions.
Students are given the first of six different colored pieces of construction paper cut to two inches by 12 inches to use for their fraction strips.
The first strip is red, and is marked whole. The colors for each fraction are not important, except that all students are using the same color for each fractional piece as they will use them together in future lessons with partners and groups.
The students write the numeral 1 and write the word "whole" on the red fraction strip.
Next students are given a yellow strip of paper, and I model how to precisely fold the fraction strip in half. The fold line is traced with a crayon or colored pencil, and each part is marked with fraction ½.
Because the Common Core Math Practices require students to attend to precision, the folding of the fraction strips accurately is very important especially as each fractional pieces decrease in size.
The folding continues with orange for the fourths. The strip is folded in half, and then each end is folded to the middle half fold mark. This prevents the paper from sliding as layers are created. Each one-fourth section is marked ¼, rather than increasing in size ¼, 2/4, ¾.
Next, I model for the students folding eighths and the students use green paper for this fraction. Each section is marked 1/8. Folding the eighths follows the procedures for the fourths, but it will be necessary to make a final fold in half once the paper matches the fourths. This is the ideal time to emphasize precision by aligning the edges of the paper and creasing the paper.
The last two fraction strips, blue for thirds and purple for sixths, can be more challenging, and it may be helpful to pre-mark these fold marks using a ruler for the students. The paper can be turned into fourths, but the measurement is less precise because the ends of the paper are not matched. Since the paper is twelve inches across, thirds can be marked at 4 inches and 8 inches. Sixths can be done the same way and folded in half, or marked every two inches.
Each section continues to be marked with 1/3 and 1/6 on all sections of the fraction strips.
To close the lesson, I ask students to hold up show different fractions on different strips and compare. Then I ask them to show me two-fourths, four-sixths, and five-eighths. The purpose is to create an experience of using the fraction strips to represent specific fractions. Once the students are accustomed to connecting fraction words to each representation, I ask them to show one-half and two-fourths to compare the sizes. I share that we are just beginning our fraction investigation.
Fraction strips are kept unfolded in their math folders for use at any time.