To assess students' prior knowledge, invite students to reflect on the previous lesson. Ask them to describe what they have learned about fractions using the length model.
To begin the lesson, give students one set of relationship rods (either homemade or commercial) and a copy of the Investigating Equivalent Fractions Activity Sheet.
Review the work done yesterday by designating one of the rods/colors as the whole and finding the value of all the rods when this color is the whole. For example, if brown equals one, what value would you assign to all the other rods? Discuss student responses as a class.
Demonstrate the correct answer by lining up the two relationship rods being compared on an overhead projector, or by using the Integer Bar Applet
When comparing the lengths for demonstration purposes, the smaller length should be duplicated to simulate the length of the longer rod.
For example, when comparing red to brown, where brown is one, four red relationship rods should be used to directly compare to one brown. Students can easily see that it takes four reds to make one brown; therefore, if brown = 1, then red = 1/4.
Challenge students to determine the value of the rods when two rods are used to make a new rod. For example, orange and yellow might be combined to make orange/yellow.
Have students consider the value of all the other relationship rods if orange/yellow = 1 (one).
[Students should determine that white = 1/15, red = 2/15, light green = 3/15, purple = 4/15, yellow = 5/15 or 1/3, dark green = 6/15 or 2/5, black = 7/15, brown = 8/15, blue = 9/15 or 3/5, and orange = 10/15 or 2/3.]
Ask students to take out one brown rod to use as the whole. Ask them if they can find another color that they can use in duplicate to generate the same length as the brown rod. Begin with the white rod and demonstrate using various rods until students understand what they are expected to do.
For example, ask students if white rods can be used to create the same length as brown. If so, how many lengths are needed to do this? Students should discover that it takes eight white rods to make one brown. Students should model this relationship as follows:
Ask students if there is another color that can be used in duplicate to generate the same length as the brown rod. Students might discover that four red rods are the same length as one brown rod, or two purple rods are the same length as one brown rod. Have students line up one color and then the other as follows:
Have students name as many fraction relationships as possible. For example, students might note that when brown is equal to one, white is 1/8, red is 2/8 or 1/4, and purple is 4/8 or 1/2. From this observation, students might identify the following fraction relationships:
2/8 (2 white rods) = 1/4 (1 red rod) OR
4/8 (4 white rods) = 2/4 (2 red rods) = 1/2 (1 purple rod)
Ask students if they see any other relationships. Students might indicate that 6/8 (6 white rods) is the same as 3/4 (3 red rods).
Students might also discover that 8/8 (8 white rods) is the same as 4/4 (4 red rods) and 2/2 (2 purple rods) and 1 (1 brown rod). Tell students that when two fractions are the same length, they are equivalent. Explain that when comparing equivalent fractions, the group with the smallest number of rods represents the fraction in lowest terms.
Have students identify the fraction that is in lowest terms from each of the equivalent groups mentioned above.
Students should identify that when comparing 2/8 and 1/4, 1/4 uses fewer rods and is in lowest terms. Similarly, when comparing 4/8, 2/4 and 1/2, 1/2 uses fewer rods and is the fraction in lowest terms. When comparing 6/8 and 3/4, 3/4 is the fraction in lowest terms.
Ask students to work with a different “whole” to find equivalent fractions. Suppose the orange rod is equal to one. Have students line up various colors in duplicate to generate the same length as the orange rod. Students should include white, red, and yellow rods in their comparison.
Have students name as many equivalent fractions as possible. They should identify the following equivalent fractions:
2/10 (2 white rods) = 1/5 (1 red rod)
5/10 (5 white rods) = 1/2 (1 yellow rod)
6/10 (6 white rods) = 3/5 (3 red rods)
8/10 (8 white rods) = 4/5 (4 red rods)
10/10 (10 white rods) = 2/2 (2 yellow rods) = 1 orange
Have students identify the fraction that is in lowest terms from each of the equivalent groups named above.
Students should identify that when comparing 2/10 and 1/5, 1/5 uses fewer rods and is in lowest terms. Similarly, when comparing 5/10 and 1/2, 1/2 uses fewer rods and is the fraction in lowest terms. When comparing 6/10 and 3/5, 3/5 uses fewer rods and is in lowest terms. When comparing 8/10 and 4/5, 4/5 uses fewer rods and is in lowest terms. When comparing 10/10, 2/2 and 1, 1 uses fewer rods and is in lowest terms.
Have students continue working through the questions on the Investigating Equivalent Fractions Activity Sheet. This activity gives students additional experience finding equivalent fractions using the blue rod as the whole and the dark green rod as the whole. Students should line up their relationship rods as follows for each of the various "wholes."
Students should discover the following equivalent fractions when blue is used as the unit (whole):
3/9 (3 whites) = 1/3 (1 light green)
6/9 (6 whites) = 2/3 (2 light greens)
9/9 (9 whites) = 3/3 (3 light greens) = 1 (1 blue)
Have students identify the fraction that is in lowest terms from each of the equivalent groups named above.
Students should identify that when comparing 3/9 and 1/3, 1/3 uses fewer rods and is in lowest terms. When comparing 6/9 and 2/3, 2/3 uses fewer rods and is the fraction in lowest terms. When comparing 9/9, 3/3 and 1, 1 uses fewer rods and is in lowest terms.
Students should discover the following equivalent fractions when dark green is used as the unit (whole):
2/6 (2 whites) = 1/3 (1 red)
4/6 (4 whites) = 2/3 (2 reds)
3/6 (3 whites) = 1/2 (1 light green)
6/6 (6 whites) = 3/3 (3 reds) = 2/2 (2 light greens) = 1 (1 dark green)
Have students identify the fraction that is in lowest terms from each of the equivalent groups named above.
Students should identify that when comparing 2/6 and 1/3, 1/3 uses fewer rods and is in lowest terms. When comparing 4/6 and 2/3, 2/3 uses fewer rods and is the fraction in lowest terms. When comparing 6/6, 3/3, 2/2 and 1, 1 uses fewer rods and is in lowest terms.
