Objectives
Students should understand and explain that if two fractions represent the same whole and have the same denominator, their sum is represented by joining end to end the segment of length for one fraction to the segment of the length represented by the second.
Vocabulary
properties of addition
As students observe what is happening in this file, help them focus on how subtraction is represented on the number line.
Have students illustrate the subtraction on number lines they have drawn. Then have them model the subtraction on the interactive number lines.
In how many ways can you decompose (5/4) into the sum of two fractions with a denominator of 4?
Answer: (1/4)+(4/4); (2/4)+(3/4); (0/4)+(5/4).
Subtracting fractions with like-denominators can be thought of as taking away the number of copies of (a/b) from the number of copies of (c/b). Adding two fractions with like-denominators is the same as joining the first segment (a/b) end to end with the second segment (c/b).
Students explore adding and subtracting fractions with the same denominator by using an interactive number line.
Use the interactive number line to explain why the sum of two fractions has the same denominator as the addends. Guide students in understanding that the denominators of the fractions are not added.
