Today we are going to talk about 5 strategies for comparing fractions. Discussing and exploring each of these strategies with your students provides them with some great tools for comparing fractions as well as builds their number sense and understanding of fractions. The visual is key to students understanding. I believe using actual manipulatives that students can touch and move is ideal. If you prefer, you can print and laminate a set of fractions tiles for free.
Begin by having students line up all of the fraction tiles. Have students write down everything they notice.
- As the denominator gets bigger, the size of the pieces gets smaller
- The colors are all different
- There are no 7ths, 9ths or 11ths
- The number in the denominator is the same number of pieces it takes to make a whole
Have a class discussion about everything that students came up with and write all responses on the board.
On the board write:
Number if pieces (numerator)
Size of the pieces (denominator)
Have a discussion with students that the numerator tells us how many pieces we have and the denominator tells us how big the pieces are. For example, if we have the fraction ⅔, the two tell us that we have 2 pieces that are the size of 3rds.
Strategy 1: Common Denominator
If the denominator is the same, you can compare the numerator which tells us the number of pieces. If we are comparing 3/12 and 7/12, we can see that 7/12 is bigger because the pieces are the same size and 7 is more than 3. Have students compare several fractions where the denominators are the same. For example, 4/5 and 2/5, 3/10 and 4/10.
Strategy 2: Common Numerator
If the numerators are the same, you can compare the denominators (the size of the pieces). The smaller the denominator, the larger the piece. For example, if we compare 2/3 and 2/5, we can see that both fractions have 2 pieces but since thirds are larger pieces, 2/3 is greater than 2/5. Have students compare several fractions where the numerators are the same. For example, 4/10 and 4/8, 1/6 and 1/8.
Strategy 3: Compliments
Line up the fractions bars and remove one fraction tile from each whole. Have students look at the fraction bars and discuss what they notice. Guide students to notice that the fractions at the bottom are larger because they are missing a smaller piece. Have a discussion with students about this. Have students compare 7/8 and 11/12. 11/12 is bigger because it is missing a smaller piece and therefore leaving more.
Strategy 4: Benchmark to 1/2
For this strategy, we will be compare our given fractions to 1/2. Have students take the 1/2 fraction bar out and we will put one fraction above and one fraction below. First we will compare 3/8 and 6/10. Discuss how 3/8 is less than 1/2 (4/8) and 6/10 is greater than 1/2 (5/10). Therefore, 6/10 is larger.
It gets a little trickier when both fractions are greater than or less than 1/2. For example, let’s compare 5/8 and 6/10. Both fractions are greater than 1/2. Therefore, we have to look at how much greater they are to 1/2. 5/8 is 1/8 greater and 6/10 is 1/10 greater. Since 1/8 is larger than 1/10, 5/8 is greater than 6/10.
When both fractions are less than 1/2 we have to think carefully. Let’s compare 4/10 and 5/12. Both fractions are less than 1/2. 4/10 is 1/10 less than 1/2 and 5/12 is 1/12 less than 1/2. Since 1/10 is “more less than” 1/2, it is smaller. Therefore, 4/10 is less than 5/12.
Strategy 5: Common Sense
Sometimes when we compare fractions, common sense tells us which fraction is larger. For example, if we look at 1/8 and 3/4 we could say that 3/4 is larger because it is close to 1 whole and 1/8 is closer to 0. Give students some examples to try and have them discuss their reasoning on why one fraction is larger than the other.
I hope you enjoy all of the great math discuss that take place with exploring these strategies with your students. I would love your feedback! Please comment below with any questions or comments.