Comparing Fractions with Common Denominators & Common Numerators

If students understand what a fraction is and have a good understanding of comparing unit fractions, comparing fractions with a common denominator and numerator will be a confidence booster!

Check out these previous posts:
Fractions Introduction
Unit Fractions

Like I’ve said in my previous post, first, I get students to practice by using fraction bars and then we move onto comparing using number lines. I have found that making students prove their conclusion with a picture and with a sentence has helped their understanding of fractions and helped boost their confidence with fractions! After ample amount of practice, we move away from both.

Practice using Number Lines: Common Denominators

When comparing fractions that have the same denominator, they are same size pieces. Because they are the same size, we look at the numerator, which tells us how many pieces there are. When comparing fractions with a common denominator, the more pieces it has, the larger the fraction.

Activity Idea: Fraction Memory Match

Directions
1) Lay out the cards, face down, in a 4 x 3 array
2) On your turn, turn two cards face up
3) If the denominators match, compare the fractions, explain your comparison, and take the cards
4) If the denominators don’t match, turn the cards back face down

 

Sentence Stem
5/8 is larger than 2/8. They have a common denominator (same size pieces), so we need to look at the numerator, (the number of pieces). 5 pieces is more than 2 pieces.”

 

Practice using Number Lines: Common Numerators

When comparing fractions that have the same numerator, they have the same number of pieces. Because of this, we look at the denominator, which tells us how big the pieces are or the size of the piece. When comparing fractions with a common numerator, the smaller the denominator, the larger the fraction.

 Activity Idea: Fraction War
Directions
1) Players will split up the fraction cards
2) Flip over one fraction card
3) The player with the larger fraction needs to explain why they have the larger fraction. They will take the card if they explain correctly
4) Try to collect the most fraction cards

Sentence Stem: “2/9 is larger than 2/12. They have a common numerator (the same number of pieces), so we need to look at the denominator, (the size of the pieces). Ninths is larger than twelfths.”

Here is another game for comparing fractions with a common numerator. Click here if you’re interested!

Timeline:
1) Introduce Fractions: 1 day
2) Unit Fractions: 1 day
3) Comparing fractions with a common numerator // common denominator: 1 day
4) Mix comparing fractions + introduce making half: 1 day
5) Mix comparing fractions + making half practice + comparing to a half: 1 day

As you can see, I continue to spiral the skills. Spiral practice is very important. One day, I will post my routine for daily math review and daily spiral review. I make time to do both, because both are very important!

This is a part of our fraction series. Check out these other blogposts for more!

– http://mustardseedteaching.com/fractions-introduction/
– http://mustardseedteaching.com/pizza-fractions-unit-fractions/
– http://mustardseedteaching.com/making-half/

How do you teach comparing fractions in a conceptual way?

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