• building conceptual understanding
• # 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!

How do you teach comparing fractions in a conceptual way?

• building conceptual understanding
• # Pizza Fractions – Unit Fractions I always start with this activity as a foundation for comparing unit fractions. Every year, this activity is a huge hit with my students! Fraction Pizza Activity: Team Challenge Group students into groups of 4 and put the timer on for 30 minutes. 1) Work with your group to make pizzas 2) Everyone will be assigned […]

• best teaching practices
• # Fractions Introduction Start off with a quick conversation to activate prior knowledge *tip: have visual pictures available for students to see “Where and where do we use fractions in everyday life?” on the highway, music, shoe size, cooking, pizza, etc “What does ½ mean to you?” there are two total pieces and one is shaded “What does […]

• resources
• # Hedbanz Game I love the recent hit activity Hedbanz. It is an activity that has been around for a while but it is now finding its way around the classrooms. This activity lends itself for great math conversations and engagement, for whichever concept that is being taught. For the concept of writing and solving equations with an […]

• building conceptual understanding
• # Multiplying Decimals | Why does it get smaller? We were doing a lesson on multiplying decimals with models when a student asked a question: “Why does our answer get smaller if we’re multiplying?” Great question! This makes us stop and think “How are we teaching the basic understanding of multiplication?” Is it right for us to be saying ‘the number gets larger when we […]

• best teaching practices
• # Decimal Investigation Building a strong understanding of how our base ten system works is always so important. Taking the time to help students understand this will help with ‘regrouping’ when it comes to adding, subtracting, multiplying, and dividing – it’s worth the time! Ones – Tenths – Hundredths – Thousandths  One whole 1.00 One whole is […]

• real talk
• # “I’m going into the teaching field” What’s the first thought you get when you hear this? We know everyone has different experiences with teaching but we’re sure you can agree with some of these points as a fellow teacher. For reference: Our background = working in a low-income school. After asking the person why they want to become a teacher, our […]