Something we did much earlier in the year was to compare different numbers, and remember that we learned something about an alligator mouth. Who can remind me about why the alligator opens his mouth? (He opens his mouth for the larger number.) Well I’m glad you remember that, because you’re going to need to use that knowledge today when we compare fractions!
One thing I always get tricked by is thinking the bigger number means that something is actually bigger. But in fractions, a bigger numbers means I’m breaking something into more pieces, or I’m having to make more pieces. Thankfully, there are things that I can draw or use that help me figure out which part of a set or whole is actually larger or smaller than another part.
We pause to review the greater than, less than and equal to symbols. I have a few problems on the board that we will solve together to explore comparing fractions.
I give each student Fraction Strips to cut out so that they can use them to make sense of the work ahead.
Now, who can help me with this problem - Trina and Cal are painting two walls that are the same size and shape. It is important to emphasize here that the walls are the same size. If the walls were different sizes than we would be comparing a different quantity. Trina has painted ¾ of one wall. Call has painted 2/5 of the other wall. Who painted more of the wall, Triana or Cal?
I model this problem by drawing fraction strips on the board. How much of the wall did Trina paint? (3/4). What fraction strip can you use to show that part of the wall? (The ¼ strip). How many parts of the strip do you need to color to show ¾? (3) Give students time to color ¾ of the strip, if the have not already done so. Repeat for the 2/5 of the wall Cal painted. Compare the colored parts of the strips. Which colored part is longer? (3/4). So which is greater? Who painted more?
It is important to emphasize the use of fractions to solve real world problems (MP4) and to be able to use tools like fractions strips to represent their parts. I also spend time using word problems to help students solve problems, because they must first understand what the problem is asking them to do, and then they must apply their understanding and the tools they have for problem solving in order to complete it (MP1).
Sometimes, the fractions I’m comparing don’t have the same denominator. What is a denominator? What does it represent?
I always stop when I use the academic vocabulary to do a quick review of what it means and to put it into context. If what I'm teaching is dependent on an understanding of the vocabulary, it is important that I make a concrete connection for students.
Am I still able to compare numbers if they have different denominators? I’m glad you know that we can, because today you’re going to be the authors of some very important math problems comparing fractions. This is the example that I wrote. What tools do I have that will help me solve it? I expect students to say they can use fraction strips or draw a model
You will be writing word problems today to compare fractions. You will need a word problem, a model or picture, and then the steps you used to solve it. Make sure your work is your very best, because I want to showcase your hard work outside in the halls for all of the other students to see!
I always make a very big deal about celebrating student work. We incorporate celebrating our work in every subject, each day. At times I allow students to come up to share and we do a quick celebration cheer and other times we display it outside of our class. Students develop a sense of pride in their work and feel their work is meaningful when we share it.
Your work today was exceptional. I am so impressed by the word problems that you were able to create and model.
I have one last problem on the board that I’m going to need your help with, and I’m going to need you to think about what you know about comparing fractions in order to solve it! (MP1)