What's in the Set?

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Objective

SWBAT apply their understanding of fractions to various sets of objects.

Big Idea

A fraction is made of parts of a whole, or set, and are found all around me.

Intro

10 minutes

One thing I noticed last night when I was baking cookies was that fractions are all around us! I made pizza for dinner, and I had to cut it into 8 slices. They had to be equal so Mr. Maffei got the same amount of pizza as I did. Fractions! They're everywhere.

Then I decided to bake cookies! I realized that I broke 2 out of 12 of them. That's a fraction -- 2/12 were broken.

I want you all to take a minute to look around our classroom, and see the things all around our room that can be described as fractions. Don't tell anyone what you see, give us your problem and see if we can solve it! 

I am checking to ensure that students are thinking about parts of a whole, not just groups of things. Students are posing questions such as: "What fraction of the tables in our room are rectangle? What fraction of college pennants are from schools Mrs. Maffei attended? What fraction of bulletin board have red on them?"

I also am looking to make sure they know the total, and what part they are identifying. I ask other students to answer each question that a student poses to draw them into the lesson and ensure students can explain their thinking. Students should be able to apply math to solve problems in everyday life (MP4) so I ensure we spend the time to explore this.

Warm-Up Questions

5 minutes

I need your help with these 2 pictures on the board. I can’t quite tell if they’re all fractions, and I’m having trouble figuring out what the answers are. I show students 2 pictures for each fraction that I've drawn on the whiteboard. I give students some quiet think time, and then we're ready to discuss.

We discuss why example 1 has one correct answer, because only 1 picture has equal parts. In the 2nd example, I expect students to struggle. I encourage a little back and forth time for students to defend their answer of why they are both half, or why only 1 is half (MP6)

Station Rotation

35 minutes

I know it’s been a little while since we have rotated between stations, but there is so much to learn about fractions that I think we need to practice what we know in all of these ways!

I do station rotations sometimes when I want students to have a given amount of time to practice seeing a concept or idea in different ways. Today we have 4 stations that students will rotate between.

-Pattern Block/Sea Animal/Manipulative Station: Students take a pre-made bag of manipulatives and create fractions to represent what is in the bag. They are creating models using the tools available to them to represent fractions within their set (MP5).

 

If done correctly, students should recognize that within each bag there is the same denominator (MP7). Students can classify what is in the bag however they want, there are many ways to show parts of a set with fractions. Remember, labeling is important when we show our work.

-Fraction Pie Station: Students will create a whole by using fraction pies. The goal is for students to see that each piece of a fourth represents ¼ and that if they have ¼, ¼, ¼ and ¼ they have a whole. This is repeated for all fractions up to 1/10.  

-Problem Solving Station: I use word problems from the Motivation Math workbook that ask students to think about fractions within word problems, from visual examples and with open ended and multiple choice options for solving. I believe that students need to see concepts within word problems so that they can understand the language, show their steps for problem solving and show mastery in a variety of ways.

Close

5 minutes

What I noticed today about your work was that you are finding fractions everywhere, like I was last night! Math is all around us, and fractions are things that we can see all around us, too. With fraction pies, problem solving and even dinosaurs we can show parts of a whole. Who can share something they noticed about fractions today?

Here I want students to describe the differences between a set of objects (dinosaurs and other math tools) and how fractions within that set can be created and what fractions look like as part of a whole (fraction pies).