Comparing and Ordering Fractions

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Objective

Students will be able to compare fractions in order to build knowledge of benchmark fractions.

Big Idea

A Piece of Cake!

Lesson Author

Erin Doughty

Grand Rapids, MI

Grade Level

Fifth grade

Subjects

Math

Fractions

Standards

5.NF.A.1

Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)

5.NF.A.2

Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7 by observing that 3/7 < 1/2.

MP1

Make sense of problems and persevere in solving them.

MP3

Construct viable arguments and critique the reasoning of others.

MP4

Model with mathematics.

MP6

Attend to precision.

Opener

15 minutes

In this lesson students will be using Fraction Piece Models to compare and order fractions. Students will then draw similar models to justify their reasoning of relative sizes of fractions.

To activate student thinking, I display a question to the students and have them discuss their thinking with a partner.

What is the difference between 1/3 of a large pizza and 1/3 of a medium pizza? Is there a model that would aid in your thinking?

The goal is that students rationalize that the size of the whole can change and therefore a fraction of something can have a different value(MP 3 and 4).

Practice

30 minutes

Students will be a completing a hands-on investigation using Fraction Piece Models. The investigation is taken from NCTM’s Illuminations website. Each student is provided with a set of Fraction Pieces and a copy of the investigation. Students complete the investigation individually but may ask questions to neighbors and discuss observations.

While students are completing the investigation I circulate the room and aid in struggling students by helping guide them in their thinking.

Closer

15 minutes

Justify, justify, justify!

Although Fraction Piece Models are a great tool to use when building knowledge of fractions students will not always have these tools as a manipulative to use. In that case, it is important that students are comfortable drawing models of fractions.

To close this activity I bring students back to a whole group setting and model how to draw models for problems similar to what they just completed. I have them use their whiteboards to model with me. I do a few examples of how to draw two fraction sticks and then I give students a few problems to do on their own.

What fraction is bigger, 2/3 or 1/2? Use a model to justify your thinking.

What fraction is smaller, 2/5 or 2/4? Use a model to justify your thinking.

What is the order of these fractions from least to greatest, 1/4, 4/5, 3/4? Use a model to justify your thinking?

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