Comparing Fractions Using Benchmarks

by Math Solutions Professional Learning Team, February 08th, 2017

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The benchmark of a 1/2 on a number line is perhaps one of the most important visual tools in building fraction sense. With the aid of either of a number line or pie chart (or both!), we suggest a visual aid with a fraction question so that students may connect abstract and concrete reasoning.

Try this class activity with your class as you begin your fraction discussions and number talks. Students will exercise sense-making with an added emphasis on patterns to learn how repetition can be a useful tool in learning and mastering fractions.

Open your lesson by asking students: “If I have 1/4 of something, how much more do I need to make a half?”

1/4 + ? = 1/2

Once students reach the answer of 1/4+1/4=1/2, move to another question with a different denominator. As you continue, remind your students that patterns are very important in math, and that they should looks for patterns in the fractions you are solving for. Invite your students to raise their hand if they notice a pattern, so they may explain to the class, as well as provide a strategy for reasoning.

 “If I have 1/3 of something, how much more do I need to make a half?”

1/3+ ? = 1/2

Once a student brings up the need for a common denominator, progress to:

1/3+1/6 OR 2/6+1/6+3/6 = 1/2

Progress throughout an entire number line with finding the 1/2 for these fractions:

1/2 + ? = 1/2
1/3 + ? = 1/2
1/4 + ? = 1/2
1/5 + ? + 1/2
1/7 + ? + 1/2
1/8 + ? = 1/2
1/9 + ? = 1/2
1/10 + ? =1/2

What other problems do you suggest for introducing 1/2 as a benchmark? Share your ideas with us in the comments!


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