Lesson on Multiplying Fractions Greater or Less Than One

Improper Fractions
Teaching math should be a lot of fun!

So, sometimes I find a random standard and think about lessons I could do to teach those. I find the exercises not only help inspire me as to why I’m working on a standards alignment tool, but also help me think about new ideas in general! Obviously this would be one lesson in a series teaching the concept and doesn’t cover the whole standard!

Lesson Title: Prove your Classmates Wrong! (Horrible title but… something…)

Time: About 40 minutes

Standard: 5.NF.5.b Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1.

Objective: Help students understand rules of multiplying by fractions greater than or less than 1.

ELD: Use visual clues and small group discussion to help students understand the rules of multiplying by fractions greater than or less than 1.

Technology: None.

Materials: Different colored notecards are a plus; clothesline or whiteboard will do. the numbers 0, 1, and 2 affixed for a standing number line activity.

Narrative: Hand students different colored cards in their table groups. Have group 1 write a fraction less than 1 and group 2 write a fraction greater than 1 and less than 2. Numerators and Denominators have to be less than 100 as well.

Iteration 1: A few kids come up to the board to show on the number line where their number would be.

Iteration 2: Have students multiply Group 1 and Group 2 fractions and see what happens – have those students then go up to the number line and explain what numbers were multiplied and if the end result number was less than or greater than the previous two numbers.

Iteration 3: Have students multiply with the SAME Group and a sample from each group comes up. Ask different students to summarize what they’re noticing.

Create three groups: Have students in the same fraction-type groups summarize their findings – ask what happens when fractions less than one are multiplied together, fractions greater than 1 are multiplied together, and make a third mixed group that tackles happens when a number less than 1 and a number greater than 1 are multiplied together.

After a few minutes have each group summarize their hypothesis in writing and.

Now rotate the written hypotheses within the groups. The new group is going to spend some time trying to find a counterexample to the hypothesis – kids love it if you say “TRY TO BREAK THE HYPOTHESIS!”.

After a few minutes of trying to find a counterexample, kids usually aren’t able too but this gives all students a chance to try a set of numbers that wasn’t theirs originally hopefully in a way that is motivating as well.

Now do one example on the board of each type of operation and have students see what is going to happen. Talk about the power of knowing what SHOULD happen as way to check their work… that is, if they are multiplying 3/4 by 1/2 and they get a number larger than 1, they know they did something wrong.

Closure: Write an example set of 3 questions on the board that cover various cases. Have students write those answers on the back as an exit ticket to hand in as they leave the classroom.

Sample:

1 and 2/5 multiplied by 4/5

3/7 * 9/10

5/4 * 1/8

1 thought on “Lesson on Multiplying Fractions Greater or Less Than One”

  1. If that’s the standard, it’s erroneous. If x is the number being multiplied by a positive fraction greater than 1, the claim is false if x is negative, 0, or 1.

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