Lesson Plan

Dividing Fractions

An exercise in inverting one’s thinking
Darri S.
Senior Director, Education Content Common Sense Education
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Objectives

Students will be able to...

  • determine the inverse/reciprocal of an integer or fraction
  • outline the steps for dividing one fraction by another
  • apply the steps for finding the quotient of two fractions 
Subjects
Math
Grades 6 - 8
All Notes
Teacher Notes
Student Notes

1 Hook

Slice It!
Free, Paid

Review the concept of fractions – part of a whole – with Slice It! Have students test their spatial skills by splitting unconventional into equal parts. Reinforce key vocabulary such as numerator, denominator, and equivalent.    

2 Direct Instruction

In order to understand how fractions are divided, ask students to reconceptualize integer division problems. For instance, when trying to solve 12 ÷ 3, show that you are actually trying to figure out how much 1/3 of 12 is. For division problems, fractions and otherwise, we are actually multiplying by the inverse 12 ÷ 3 = 12 x 1/3. This tactic will set the foundation for more complex problems. Next, demonstrate how to apply this procedure to dividing an integer by a fraction: 2 ÷ 4/5 = 2 x 5/4 or 2/1 x 5/4. Finally, apply this process to dividing one fraction by another: 3/5 ÷ 1/4 = 3/5 x 4/1. Again, the rule of thumb is: find the inverse (or reciprocal) of the divisor (second number), then multiply. Show Khan Academy’s video, Dividing Fractions (8:59). Follow up with several practice problems, and try to apply to real world examples. When possible, diagram the quotients with rectangles to show how to simplify the answer (especially when changing improper fractions into mixed numbers). Make sure to introduce key vocabulary as necessary: inverse, invert, reciprocal, dividend, divisor, quotient.

3 Guided Practice

ExploreLearning Gizmos
Free to Try, Paid

Have students work in small collaborative groups to experiment with Explorelearning’s Dividing Fractions Gizmo (http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=1006). This interactive will give students a visual model to help explain the rule for dividing fractions (find the inverse of the divisor, then multiple). Together, students should answer the accompanying Student Exploration: Dividing Fractions packet.

4 Independent Practice

Have students create their own tutorial videos for dividing fractions with Educreations Interactive Whiteboard. They can record themselves explaining the problem solving process, including any tips and hints they value. They can end with challenging practice questions for fellow classmates.

5 Wrap-Up

Mangahigh
Free, Free to Try, Paid

Student can play with Managhigh’s Division with Fractions game, receiving scaffolded support as they go. Players earn more points with increased speed, increased difficulty (three levels), and by solving three problems in a row.