Learning Goal
Interpret and compute quotients of fractions
Teacher tools for this standard
Lesson Plan · Guided Notes · Exit Ticket · Re-teach · Homework
Teacher tools for this standard
Lesson Plan · Guided Notes · Exit Ticket · Re-teach · Homework
- Lesson Plan →Objectives, pacing and practice, built from this lesson's brief.
- Guided Notes →One page your students fill in and keep.
- Exit Ticket →Three items at the end of class. No student accounts.
- Re-teach →After an exit ticket: who missed what, and what to do tomorrow.
- Homework →Assign practice; it grades itself.
Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) / (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) / (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) / (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?
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Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) / (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) / (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) / (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?
What you'll learn
- Interpret a fraction division problem as either *measurement* division (how many groups of the divisor fit in the dividend) or *partitive* division (size of one group when the dividend is split equally), and identify which interpretation a word problem calls for.
- Use a visual fraction model -- number line, bar model, or area model -- to represent and find the quotient of two fractions.
- Use the relationship between multiplication and division -- *(a/b) / (c/d) = q* if and only if *q x (c/d) = a/b* -- to verify and explain a fraction quotient.
- Compute *(a/b) / (c/d) = (a/b) x (d/c) = ad/bc*, recognizing the rule as a consequence of multiplying by the reciprocal of the divisor.
- Solve word problems involving division of fractions by fractions, including the three contexts named by the standard (sharing equally, counting servings, finding a missing dimension).
- Recognize that when the divisor is between 0 and 1, the quotient is *larger* than the dividend -- and explain why using the measurement interpretation.
Slides
Step through the lesson, or watch it as a narrated video • 2 slide decks
Fraction division meaning
✓ Start hereFraction division procedure
Practice
Try it on your own