Lesson Plan: Fraction Word Problems

Lesson Objectives

  • Understand how to interpret and solve fraction word problems
  • Apply strategies for solving fraction word problems
  • Compare and contrast different fraction representations in word problems

Common Core Standards

  • 3.NF.A.1 - Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.
  • 3.NF.A.3.D - Compare two fractions with the same numerator or the same denominator by reasoning about their size.
  • 4.NF.A.2 - Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2.

Prerequisite Skills

  • All prior fraction concepts
  • Basic problem-solving

Key Vocabulary

  • Word problem

Warm-up Activity (5 min)

Practice converting verbal statements into fraction expressions:

"One out of three."1/3
"Three out of four items"3/4
"There are total of five items. Two of them are selected."2/5

For each verbal statement that can be written as a fraction, identify which word corresponds to the numerator and which corresponds to the denominator.

Teach (15 min)

Analyze fraction word problem examples:

Example 1. Present this word problem:

"A pizza is divided into 8 slices. You and your friends eat 5 slices. What fraction of the pizza is left?"

Use this slide show to show the complete pizza and the partially eaten pizza:

https://www.media4math.com/library/slideshow/pizza-fractions-example-1

  • Show the full pizza divided into eight slices. Reinforce that this is the whole and becomes the denominator of the fraction.
  • Then show the slide that shows the three slices. This is the part of the whole and becomes the numerator of the fraction. 
  • Use this information to model the fraction of the pizza left: 3/8.
  • Ask students to determine what fraction of the pizza that was eaten: 5/8.

Example 2. Present this word problem:

"A pizza is divided into 6 slices. You and your friends eat 2/3 of the pizza. How many slices did you eat?"

Use this slide show to show the complete pizza and the partially eaten pizza:

https://www.media4math.com/library/slideshow/pizza-fractions-example-2

  • Show the full pizza divided into six slices. Point out to students that since 2/3 of the pizza has been eaten, that only 1/3 of it remains.
  • The next slide shows one third of a pizza remaining. Notice that this pizza is divided into thirds.
  • The next slide that shows one third of the pizza when the pizza is divided into six slices. Point out that this is equivalent to the one third. Go back and forth from one slide to the other.
  • Use this information to model the fraction of the pizza left: 2/6.
  • Finally show that 1/3 and 2/6 are equivalent fractions by factoring a two from the numerator and denominator of the second fraction.

Example 3. Present this word problem:

"Maria has a bag of 20 candies and she eats five of them. Isaac has a bag of 25 candies and also eats five of them. Who ate the larger fraction of candies?"

Use the information from the problem to complete this table:

 

 

Number of Candies Eaten

Total Number of Candies

Maria

5

20

Isaac

5

25

 

Use the information to find the fractional amount each child has eaten:

Maria: 5/20 = 1/4

Isaac: 5/25 = 1/5

Since these are unit fractions, the one with the smaller denominator is the larger fraction. This means Maria ate the larger fraction of candies.

Review

Provide additional fraction word problems for students to solve in pairs or small groups, such as:

  • "A pizza is divided into 10 slices. You and your friends eat 7 slices. What fraction of the pizza is left?"
  • "A case of sodas has 24 cans. What is the minimum number of sodas that need to be consumed before you can say that more than half of the sodas have been drunk?"

Encourage them to discuss their thought processes and strategies with each other.

Assess

Give students the following 5-question quiz to assess their understanding of solving fraction word problems. 

Quiz

  1. A pizza is divided into 6 equal slices. You and your friends eat 4 slices. What fraction of the pizza is left?
  2. There are 25 candies in a bag. You and your friends eat 15 of the candies. What fraction of the candies have been eaten?
  3. In a game of bowling, there are 10 pins in total. You knock down 6 pins. What fraction of the pins did you knock down?
  4. A rectangular pizza is cut into a 4 by 5 array of slices, making 20 slices total. You and your friends eat 15 slices. What fraction of the pizza did you eat?
  5. There are 3 dozen cookies (36 total). You eat 1/4 of the cookies, and your friend eats 1/6 of the cookies. What fraction of the cookies is left?

Quiz Answers

  1. 2/6 or 1/3
  2. 3/5
  3. 6/10 or 3/5
  4. 3/4
  5. 5/12

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