options: Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?

Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. (Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division. But division of a fraction by a fraction is not a requirement at this grade.)

Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.

Interpret multiplication as scaling (resizing), by:
- 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.
- Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.
problem_activity: Narrative
The purpose of this activity is for students to continue to solve problems about dividing a unit fraction by a whole number. The unit fraction in both problems is
\(\frac{1}{2}\)
so that students will consider the relationship between the number of people sharing the macaroni and cheese and the size of the serving each person gets. When students connect the quantities in the story problem to an equation and a diagram representing the story, they reason abstractly and quantitatively (MP2).
Launch
Groups of 2
Activity
1–2 minutes: independent think time
5–8 minutes: partner work time
Monitor for students who :
draw diagrams like the ones in the student responses
describe the amount each person gets as a fraction of the whole pan
describe a relationship between the number of people sharing and the size of the serving each person gets
Student Facing
4 people equally share
\(\frac {1}{2}\)
a pan of macaroni and cheese.
Draw a diagram to represent the situation.
Explain how your diagram represents
\(\frac {1}{2} \div 4\)
.
How much of the whole pan of macaroni and cheese did each person get? Be prepared to explain your reasoning.
5 people equally share
\(\frac {1}{2}\)
a pan of macaroni and cheese.
Draw a diagram to represent the situation.
Explain how your diagram represents
\(\frac {1}{2} \div 5\)
.
How much of the whole pan of macaroni and cheese did each person get? Be prepared to explain your reasoning.
How are the problems the same? How are they different?
Student Response
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Advancing Student Thinking
If students do not identify or explain how much macaroni and cheese each person gets, consider asking, “How much of the whole pan of macaroni and cheese did each person get?”
Activity Synthesis
“How are the situations the same? How are they different?” (Both situations are about
\(\frac {1}{2}\)
a pan of macaroni and cheese, but this one has more people sharing it, so each person gets less macaroni and cheese. When 4 people share, each person gets
\(\frac {1}{8}\)
of the whole pan. When 5 people share, each person gets
\(\frac {1}{10}\)
of the whole pan.)


correct_option_index: 2