standard_description: Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
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.)


aligns: no