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 determine how a number line is partitioned and what fraction is marked on it with only 0, 1, and 2 labeled. Students partition and locate and mark, but don’t label, a fraction on a number line and then trade with a partner to determine the fraction their partner has marked. Remind students to mark, but not to label their partitions and their fraction, so that their partner only has the 0, 1, and 2 to use to determine what fraction is on their number line.
Launch
Groups of 2
“Complete the first part of the activity on your own. Partition the number line and mark, but don’t label, a fraction on the number line. Don’t tell your partner how you are partitioning or what number you are marking.”
2 minutes: independent work time
Activity
“Now, trade number lines with your partner and answer the questions about their number line. When you are both finished, share your reasoning”
1–2 minutes: independent work time
1–2 minutes: partner work time
Student Facing
Partition the number line into any number of equal-size parts. Locate and mark, but don’t label, a fraction of your choice.
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Trade number lines with a partner.
How did your partner partition their number line?
What number did your partner mark on their number line? Explain your reasoning.
If you have time, play the game again.
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Student Response
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Activity Synthesis
Display a number line partitioned by a student.
“Talk to your partner about what fraction is represented.”
Share and record responses.
Consider asking:
“How did you decide how to partition your number line and what fraction you’d put on your number line?”
“How did you decide how your partner’s number line was partitioned and decide what fraction was marked?”


aligns: no