standard_description: 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?
problem_activity: Narrative
The purpose of this activity is for students to analyze pairs of fractions to determine if they are equivalent. Students may use any representation that makes sense to them. Students will create a visual display and have a gallery walk to consider the different ways of looking for equivalence. Highlight representations such as diagrams and number lines, which will support students as they learn to compare fractions with the same numerator or denominator in this section.
This activity uses
MLR7 Compare and Connect. Advances: representing, conversing
Engagement: Develop Effort and Persistence.
Invite students to generate a list of shared expectations for group work. Record responses on a display and keep visible during the activity.
Supports accessibility for: Social-Emotional Functioning
Required Materials
Materials to Gather
Materials for creating a visual display
Launch
Groups of 2
“Decide if these pairs of fractions are equivalent and show your thinking for each one. You can use any representation that makes sense to you.”
Activity
3–5 minutes: independent work time
“Share your ideas with your partner.”
2–3 minutes: partner discussion
MLR7 Compare and Connect
“Work with your partner to create a visual display that shows your thinking about
\(\frac{4}{6}\)
and
\(\frac{5}{6}\)
. You may want to include details such as notes, diagrams, drawings, and so on, to help others understand your thinking.”
Give students materials for creating a visual display.
2–5 minutes: partner work time
5–7 minutes: gallery walk
Student Facing
Are these fractions equivalent? Show your thinking using diagrams, symbols, or other representations.
\(\frac{1}{2}\)
and
\(\frac{1}{3}\)
\(\frac{4}{6}\)
and
\(\frac{5}{6}\)
\(\frac{3}{4}\)
and
\(\frac{6}{8}\)
Student Response
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Advancing Student Thinking
If students don’t determine whether or not fractions are equivalent, consider asking:
“What do you know about these fractions?”
“How could you use your fraction strips or diagrams to decide if they are equivalent?”
Activity Synthesis
“What are the different representations we can use to decide if
\(\frac{4}{6}\)
and
\(\frac{5}{6}\)
are equivalent?” (diagrams, number lines)
“How did each representation show that
\(\frac{4}{6}\)
and
\(\frac{5}{6}\)
are not equivalent?” (In the diagram, you can see that
\(\frac{5}{6}\)
has more space shaded. On the number line, they are not at the same location.)


aligns: no