few_shots: Example:
Problem/activity:
You’re mixing ingredients for cookies. The recipe says to combine 6 tablespoons, or ¾ stick, of butter with 1 cup of sugar. You accidentally mix in a whole stick of butter (8 tablespoons) with the cup of sugar. How can you fix this?


Standard options: 
A. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.”
B. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
C. Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.” (Expectations for unit rates in this grade are limited to non-complex fractions.)


Your response:
Thought: This problem solves a real-world problem involving mixing ingredients for cookies. A student doing this problem would need to reason about equivalent ratios of butter amounts to sugar amounts.
Answer: B

Now, assign the following problem or activity to one or more relevant standards it aligns with.
shot_info: fl_problem_000972

6
options: Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.

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.
Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.

Understand a fraction as a number on the number line; represent fractions on a number line diagram.
Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.
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.)


correct_option_index: 0