few_shots: 
Example:
Concept/skill: 
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:
Task
Cruz and Erica were both getting ready for soccer.
Cruz ran 1 lap around the school.
Erica ran 3 laps around the playground.
Erica said,
I ran more laps, so I ran farther.
Cruz said,
4 laps around the school is 1 mile, but it takes 12 laps around the playground to go 1 mile. My laps are much longer, so I ran farther.
Who is right? Draw a picture to help you explain your answer.


Answer: 
Yes. This task asks students to compare two fractions that are equal. The students need to explain why the two fractions are equal by drawing a picture, which involves using visual fraction models.

Now, determine whether the following problem or activity can enable students to understand the concepts or skills in the provided description.

shot_info: im_task_000212_pos_0

4
standard_description: Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.
problem_activity: Narrative
This activity serves two main purposes. The first is to allow students to apply their understanding that the result of
\(a \times \frac{1}{b}\)
is
\(\frac{a}{b}\)
. The second is for students to reinforce the idea that any non-unit fraction can be viewed in terms of equal groups of a unit fraction and expressed as a product of a whole number and a unit fraction.
The activity uses a “carousel” structure in which students complete a rotation of steps. Each student writes a non-unit fraction for their group mates to represent in terms of equal groups, using a diagram, and as a multiplication expression. The author of each fraction then verifies that the representations by others indeed show the written fraction. A
s students discuss and justify their decisions they create viable arguments and critiqe one another’s reasoning (MP3).
MLR8 Discussion Supports.
Display sentence frames to support small-group discussion after checking their fraction diagram and equation: “I agree because . . .”, “I disagree because . . . .”
Advances: Conversing
Required Materials
Materials to Gather
Paper
Launch
Groups of 3
“Let's now use the patterns we saw earlier to write some true equations showing multiplication of a whole number and a fraction.”
Activity
3 minutes: independent work time on the first set of problems
2 minutes: group discussion
Select students to explain how they reasoned about the missing numbers in the equations.
If not mentioned in students' explanations, emphasize that: “We can interpret
\(\frac{5}{10}\)
as 5 groups of
\(\frac{1}{10}\)
,
\(\frac{8}{6}\)
as 8 groups of
\(\frac{1}{6}\)
, and so on.”
“In an earlier activity, we found that we can write any fraction as a multiplication of a whole number and a unit fraction. You'll now show that this is the case using fractions written by your group mates.”
Demonstrate the 4 steps of the carousel using
\(\frac{7}{4}\)
for the first step.
Read each step aloud and complete a practice round as a class.
“What questions do you have about the task before you begin?”
5–7 minutes: group work time
Student Facing
Use the patterns you observed earlier to complete each equation so that it’s true.
\(5 \times \frac{1}{10} =  \underline{\hspace{0.5in}}\)
\(8 \times \frac{1}{6} = \underline{\hspace{0.5in}}\)
\(4 \times  \underline{\hspace{0.5in}} = \frac{4}{5}\)
\(6 \times  \underline{\hspace{0.5in}} = \frac{6}{10}\)
\( \underline{\hspace{0.5in}} \times \frac{1}{4}= \frac{3}{4}\)
\( \underline{\hspace{0.5in}} \times \frac{1}{12}= \frac{7}{12}\)
Your teacher will give you a sheet of paper. Work with your group of 3 and complete these steps on the paper. After each step, pass your paper to your right.
Step 1: Write a fraction with a numerator other than 1 and a denominator no greater than 12.
Step 2: Write the fraction you received as a product of a whole number and a unit fraction.
Step 3: Draw a diagram to represent the expression you just received.
Step 4: Collect your original paper. If you think the work is correct, explain why the expression and the diagram both represent the fraction that you wrote. If not, discuss what revisions are needed.
Student Response
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Activity Synthesis
See lesson synthesis.


aligns: no