few_shots: 
Example:
Concept/skill: 
Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model.
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: 
No. This task does not involve comparing decimals to hundredths. Instead, it involves fraction comparisons.

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_neg_0

4
standard_description: Classify two-dimensional figures in a hierarchy based on properties.
problem_activity: Narrative
The purpose of this activity is for students to draw two diagrams that represent a unit fraction of a unit fraction. Students work with the same unit fractions in both diagrams. The directions were intentionally written to encourage students to partition a unit square in different ways. Students initially partition the square into thirds in the first problem and into fourths in the second problem. Students may complete the diagrams in a way that makes sense to them. During the synthesis, students will connect both of the diagrams to the expressions
\(\frac {1}{4} \times \frac {1}{3}\)
and
\(\frac {1}{3} \times \frac {1}{4}\)
.
Launch
Groups of 2
Activity
2 minutes: Independent work time
10 minutes: partner work time
Monitor for students who:
draw diagrams like those in the student responses
recognize that both diagrams have the same amount shaded
can explain the different ways they partitioned each diagram
Student Facing
Show
\(\frac{1}{3}\)
of the square.
Shade
\(\frac{1}{4}\)
of
\(\frac{1}{3}\)
of the square.
How much of the whole square is shaded?
[IMG]
Show
\(\frac{1}{4}\)
of the square.
Shade
\(\frac{1}{3}\)
of
\(\frac{1}{4}\)
of the square.
How much of the whole square is shaded?
[IMG]
How are the diagrams the same and how are they different?
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Advancing Student Thinking
If students do not identify how much of the whole square is shaded, ask: “How can you adapt your diagram to show how many pieces would be in the whole square?”
Activity Synthesis
Ask previously selected students to share their responses in the order given.
“How are the diagrams the same?” (They both have
\(\frac {1}{4}\)
and
\(\frac {1}{3}\)
in them. They both have
\(\frac {1}{12}\)
of the whole square shaded.)
“How are the diagrams different?” (In one diagram, I started by showing
\(\frac {1}{3}\)
of the square and then shaded in
\(\frac {1}{4}\)
of
\(\frac {1}{3}\)
. In the other diagram, I started by showing
\(\frac {1}{4}\)
of the square and then shaded in
\(\frac {1}{3}\)
of
\(\frac {1}{4}\)
.)
Display:
\(\frac{1}{12}\)
,
\(\frac{1}{4}\times\frac{1}{3}\)
,
\(\frac{1}{3}\times\frac{1}{4}\)
“How do the diagrams represent these expressions?”
Adapt diagrams as needed in order to show all three expressions.
“How do we know that both squares have the same amount shaded?” (They both have
\(\frac {1}{12}\)
shaded.)


aligns: no