few_shots: 
Example:
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.


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.

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, does the problem or activity shown below enable students to learn the full intent of the following concept or skill?

shot_info: im_task_000212_pos_0

4
standard_description: Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 × 108 and the population of the world as 7 × 109, and determine that the world population is more than 20 times larger.
problem_activity: Narrative
The purpose of this activity is for students to write expressions for and find the area of shaded regions whose side lengths are a unit fraction and a non-unit fraction. Students look at a series of diagrams with an increasingly large shaded region so they can look for and make use of structure (MP7).
It is important to relate the work here to what students have already learned about the product of a unit fraction and a unit fraction and this is the goal of the synthesis. For example, students have seen that
\(\frac{1}{5} \times \frac{1}{3} = \frac{1}{15}\)
. Since
\(\frac{6}{5}\)
is 6
\(\frac{1}{5}\)
s, the product
\(\frac{6}{5} \times \frac{1}{3}\)
will be 6
\(\frac{1}{15}\)
s or
\(\frac{6}{15}\)
.
MLR8 Discussion Supports.
Prior to solving the problems, invite students to make sense of the situations and take turns sharing their understanding with their partner. Listen for and clarify any questions about the context.
Advances: Listening, Conversing
Launch
Groups of 2
Display image A from the student workbook.
“What is a multiplication expression that represents the shaded region?”(
\(\frac{2}{5} \times \frac{1}{3}\)
,
\(2 \times \frac{1}{15}\)
)
“How does the diagram represent your expression?”(There is
\(\frac{2}{5}\)
of the first row shaded and that row is
\(\frac{1}{3}\)
of the square. There are 2 shaded pieces and each is
\(\frac{1}{15}\)
of the whole square.)
Activity
3–5 minutes: independent work time
3–5 minutes: partner discussion
Monitor for students who:
notice that the product of the numerators represents how many pieces of the square are shaded.
notice that the product of the denominators represents the number of pieces in the whole square.
Student Facing
Write a multiplication expression that represents the shaded region in each diagram.
A
[IMG]
B
[IMG]
C
[IMG]
What patterns do you notice in the multiplication expressions?
Han wrote this equation to represent the area of the shaded region. Explain how the diagram represents the equation.
\(\phantom{2.5cm} \\ \frac {6}{5} \times \frac {1}{3} = \frac {6}{15}\)
[IMG]
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 write mathematically correct multiplication expressions that do not represent the product of a unit fraction and a non-unit fraction, write this type of multiplication expression that represents the diagram and ask “How does this expression represent the area of the shaded region in the diagram?”
Activity Synthesis
Ask previously selected students to share the patterns they noticed in the table.
Display the expression from the last problem:
\(\frac {6}{5} \times \frac {1}{3} = \frac {6}{15}\)
.
“How does the diagram show
\(\frac {1}{3}\)
?” (The first row of pieces in a square is
\(\frac{1}{3}\)
of the square.)
“How does the diagram show
\(\frac {6}{5}\)
?” (There are 6 pieces shaded and each one is
\(\frac{1}{5}\)
of the row.)
“How does the diagram show
\(\frac {6}{5} \times \frac {1}{3}\)
?” (There is
\(\frac{6}{5}\)
of a row shaded and that row is
\(\frac{1}{3}\)
of a square unit.)


aligns: no