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: Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students’ ages.
problem_activity: Optional activity
This activity extends the work with rectangles and fractions to continued fractions. Continued fractions are not a part of grade-level work, but they can be reasoned about and rewritten using grade-level skills for operating on fractions (MP8). In particular, the insight that
\(\frac{1}{\frac{a}{b}}=\frac{b}{a}\)
(a special case of invert and multiply) is helpful.
In this activity, students consolidate their understanding about how the greatest common factor of the numerator and denominator of a fraction can help them write an equivalent fraction whose numerator and denominator have greatest common factor 1—sometimes called “lowest terms.”
Launch
Arrange students in groups of 2. Students work alone and compare their work with a partner.
Consider a quick warm-up like this:
Write a fraction that is equal to each expression:
\(3+\frac15\)
\(\frac{1}{3+\frac15}\)
\(2+\frac{1}{3+\frac15}\)
Representation: Develop Language and Symbols.
Eliminate barriers and provide concrete manipulatives to connect symbols to concrete objects or values. For example, provide students with access to the four large rectangles prepared on graph paper.
Supports accessibility for: Visual-spatial processing; Fine-motor skills
Student Facing
Accurately draw a 37-by-16 rectangle. (Use graph paper, if possible.)
In your rectangle, draw a line segment that decomposes the rectangle into a new rectangle and a square that is as large as possible. Continue until your original rectangle has been entirely decomposed into squares.
How many squares of each size are there?
What are the dimensions of the last square you drew?
What does this have to do with
\(2+\frac{1}{3+\frac15}\)
?
Consider a 52-by-15 rectangle.
In your rectangle, draw a line segment that decomposes the rectangle into a new rectangle and a square that is as large as possible. Continue until your original rectangle has been entirely decomposed into squares.
Write a fraction equal to this expression:
\(3+\frac{1}{2+\frac17}\)
.
Notice some connections between the rectangle and the fraction.
What is the greatest common factor of 52 and 15?
Consider a 98-by-21 rectangle.
In your rectangle, draw a line segment that decomposes the rectangle into a new rectangle and a square that is as large as possible. Continue until your original rectangle has been entirely decomposed into squares.
Write a fraction equal to this expression:
\(4+\frac{1}{1+\frac{7}{14}}\)
.
Notice some connections between the rectangle and the fraction.
What is the greatest common factor of 98 and 21?
Consider a 121-by-38 rectangle.
Use the decomposition-into-squares process to write a continued fraction for
\(\frac{121}{38}\)
. Verify that it works.
What is the greatest common factor of 121 and 38?
Student Response
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