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.


Standard options: 
A. 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.
B. Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.


Your response:
Thought: This task asks students to compare two fractions that are equal. The two fractions have different numerators and denominators (e.g. 1/4 and 3/12). The students need to explain why the two fractions are equal by drawing a picture, which involves using visual fraction models.
Answer: A, B

Now, assign the following problem or activity to one or more relevant standards it aligns with.
shot_info: im_task_000212

4
options: Understand ordering and absolute value of rational numbers.

Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.

Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.

Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.
problem_activity: Activity
The purpose of this task is for students to develop their understanding of the
\(|x|\)
notation in familiar contexts. They should build their understanding that
\(|x|\)
represents the distance from zero to
\(x\)
and that
\(|\text-x|\)
and
\(|x|\)
are equal.
Launch
Allow students 10 minutes quiet work time followed by whole-class discussion.
Student Facing
A part of the city of New Orleans is 6 feet below sea level. We can use “-6 feet” to describe its elevation, and “
\(|\text-6|\)
feet” to describe its vertical distance from sea level. In the context of elevation, what would each of the following numbers describe?
25 feet
\(|25|\)
feet
-8 feet
\(|\text-8|\)
feet
The elevation of a city is different from sea level by 10 feet. Name the two elevations that the city could have.
We write “
\(\text-5^\circ \text{C}\)
” to describe a temperature that is 5 degrees Celsius below freezing point and “
\(5^\circ \text{C}\)
” for a temperature that is 5 degrees above freezing. In this context, what do each of the following numbers describe?
\(1^\circ \text{C}\)
\(\text-4^\circ \text{C}\)
\(|12|^\circ \text{C}\)
\(|\text-7|^\circ \text{C}\)
Which temperature is colder:
\(\text-6^\circ \text{C}\)
or
\(3^\circ \text{C}\)
?
Which temperature is closer to freezing temperature:
\(\text-6^\circ \text{C}\)
or
\(3^\circ \text{C}\)
?
Which temperature has a smaller absolute value? Explain how you know.
Student Response
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Student Facing
Are you ready for more?
At a certain time, the difference between the temperature in New York City and in Boston was 7 degrees Celsius. The difference between the temperature in Boston and in Chicago was also 7 degrees Celsius. Was the temperature in New York City the same as the temperature in Chicago? Explain your answer.
Student Response
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click here to register or sign in
for free access to Extension Student Response.
Activity Synthesis
To summarize students’ work, consider displaying the following diagram and these four expressions. Give students a minute to study the diagram and match each letter on the diagram to an appropriate expression.
-4 feet
\(|{15}|\)
feet
\(|{\text -4}|\)
feet
15 feet
[IMG]
Representation: Develop Language and Symbols.
Create a display of important terms and vocabulary. Invite students to suggest language or diagrams to include that will support their understanding of: absolute value of a number, elevation, sea level, less than, greater than.
Supports accessibility for: Conceptual processing; Language; Memory
Representing, Speaking: MLR7 Compare and Connect
. To help students connect the numerical values with the diagram in the activity synthesis, provide students phrases that also connect to the situation (e.g., “4 feet below sea level,” “15 feet from sea level,” “4 feet from sea level,” and “15 feet above sea level”). Emphasize the language needed to say what the numerical values mean and how those values connect to the diagram and the phrases.
Design Principle(s): Maximize meta-awareness


correct_option_index: 0