few_shots: Example:
Problem/activity:
For each pair of numbers, determine if the values are equivalent. Explain your reasoning for each one.
a.
$$-0.25$$
and
$$\frac{1}{-4}$$
b.
$$-\left ( \frac{1}{4} \right )$$
and
$$\frac{-1}{-4}$$
c.
$$\frac{-1}{4}$$
and
$$-\frac{1}{4}$$


Standard options: 
A. Solve real-world and mathematical problems involving the four operations with rational numbers. (Computations with rational numbers extend the rules for manipulating fractions to complex fractions.)
B. Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.
C. Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.


Your response:
Thought: This problem involves understanding fractions and division to divide rational numbers, such as 1, -4, 4, and -1. This problem also involves an understanding of multiplication: if p and q are integers, then -(p/q) = (-p)/q = p/(-q).
Answer: B

Now, assign the following problem or activity to one or more relevant standards it aligns with.
shot_info: fl_problem_001097

7
options: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)

Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.
problem_activity: Narrative
The purpose of this activity is for students to reason about adding fractions with unlike denominators to add two equations to a partially-completed True or False activity. If there is time, students can facilitate their True or False with another group.
Launch
Groups of 2 or 4
“Now you will work with your group to complete a True or False activity. This activity has two equations missing. Decide on equations that would complete the True or False and write them on the blank lines.”
Activity
10 minutes: small-group work time
As students work, monitor for groups who discuss and design equations based on some of the following:
They create equations where the fractions on one side of the equation have unlike denominators and the other side consists of fractions with like denominators.
They create an equation where the common denominator is appropriate, but the corresponding fraction used is not equivalent.
They create an equation that is similar to a previous equation.
They create an equation where a similar strategy can be used to determine if it’s true.
Student Facing
Write two equations to complete the True or False task. Be prepared to share your reasoning for the equations.
\(\frac{8}{14}+\frac{3}{7}=\frac{4}{7}+\frac{3}{7}\)
_______________________
_______________________
Student Response
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Activity Synthesis
Choose small groups to share that had different reasons for their equations.
Ask students to share their completed True or False and ask the class to share reasons for the equations.
As each group shares, continually ask others in the class if they agree or disagree and the reasons why.


correct_option_index: 0