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
$$-\frac{1}{4}$$


Concept/skill: 
Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

Answer: 
Yes. 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).

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

shot_info: fl_problem_001097_pos_0

7
standard_description: Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.
problem_activity: Narrative
The purpose of this activity is for students to write a
\(10 + n\)
expression that is equal to a given expression. Each expression given has three addends, two of which make a ten.
Required Materials
Materials to Gather
Connecting cubes or two-color counters
Double 10-frames
Launch
Groups of 2
Give students access to double 10-frames and connecting cubes or two-color counters.
“Now you will write a
\(10 + n\)
expression with the same value as each of the given expressions.”
Activity
5 minutes: independent work time
3 minutes: partner discussion
Student Facing
Write a
\(10 + \boxed{\phantom{3}}\)
expression that has the same value as each expression.
\(5 + 7 + 5\)
\(3 + 7 + 6\)
\(1 + 9 + 9\)
\(4 + 8 + 6\)
\(8 + 10 + 2\)
If you have time, write as many expressions as you can with 3 numbers that are equal to
\(10 + 5\)
.
Student Response
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Activity Synthesis
Display each
\(10 + n\)
expression.
“In order to make adding three numbers easier, we can rewrite each expression as a
\(10 + \boxed{\phantom{3}}\)
expression.”
Invite students to say the value of each
\(10 + n\)
expression together.


aligns: no