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

shot_info: fl_problem_001097_pos_0

7
standard_description: Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.
problem_activity: Narrative
The purpose of this activity is for students to analyze strategies for adding and subtracting numbers to the ten-thousands place. Students look at addition problems that require composing new units, when the sum of the digits in a particular place value exceeds 10. The subtraction problems do not require students to decompose a unit, as this will be addressed in future lessons. They look at 2 strategies.
Strategy A allows students to add each number in terms of the value of each digit, written in expanded form. Strategy B follows the same logic, but without writing the full value that each digit represents. Then, students use the same strategies to subtract without decomposing a unit.
When students perform operations on the quantities in the situation, they reason abstractly and quantitatively (MP2).
Required Materials
Materials to Gather
Grid paper
Launch
Groups of 2
“Now let’s look at the weekend activity,”
Display the image in the task.
“What do you notice about the number of steps the teacher took during the week versus on the weekend?” (The teacher took a lot more steps each day during the weekend.)
Activity
2 minutes: quiet think time
6–7 minutes: partner work time
Student Facing
The teacher also keeps track of the number of steps she took during the weekend. The data from Saturday and Sunday of that same week are shown.
[IMG]
Here are two strategies to compute the total number of steps she took over the weekend.
Strategy A
[IMG]
Strategy B
[IMG]
Analyze the strategies. Discuss with your partner:
What is happening in each strategy?
How are they alike? How are they different?
Use both strategies to find the difference between the number of steps the teacher took on Saturday and on Sunday.
During another week, the teacher took 26,815 steps during the weekdays and 11,403 steps during the weekend. Use both strategies to find the total number of steps she took that week.
Student Response
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for free access to Student Response.
Advancing Student Thinking
Students may accurately write numbers in expanded form to subtract, but add the values instead of subtracting them because of the addition symbols they see. Consider refocusing students to the original problem and asking: “How might you find the difference between the values in each place?”
Activity Synthesis
Ask students to explain how the strategies are alike and how they are different. (They both add by place value and get the same answer, but one strategy breaks each number up and the other does not.)
“Why might a student have used one of the strategies instead of the other?”
“Strategy B is called the
standard algorithm
and is useful when we add and subtract large numbers.”


aligns: no