few_shots: 
Example 1:
Concept/skill: 
Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.

Problem/activity:
You’re mixing ingredients for cookies. The recipe says to combine 6 tablespoons, or ¾ stick, of butter with 1 cup of sugar. You accidentally mix in a whole stick of butter (8 tablespoons) with the cup of sugar. How can you fix this?


Answer: 
Yes. This problem solves a real-world problem involving mixing ingredients for cookies. A student doing this problem would need to reason about equivalent ratios of butter amounts to sugar amounts.

Example 2:
Concept/skill: 
Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

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


Answer: 
No. The expressions shown in this problem do not involve multiplying fractions with other fractions, nor whole numbers with fractions.

Example 3:
Concept/skill: 
Analyze and solve pairs of simultaneous linear equations.

Problem/activity:
Problem 1
The table below contains single equations in a single variable, single equations in two variables, and pairs of simultaneous equations in two variables. Check the appropriate box to show whether there is no solution, exactly 1 solution, or if there is an infinite number of solutions.
|                                                          | **           No solution          ** | **           Exactly 1 solution          ** | **           Infinite number of solutions          ** |
|----------------------------------------------------------|--------------------------------------|---------------------------------------------|-------------------------------------------------------|
|                       $${9=4x+7}$$                       |                                      |                                             |                                                       |
|                       $${y=3y+5}$$                       |                                      |                                             |                                                       |
|                    $${y={x\over2}}$$                     |                                      |                                             |                                                       |
|                     $${3x+6y-9=0}$$                      |                                      |                                             |                                                       |
|    $${x=y}$$                        $${1.25x=1.25y}$$    |                                      |                                             |                                                       |
| $${9.9=6x+8y}$$                        $${9x=2.5y-8.8}$$ |                                      |                                             |                                                       |
| $${11x-2y=1.5}$$                        $${11x-2y=2.5}$$ |                                      |                                             |                                                       |
Problem 2
Kim has a small container and a large container as shown.
[IMG]
It takes 16 of the small containers to fill the large container. Three small containers leave 1.95 gallons of space in the big container.
What is the size of each of the two containers?


Answer: 
Yes. The last three rows of the table in the first problem involves solving pairs of simultaneous linear equations. The second word problem can also be represented as two simultaneous linear equations.

Now, determine whether the following problem or activity can enable students to understand the concepts or skills in the provided description.

shot_info: fl_problem_000972_pos_0

6

fl_problem_001097_neg_0

7

fl_problem_001392_pos_0

8
standard_description: Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).
problem_activity: Narrative
The purpose of this activity is for students to analyze a line plot that represents lengths that are measured to the nearest half inch. They make observations and write statements about the data represented in the line plot, and then generate questions that could be answered with the line plot. When students recognize how organizing data helps to read the information and to answer questions, they learn that line plots are a powerful tool to present data (MP5).
Launch
Groups of 2
Display the list and line plot.
“The list and the line plot both show the heights of seedlings. A seedling is a young plant. Where have you seen seedlings before?” (At the park. In a garden.)
“Looking at the list, can we tell the height of the shortest seedling?” (Yes,
\(\frac{1}{2}\)
inch). “What about the tallest seedling?” (Yes, 5 inches)
“Draw a quick sketch of the shortest seedling and the tallest seedling at their actual heights. Use what you know about the length of an inch.”
1 minute: independent work time
“Share your sketches with your partner.”
“What else can we tell about the seedlings from looking at the list?” (Twenty-two seedlings were measured. There are two seedlings that are 3 inches tall.)
1 minute: partner discussion
Share responses.
Activity
“Now, take a close look at the line plot. Think about what information we can gather from the line plot and what questions it can help to answer.”
“Work with your partner to complete these problems.”
7–10 minutes: partner work time
Student Facing
heights of seedlings (in inches)
\(\frac{1}{ 2}\)
1
1
\(\frac{1}{ 2}\)
\(1\frac{1}{ 2}\)
\(2\frac{1}{ 2}\)
4
\(\frac{1}{ 2}\)
3
\(1\frac{1}{ 2}\)
5
\(1\frac{1}{2}\)
\(1\frac{1}{2}\)
\(2\frac{1}{2}\)
3
\(\frac{1}{2}\)
\(2\frac{1}{2}\)
\(1\frac{1}{2}\)
1
\(1\frac{1}{2}\)
4
2
[IMG]
[IMG]
Write 3 statements about the measurements represented in the line plot.
What questions could be answered more easily with the line plot than the list? Write at least 2 questions.
Student Response
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Activity Synthesis
Display the list and the line plot.
“How is the information displayed in the line plot different from that in the list?” (In the line plot, all the measurements that are the same length are together. The measurements go from smallest to largest along the bottom. In the line plot, we don’t keep writing the numbers over and over, we would just use an x for each measurement.)
“What were some questions that could be more easily answered with the line plot than the list?” (“How many seedlings were 3 inches tall?” because we could just count the x’s at 3 instead of searching through the list. “What’s the shortest seedling?” because we can find the x on the left end of the scale. “Which seedling height was the most common?” because we can see which number has the most x’s.)


aligns: no