few_shots: Example 1:
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?


Standard options: 
A. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.”
B. 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.
C. Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.” (Expectations for unit rates in this grade are limited to non-complex fractions.)


Thought: 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.
Answer: B

Example 2:
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.


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

Example 3:
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?


Standard options: 
A. Solve linear equations in one variable.
B. Analyze and solve pairs of simultaneous linear equations.


Thought: 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.
Answer: B

Now, assign the following problem or activity to one or more relevant standards it aligns with.
shot_info: fl_problem_000972

6

fl_problem_001097

7

fl_problem_001392

8
options: Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.

Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.
problem_activity: Narrative
The purpose of this activity is for students to make sense of the structure of a Take From, Result Unknown story problem. Students have access to connecting cubes or two-color counters and 10-frames, which they may choose to use strategically to represent and solve the problem (MP5). Some students may apply the ideas from the previous unit where they related subtraction to counting back. As students share their methods, the teacher records their thinking. It is important for the teacher to focus attention on the expression during the activity synthesis. Although some students may attempt to write equations and do so accurately, this representation will be the focus in a later lesson.
Students keep their books closed for the launch of the activity, as the teacher displays and reads the problem.
MLR8 Discussion Supports.
Synthesis: Display sentence frames to support whole-class discussion: “_____ and _____ are the same/alike because . . .” and “_____ and _____ are different because . . .” Encourage students to use these sentence frames to compare and contrast representations.
Advances: Speaking, Conversing
Required Materials
Materials to Gather
10-frames
Connecting cubes or two-color counters
Launch
Groups of 2
Give students access to 10-frames and connecting cubes or two-color counters.
Display the image from the warm-up.
“This is a picture of a library. Talk to your partner about what you know and what you wonder about libraries.”
3 minutes: partner discussion
Share and record what students know and wonder about libraries.
"We are going to solve a lot of story problems about libraries."
Display and read the numberless story.
30 seconds: quiet think time
1 minute: partner discussion
Share responses.
If not already mentioned, ask, “Are there more or fewer kids at the library after some go home?”
Activity
Ask students to open their books.
Read the problem with numbers.
2 minutes: independent work time
“Share your thinking with your partner.”
2 minutes: partner discussion
Monitor for students who solve or represent the problem in the following ways:
objects
drawings
count back
an expression (
\(9 - 2\)
)
Student Facing
Some kids were at the library.
Then some of the kids went home.
What do you notice?
What do you wonder?
[IMG]
There were 9 kids at the library.
Then 2 of the kids went home.
How many kids are at the library now?
Show your thinking using drawings, numbers, or words.
Student Response
Teachers with a valid work email address can
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for free access to Student Response.
Advancing Student Thinking
If students use more or fewer than nine objects to represent the kids at the library, consider asking:
“How did you choose how many connecting cubes to take out?”
“There are nine kids at the library. Which connecting cubes show the nine kids? Which connecting cubes show the two kids that went home?”
Activity Synthesis
Invite previously identified students to share in the order listed above.
“How are these representations the same? How are they different?”
If needed, display
\(9 - 2\)
.
“How does this expression match the story problem?”


correct_option_index: 1