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: Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies (include groups with up to ten objects).

Compare two numbers between 1 and 10 presented as written numerals.
problem_activity: Narrative
The purpose of this activity is for students to learn stage 3 of the Less, Same, More center. Students draw groups that have more, fewer, or the same number of images as a given group. Consider using a sheet protector or laminating the mats for students to use with dry erase markers. Otherwise, make multiple copies of the mats for each group.
MLR8 Discussion Supports.
If necessary, invite students to repeat their reasoning to describe their comparison to a partner using mathematical language: “Can you say that again using the words more/fewer/the same?”
Advances: Listening, Speaking
Required Materials
Materials to Gather
Sheet protectors
Materials to Copy
Less, Same, More Mat
Image Cards Grade K
Required Preparation
Each group of 2 needs a set of cards from the blackline master.
Launch
Groups of 2
Give students the mats and cards.
“We are going to learn a new way to play the Less, Same, More center. It is called Less, Same, More, Drawings.”
“First, draw a card and place it at the top of the mat. Figure out how many things are on the card.”
Point to each square as you explain: “Draw three groups in the squares below. Draw one group that has fewer things, one group that has the same number of things, and one group that has more things.”
“Switch mats with your partner. Check to be sure you agree with the groups your partner made.”
“Choose one of the groups you drew to describe with a sentence using ‘more,’ ‘fewer,’ or ‘the same number’.”
“When you are finished, place a new card at the top of your mat and draw groups that have more, fewer, and the same number in the squares.”
Activity
10 minutes: partner work time
Activity Synthesis
Display the card with 5 dots in a number cube arrangement:
[IMG]
“Draw a group that has fewer images.”
1 minute: independent work time
“How many images are in the group you drew?”
Share responses.
“Did all of our groups have the same number of things? Why?” (No, some people drew groups with 2 things and some people drew groups with 4 things. 4 and 2 are both less than 5.)
“Did all of our groups have fewer than 5 things?” (Yes.)


correct_option_index: 0