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: For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation.

Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.

Fluently add and subtract within 5.

Represent addition and subtraction with objects, fingers, mental images, drawings (Drawings need not show details, but should show the mathematics in the problem. (This applies wherever drawings are mentioned in the Standards.)), sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.

Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1).
problem_activity: Narrative
The purpose of this activity is for students to create stories and relate the action in the stories to the action of adding or taking away counters. While in the first activity, the story was provided, in this activity students create the action in the story, which is an opportunity to hear what language students associate with addition and subtraction (MP6). Mats with pictures of each setting are provided to help students make connections between what they do with their cubes and what is happening in the story. The goal of the activity synthesis is to relate the action in the story to the action with counters and show students expressions that represent these actions (MP2).
MLR8 Discussion Supports.
Synthesis: Provide all students with an opportunity to produce these words and numbers by inviting students to chorally repeat the expression in unison 1-2 times. For example: “7 take away 3” and “
\(7 - 3\)
”.
Advances: Listening, Speaking
Representation: Internalize Comprehension.
Synthesis: First demonstrate, then invite students to name each action they take as they tell their stories. For example, “Four ducks are swimming in a lake. Two ducks fly away. When the ducks fly away, I take away 2 counters.”
Supports accessibility for: Conceptual Processing, Organization
Required Materials
Materials to Gather
Two-color counters
Launch
Groups of 2
“We have heard and acted out some stories about students playing at school. Where else in your community do you see people playing outside? Describe it to your partner.”
30 seconds: quiet think time
1 minute: partner discussion
Share and record responses.
Display images from the student book.
“Some of the places where we play and walk around outside are parks and playgrounds. These stories all take place in different parks and playgrounds. How are these pictures the same as parks and playground that you have been to? How are they different?”
Give each student a bag of 10 two-color counters.
“We’re going to use our counters to show what is happening in our stories, but this time, the stories aren’t finished yet.”
Activity
Display the student workbook page of a field and read the first question. Count out 7 counters and place them on the field.
“I’ve got 7 kids playing tag in the field. What do you think happens next in the story?”
30 seconds: quiet think time
1 minute: partner discussion
Share responses.
Choose one student response and demonstrate the action with the counters.
“Now it’s your turn. I’m going to read you the first part of the story. Your job is to think about what happens next in the story. Then tell the story to your partner and show them what happens with your counters.”
Read each question. Give students quiet think time and partner discussion time for each question.
Student Facing
There were 7 kids playing tag on the field.
[IMG]
There were 2 kids eating at the picnic table.
[IMG]
There were 4 ducks swimming in the lake.
[IMG]
There were 5 kids playing hopscotch.
[IMG]
Student Response
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Advancing Student Thinking
If students represent the given sentence with counters but need encouragement to make up the rest of the story, consider asking:
“Can you use your counters to show me what happened first in the story?”
“What do you think happened next? Do you think more kids came to play tag or do you think some kids went home?”
Activity Synthesis
For each question, choose a student to share their story and demonstrate what happens with their counters. Record the action with words and numbers and an expression. For example: “7 take away 3” and “
\(7 - 3\)
”.
As each student shares, ask: “What do the counters represent?”


correct_option_index: 3