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: Count to answer “how many?” questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1–20, count out that many objects.

Understand the relationship between numbers and quantities; connect counting to cardinality.
problem_activity: Narrative
The purpose of this activity is for students to count their collection in a way that makes sense to them.  Students are invited to represent how many objects are in their collection. Some students may choose to create a drawing, make a group with the same number of objects, or just demonstrate how they counted. Students will focus more on creating written representations of how many in a later unit. Monitor and select students with the following strategies to share in the synthesis:
demonstrate or explain how they counted
take out the same number of objects
draw a picture
Students are provided with a counting mat and 5-frames to help them accurately count or organize their collections. Students use appropriate tools strategically as they choose which tools help them count their collections (MP5).
Action and Expression: Internalize Executive Functions.
Invite students to plan a strategy, including what drawings, numbers, words, or objects they will use, to show how they counted their collection.
Supports accessibility for: Conceptual Processing, Organization
Required Materials
Materials to Gather
5-frames
Collections of objects
Counting mats
Launch
Groups of 2
“Today you’re going to count another collection of objects. During Questions About Us, we showed how many of us are here today. As you’re counting your collection, think about how you can show how you counted your collection.”
Activity
Give each student a bag of objects. Give students access to 5-frames and a counting mat.
“Figure out how many objects are in your collection."
2 minutes: independent work time
“Switch collections with a partner. Figure out how many objects are in your new collection.”
2 minutes: independent work time
“Tell your partner how many objects are in your collection. Show them how you counted the objects.”
30 seconds: quiet think time
2 minutes: partner discussion
“Show how you counted your collection. Show your thinking using objects, drawings, numbers, or words.”
2 minutes: independent work time
Monitor for students who use the strategies in the synthesis to represent how they counted.
Student Facing
Show how many objects are in your collection.
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Advancing Student Thinking
If students have difficulty representing their count on paper, consider having them explain how they counted verbally. Students can also be provided stickers that they can put on their paper to represent each object in place of a drawing.
Activity Synthesis
Ask selected students to share in the order listed in the activity narrative.
“What is the same about how they each counted their collections?” (They all counted each object 1 time.)
“What is different about how they each showed how they counted?” (Some people drew a picture and some used objects.)
After each student shares, write or display the number and say, “There are _____ objects in their collection.”


correct_option_index: 0

1