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 compose and decompose numbers 11–19 as 10 ones and some more ones. Students work with groups of 11–19 objects to represent a context about students in a classroom where there is room for 10 students to sit at a table and the rest of the students sit on a rug. To solve the problem, students may count the total number of objects and then find a group of 10 or they may start by putting 10 objects at the table and see how many cubes are left on the rug and count all, count on, or know the total without counting. They record the two groups and the total by filling in equations.
Students work with multiple collections of 11–19 objects. They can be given access to a variety of collections of objects to choose from and then switch collections with other groups.
MLR8 Discussion Supports.
Invite students to act out the scenario. Listen for and clarify any questions about the context.
Advances: Speaking, Representing
Action and Expression. Develop Expression and Communication:
Give students access to 10-frames to help them figure out the number of students that will be sitting at the table and rug.
Supports accessibility for: Conceptual Processing, Visual-Spatial Processing
Required Materials
Materials to Gather
Collections of objects
Required Preparation
Each group of 2 needs access to at least 2 collections of 11–19 objects.
Launch
Groups of 2
Give each group of students access to collections of 11–19 objects.
“We are going to pretend that the objects in the collection are students.”
“The students will either sit at the table or on the rug.”
Display the image.
“All of the students want to sit at the table. How many of the students can sit at the table?” (10 students)
1 minute: independent work time
“10 students can sit at the table. The students who do not fit at the table will sit on the rug.”
“Work with your partner to figure out how many students will sit at the table, how many will sit on the rug, and how many students there are altogether. Fill in an equation for each bag of objects.”
Activity
7 minutes: partner work time
Student Facing
[IMG]
[IMG]
[IMG]
[IMG]
\(\underline{\hspace{1.1 cm}}\)
\(+\)
\(\underline{\hspace{1.1 cm}}\)
\(= \phantom{la} \underline{\hspace{1.1 cm}}\)
[IMG]
[IMG]
\(\underline{\hspace{1.1 cm}}\)
\(+\)
\(\underline{\hspace{1.1 cm}}\)
\(= \phantom{la} \underline{\hspace{1.1 cm}}\)
[IMG]
[IMG]
\(\underline{\hspace{1.1 cm}}\)
\(+\)
\(\underline{\hspace{1.1 cm}}\)
\(= \phantom{la} \underline{\hspace{1.1 cm}}\)
[IMG]
[IMG]
\(\underline{\hspace{1.1 cm}}\)
\(+\)
\(\underline{\hspace{1.1 cm}}\)
\(= \phantom{la} \underline{\hspace{1.1 cm}}\)
[IMG]
[IMG]
\(\underline{\hspace{1.1 cm}}\)
\(+\)
\(\underline{\hspace{1.1 cm}}\)
\(= \phantom{la} \underline{\hspace{1.1 cm}}\)
[IMG]
[IMG]
\(\underline{\hspace{1.1 cm}}\)
\(+\)
\(\underline{\hspace{1.1 cm}}\)
\(= \phantom{la} \underline{\hspace{1.1 cm}}\)
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Activity Synthesis
“The collection Jada is working with has 14 objects. She showed 10 students sitting at the table. How many do you think will be still on the rug? Why do you think that?” (4, 10 and 4 is 14)


correct_option_index: 0