few_shots: Example:
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?


Mathematical concept/skill options: 
A. Write expressions in equivalent forms to solve problems.
B. Understand properties of multiplication and the relationship between multiplication and division.
C. Interpret the structure of expressions.
D. Solve real-life and mathematical problems using numerical and algebraic expressions and equations.
E. Use polynomial identities to solve problems.
F. Understand the relationship between zeros and factors of polynomials.
G. Write and interpret numerical expressions.
H. Work with equal groups of objects to gain foundations for multiplication.
I. Perform arithmetic operations on polynomials.
J. Create equations that describe numbers or relationships
K. Generate and analyze patterns.
L. Analyze and solve linear equations and pairs of simultaneous linear equations.
M. Understand solving equations as a process of reasoning and explain the reasoning.
N. Apply and extend previous understandings of arithmetic to algebraic expressions.
O. Rewrite rational expressions.
P. Represent and solve problems involving multiplication and division.
Q. Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.
R. Reason about and solve one-variable equations and inequalities.
S. Understand and apply properties of operations and the relationship between addition and subtraction.
T. Understand the connections between proportional relationships, lines, and linear equations.
U. Multiply and divide within 100.
V. Gain familiarity with factors and multiples.
W. Use the four operations with whole numbers to solve problems.
X. Work with addition and subtraction equations.
Y. Represent and solve problems involving addition and subtraction.
Z. Solve problems involving the four operations, and identify and explain patterns in arithmetic.
AA. Solve equations and inequalities in one variable.
AB. Solve systems of equations.
AC. Represent and analyze quantitative relationships between dependent and independent variables.
AD. Work with radicals and integer exponents.
AE. Represent and solve equations and inequalities graphically.
AF. Analyze patterns and relationships.
AG. Use properties of operations to generate equivalent expressions.
AH. Add and subtract within 20.


Your response:
Thought: This set of problems involves solving linear equations and pairs of linear equations.
Answer: L

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: fl_problem_001392

8
options: Know number names and the count sequence.

Compare numbers.

Count to tell the number of objects.
problem_activity: Narrative
The purpose of this warm-up is for students to participate in part of the Questions About Us routine. Students have worked with 5-frames in previous sections and as an option during counting collections. In this activity, 5-frames are introduced as a way to represent how many students are here today. A blackline master is provided, but the 5-frames should be modified to match the number of students in the class. For example, if there are 24 students in the class, four 5-frames and 4 extra squares should be displayed. This will allow students to use the representation to also determine how many students are absent in future lessons by referring to the empty squares. This display will be used during the  Questions About Us warm-up in later lessons, so create the display in a place in the classroom that can easily be seen by students.
In the synthesis, students look at the new 5-frame representation and compare it to the representations based on student ideas created in the previous lesson.
Required Materials
Materials to Gather
Chart paper
Materials to Copy
Questions About Us 5-Frames
Required Preparation
Gather the poster created during Questions about Us in the previous lesson.
Launch
“How can we use the 5-frames to show how many of us are here?”
30 seconds: quiet think time
1 minute: partner discussion
Share responses.
Activity
Demonstrate a student suggestion for how to use the 5-frames.
“How can we figure out how many of us are here?” (We can count each person. We can count each circle in the 5-frame.)
Count each student.
“How many of us are here today?”
Count each circle.
“How many of us are here today?”
Student Response
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Activity Synthesis
Display one of the representations based on student ideas from the previous lesson and the new representation with 5-frames.
“These are both different ways that we showed how many of us are here. What do you notice?”


correct_option_index: 0