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.
{"table": [{"_attributes": {"align": "center", "class": ["table", "table-bordered"], "style": "table-layout:fixed; width:70%"}, "tbody": [{"tr": [{"td": [{"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}, "strong": [{"_value": "No solution"}]}, {"_attributes": {"style": "text-align:center"}, "strong": [{"_value": "Exactly 1 solution"}]}, {"_attributes": {"style": "text-align:center"}, "strong": [{"_value": "Infinite number of solutions"}]}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$${9=4x+7}$$"}]}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$${y=3y+5}$$"}]}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$${y={x\\over2}}$$"}]}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}]}, {"td": [{"p": [{"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$${3x+6y-9=0}$$"}]}]}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}]}, {"td": [{"p": [{"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$${x=y}$$"}]}, {"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$${1.25x=1.25y}$$"}]}]}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}]}, {"td": [{"p": [{"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$${9.9=6x+8y}$$"}]}, {"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$${9x=2.5y-8.8}$$"}]}]}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}]}, {"td": [{"p": [{"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$${11x-2y=1.5}$$"}]}, {"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$${11x-2y=2.5}$$"}]}]}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {}]}]}]}]}
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.


Your response:
{
  "explanation": "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_001392

8
options: Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

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.)

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.
problem_activity: Activity
The purpose of this activity is for students to use the four operations on rational numbers solve real-world problems. Monitor for students who solved the problem using different representations and approaches.
Launch
Arrange students in groups of 2–4. Given them 4 minutes of quiet work time, followed by small group and then whole-class discussion.
Engagement: Develop Effort and Persistence.
Encourage and support opportunities for peer interactions. Invite students to talk about their ideas with a partner before writing them down. Display sentence frames to support students when they explain their strategy. For example, “First, I _____ because _____. Then, I…,” “I noticed _____ so I…” and “I tried _____ and what happened was…”
Supports accessibility for: Language; Social-emotional skills
Reading: MLR6 Three Reads.
Use this routine to support reading comprehension of this word problem, without solving it for students. In the first read, students read the problem with the goal of comprehending the situation (e.g., A utility company charges for energy use.). In the second read, ask students to identify the quantities and relationships, without focusing on specific values. Listen for, and amplify, the quantities that vary in relation to each other in this situation: electricity used, in kilowatt-hours; amount spent on electricity used, in dollars; electricity generated and not used, in kilowatt-hours; amount credited for electricity generated and not used, in dollars. Invite students to draw a diagram to represent the relationships among these quantities. After the third read, ask students to brainstorm possible strategies to answer the questions. This helps students connect the language in the word problem and the reasoning needed to solve the problem, maintaining the intended level of cognitive demand in the task.
Design Principle(s): Support sense-making​
Student Facing
A utility company charges
$
0.12 per kilowatt-hour for energy a customer uses. They give a credit of
$
0.025 for every kilowatt-hour of electricity a customer with a solar panel generates that they don't use themselves.
A customer has a charge of
$
82.04 and a credit of -
$
4.10 on this month's bill.
What is the amount due this month?
How many kilowatt-hours did they use?
How many kilowatt-hours did they generate that they didn't use themselves?
Student Response
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Student Facing
Are you ready for more?
Find the value of the expression without a calculator.
\((2)(\text-30)+(\text-3)(\text-20)+(\text-6)(\text-10) -(2)(3)(10)\)
Write an expression that uses addition, subtraction, multiplication, and division and only negative numbers that has the same value.
Student Response
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click here to register or sign in
for free access to Extension Student Response.
Activity Synthesis
Select students to share their solution. Help them make connections between different solution approaches.


correct_option_index: 1