few_shots: Example:
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?


Mathematical concept/skill options: 
A. Analyze proportional relationships and use them to solve real-world and mathematical problems.
B. Understand ratio concepts and use ratio reasoning to solve problems.


Your response, in json format:
{
  "explanation": "This problem focuses on the ratio between two ingredients. Students do not have to analyze proportional relationships in-depth, which is reserved for a higher grade level, but rather use ratios to find missing values.",
  "answer": "B"
}

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: fl_problem_000972

6
options: Write expressions in equivalent forms to solve problems.

Understand solving equations as a process of reasoning and explain the reasoning.

Multiply and divide within 100.

Represent and solve problems involving multiplication and division.

Interpret the structure of expressions.

Understand and apply properties of operations and the relationship between addition and subtraction.

Represent and solve equations and inequalities graphically.

Gain familiarity with factors and multiples.

Solve equations and inequalities in one variable.

Analyze patterns and relationships.

Rewrite rational expressions.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Understand the relationship between zeros and factors of polynomials.

Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

Represent and solve problems involving addition and subtraction.

Use the four operations with whole numbers to solve problems.

Use polynomial identities to solve problems.

Represent and analyze quantitative relationships between dependent and independent variables.

Create equations that describe numbers or relationships

Understand the connections between proportional relationships, lines, and linear equations.

Perform arithmetic operations on polynomials.

Write and interpret numerical expressions.

Work with radicals and integer exponents.

Work with equal groups of objects to gain foundations for multiplication.

Solve systems of equations.

Reason about and solve one-variable equations and inequalities.

Add and subtract within 20.

Understand properties of multiplication and the relationship between multiplication and division.

Work with addition and subtraction equations.

Use properties of operations to generate equivalent expressions.

Solve problems involving the four operations, and identify and explain patterns in arithmetic.

Analyze and solve linear equations and pairs of simultaneous linear equations.

Generate and analyze patterns.

Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.
problem_activity: Activity
The mathematical purpose for this activity is to allow students to practice solving for a variable in an equation with two variables. In the associated Algebra lesson, expressing one variable in terms of another is necessary before substituting an expression for a variable in another equation.
Launch
Demonstrate how to solve for a variable by showing students the equation
\(a + 2b = 5\)
. Solving for
\(a\)
results in
\(a = 5 - 2b\)
or
\(a = \text{-}2b + 5\)
. Solving for
\(b\)
results in
\(b = \frac{5-a}{2}\)
or
\(b = \frac{5}{2} - \frac{a}{2}\)
or another equivalent expression.
Student Facing
Solve for the indicated variable.
Solve for
\(k\)
.
\(2t+k=6\)
Solve for
\(n\)
.
\(10n=2p\)
Solve for
\(c\)
.
\(12-6d=3c\)
Solve for
\(g\)
.
\(h=8g+4\)
Solve for
\(x\)
.
\(4x+3y=12\)
Solve for
\(y\)
.
\(4x+3y=12\)
Student Response
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Activity Synthesis
The purpose of the discussion is to share strategies for solving for one variable in an equation including more than one variable. Select students to share their answers and strategies. As students share, consider asking another student why each step makes sense to do.
Some questions for discussion:
"How do you know when you are done solving for a variable?" (When the variable I want to solve for is the only thing on one side of the equation.)
"How is solving for
\(x\)
in an equation like
\(4x+3y=12\)
similar or different from solving for
\(x\)
in an equation like
\(4x + 6 = 12\)
?" (The steps are very similar, but when there is only one variable, we can know the value of
\(x\)
that makes the equation true.)
"If you know the value for
\(y\)
is 2 and need to know the value for
\(x\)
, would you rather begin with the equation
\(4x + 3y = 12\)
or the equivalent equation
\(x = 3 - \frac{3}{4}y\)
? Explain your reasoning." (I would rather use the second equation since I only need to substitute in the value for
\(y\)
and evaluate the expression rather than solve an equation.)


correct_option_index: 18