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: Use polynomial identities to solve problems.

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

Work with radicals and integer exponents.

Multiply and divide within 100.

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

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

Rewrite rational expressions.

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

Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.

Create equations that describe numbers or relationships

Write and interpret numerical expressions.

Reason about and solve one-variable equations and inequalities.

Add and subtract within 20.

Solve equations and inequalities in one variable.

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

Represent and solve equations and inequalities graphically.

Interpret the structure of expressions.

Use properties of operations to generate equivalent expressions.

Represent and solve problems involving multiplication and division.

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

Understand the relationship between zeros and factors of polynomials.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Represent and analyze quantitative relationships between dependent and independent variables.

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

Work with addition and subtraction equations.

Generate and analyze patterns.

Represent and solve problems involving addition and subtraction.

Solve systems of equations.

Gain familiarity with factors and multiples.

Analyze patterns and relationships.

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

Write expressions in equivalent forms to solve problems.

Perform arithmetic operations on polynomials.

Use the four operations with whole numbers to solve problems.
problem_activity: Narrative
In this activity, students examine the rectangles drawn by their classmates and learn the term
factor pairs
. Students recognize the side lengths of each rectangle as a factor pair of its area.
This activity uses
MLR7 Compare and Connect
.
Advances: representing, conversing
Launch
Groups of 2
Activity
5–7 minutes: gallery walk
Monitor for different explanations students offer for how they know whether all possible rectangles with a given area have been found.
Student Facing
As you visit each poster, discuss with your partner:
What do you notice? Use the following sentence frames when you share:
“I notice that some of the posters . . . .”
“I notice the posters for numbers _____ and _____ are alike because . . . .”
How do you know that all possible rectangles were found for the given area?
Student Response
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Activity Synthesis
MLR7 Compare and Connect
“What is the same and what is different between the rectangles on the posters?”
30 seconds: quiet think time
1 minute: partner discussion
“How do you know that all possible rectangles have been found for the given area?” (We could not find any other numbers that multiply together to make the area.)
Display the rectangles for 21: 1 by 21 and 3 by 7.
“Are there any more rectangles we can draw? Why or why not?” (No, there are no more whole-number factors of 21. Or, no, because to get 21 we can multiply only 1 and 21, 3 and 7, 7 and 3, and 21 and 1.)
“We call 1 and 21 a
factor pair
of 21 because each of them is a factor of 21 and multiplying them gives 21. Another factor pair of 21 is 3 and 7.”
“Work with your partner to write down the factor pairs for the areas you were assigned.”
2 minutes: partner work time


correct_option_index: 28