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

Work with addition and subtraction equations.

Work with radicals and integer exponents.

Represent and solve problems involving multiplication and division.

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

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

Interpret the structure of expressions.

Use the four operations with whole numbers to solve problems.

Reason about and solve one-variable equations and inequalities.

Rewrite rational expressions.

Generate and analyze patterns.

Analyze patterns and relationships.

Write expressions in equivalent forms to solve problems.

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

Understand the relationship between zeros and factors of polynomials.

Add and subtract within 20.

Multiply and divide within 100.

Represent and solve problems involving addition and subtraction.

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

Represent and analyze quantitative relationships between dependent and independent variables.

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

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

Represent and solve equations and inequalities graphically.

Solve systems of equations.

Use polynomial identities to solve problems.

Gain familiarity with factors and multiples.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Perform arithmetic operations on polynomials.

Create equations that describe numbers or relationships

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

Write and interpret numerical expressions.

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

Use properties of operations to generate equivalent expressions.

Solve equations and inequalities in one variable.
problem_activity: Narrative
The purpose of this activity is for students to draw arrays from a given arrangements of dots. Students draw an array from dots in equal groups to reinforce the definition of an array and then draw as many arrays as they can from 16 randomly placed dots. Having cubes or counters for students to physically rearrange would be helpful in this activity.
MLR8 Discussion Supports.
To support partner discussion, display the following sentence frames: “This array matches the diagram because . . .”, and “This array shows multiplication because . . . .”
Advances: Conversing, Representing
Required Materials
Materials to Gather
Connecting cubes or counters
Launch
Groups of 2
Give students access to connecting cubes or counters.
Activity
“Work independently to draw a way that the first group of dots in problem 1 could be arranged into an array.”
2 minutes: independent work time
“Discuss how you arranged your dots and how the array is related to multiplication with your partner.”
1 minute: partner discussion
“How did you rearrange the dots to make an array?” (Since there were 3 in each group, I put 3 dots in each row. I saw 2 groups of 6, so I made 2 rows of 6.)
Consider asking:
“Did anyone create a different array?”
“Now you are going to make as many arrays as you can from 16 dots.”
2–3 minutes: independent work time
“Share how you rearranged the dots into arrays with your partner. See if together you can come up with any other arrays.”
3–5 minutes: partner work time
Student Facing
Draw 1 way the dots could be rearranged into an array.
[IMG]
Explain or show how the array is related to multiplication.
Draw ways that the dots could be arranged into arrays. Draw as many ways as you can.
[IMG]
Explain or show how each array is related to multiplication.
Student Response
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Activity Synthesis
“What kinds of equal groups did you make from 16 dots? How can you see the equal groups in the arrays you made?” (I can make 2 groups of 8. I drew it as 2 rows of 8 dots.)


correct_option_index: 3