few_shots: Example:
Problem/activity:
For each pair of numbers, determine if the values are equivalent. Explain your reasoning for each one.
a.
$$-0.25$$
and
$$\frac{1}{-4}$$
b.
$$-\left ( \frac{1}{4} \right )$$
and
$$\frac{-1}{-4}$$
c.
$$\frac{-1}{4}$$
and
$$-\frac{1}{4}$$


Mathematical concept/skill options: 
A. Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.
B. Reason quantitatively and use units to solve problems.
C. Apply and extend previous understandings of numbers to the system of rational numbers.
D. Represent complex numbers and their operations on the complex plane.
E. Perform arithmetic operations with complex numbers.
F. Compute fluently with multi-digit numbers and find common factors and multiples.
G. Represent and model with vector quantities.
H. Perform operations on vectors.
I. Use properties of rational and irrational numbers.
J. Use complex numbers in polynomial identities and equations.
K. Extend the properties of exponents to rational exponents.
L. Know that there are numbers that are not rational, and approximate them by rational numbers.
M. Perform operations on matrices and use matrices in applications.
N. Apply and extend previous understandings of multiplication and division to divide fractions by fractions.


Your response, in json format:
{
  "explanation": "This problem involves understanding fractions, multiplication, and division.",
  "answer": "A"
}

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: fl_problem_001097

7
options: Represent and solve problems involving multiplication and division.

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

Multiply and divide within 100.

Write and interpret numerical expressions.

Gain familiarity with factors and multiples.

Reason about and solve one-variable equations and inequalities.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Use properties of operations to generate equivalent expressions.

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

Solve systems of equations.

Use the four operations with whole numbers to solve problems.

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

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

Add and subtract within 20.

Represent and solve problems involving addition and subtraction.

Understand the relationship between zeros and factors of polynomials.

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

Work with radicals and integer exponents.

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

Rewrite rational expressions.

Represent and analyze quantitative relationships between dependent and independent variables.

Generate and analyze patterns.

Work with addition and subtraction equations.

Perform arithmetic operations on polynomials.

Solve equations and inequalities in one variable.

Create equations that describe numbers or relationships

Use polynomial identities to solve problems.

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

Interpret the structure of expressions.

Analyze patterns and relationships.

Write expressions in equivalent forms to solve problems.

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

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

Represent and solve equations and inequalities graphically.
problem_activity: Narrative
The purpose of this activity is for students to generate two patterns from rules and then graph them on the coordinate grid. Students first identify a point on the coordinate grid with one of the pairs of numbers from the patterns and then plot the rest of the points. Students may notice that the points on the graph are regularly spaced. They are invited to share this and other observations in the synthesis.
MLR8 Discussion Supports.
Display sentence frames to support partner discussion: “First, I _____ because . . .” and “I noticed _____ so I . . . .”
Advances: Speaking, Writing, Conversing, Representing
Action and Expression: Develop Expression and Communication.
Synthesis: Develop fluency with connecting rules, tables, and a coordinate grid to the same pattern. Provide access to blank or partially completed tables.
Supports accessibility for: Conceptual Processing, Attention
Launch
Groups of 2
“You and your partner will each start some problems about patterns and the coordinate grid independently. After a couple minutes, work with your partner to complete the problems.”
Activity
2 minutes: independent time
5 minutes: partner work time
Student Facing
Partner A
Rule 1: Start at 0. Keep adding 8.
Rule 2: Start at 0. Keep adding 2.
Use the rules to complete the table.
{"table": [{"_attributes": {"border": "1", "style": "width:100%"}, "tbody": [{"tr": [{"th": [{"_attributes": {"style": "text-align:center; width:14%"}}, {"_attributes": {"style": "text-align:center; width:14%"}, "_value": "A"}, {"_attributes": {"style": "text-align:center; width:14%"}, "_value": "B"}, {"_attributes": {"style": "text-align:center; width:14%"}, "_value": "C"}, {"_attributes": {"style": "text-align:center; width:14%"}, "_value": "D"}, {"_attributes": {"style": "text-align:center; width:14%"}, "_value": "E"}, {"_attributes": {"style": "text-align:center; width:14%"}, "_value": "F"}]}, {"th": [{"_attributes": {"style": "text-align:center"}, "_value": "rule 1"}], "td": [{"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}]}, {"th": [{"_attributes": {"style": "text-align:center"}, "_value": "rule 2"}], "td": [{"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}]}]}]}]}
Which table column represents the point on the coordinate grid? Label the point with the appropriate letter.
[IMG]
Plot and label the rest of the points.
Partner B
Rule 1: Start at 0. Keep adding 10.
Rule 2: Start at 0. Keep adding 40.
Use the rules to complete the table.
{"table": [{"_attributes": {"border": "1", "style": "width:100%"}, "tbody": [{"tr": [{"th": [{"_attributes": {"style": "text-align:center; width:14%"}}, {"_attributes": {"style": "text-align:center; width:14%"}, "_value": "A"}, {"_attributes": {"style": "text-align:center; width:14%"}, "_value": "B"}, {"_attributes": {"style": "text-align:center; width:14%"}, "_value": "C"}, {"_attributes": {"style": "text-align:center; width:14%"}, "_value": "D"}, {"_attributes": {"style": "text-align:center; width:14%"}, "_value": "E"}, {"_attributes": {"style": "text-align:center; width:14%"}, "_value": "F"}]}, {"th": [{"_attributes": {"style": "text-align:center"}, "_value": "rule 1"}], "td": [{"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}]}, {"th": [{"_attributes": {"style": "text-align:center"}, "_value": "rule 2"}], "td": [{"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}]}]}]}]}
Which table column represents the point on the coordinate grid? Label the point with the appropriate letter.
[IMG]
Plot and label the rest of the points.
Student Response
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Activity Synthesis
“How did you decide where to place the points on the grid?” (I used the top row to decide how far over to go on the horizontal axis and the second rule to decide how far up to go on the vertical axis.)
Invite students to share completed graphs for parts A and B.
“How are the two graphs the same?” (There is a point at the bottom left,
\((0,0)\)
, on each. The points are regularly spaced and go up and to the right. They all lie at the intersection of gridlines.)
“How are the two graphs different?” (The numbers on the axes are different. The ones for partner B get bigger really quickly.)


correct_option_index: 29