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

Solve equations and inequalities in one variable.

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

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

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

Use properties of operations to generate equivalent expressions.

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

Apply and extend previous understandings of arithmetic to algebraic expressions.

Represent and solve equations and inequalities graphically.

Write expressions in equivalent forms to solve problems.

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

Represent and solve problems involving multiplication and division.

Rewrite rational expressions.

Represent and solve problems involving addition and subtraction.

Create equations that describe numbers or relationships

Use polynomial identities to solve problems.

Use the four operations with whole numbers to solve problems.

Work with addition and subtraction equations.

Work with radicals and integer exponents.

Multiply and divide within 100.

Represent and analyze quantitative relationships between dependent and independent variables.

Solve systems of equations.

Write and interpret numerical expressions.

Interpret the structure of expressions.

Perform arithmetic operations on polynomials.

Gain familiarity with factors and multiples.

Reason about and solve one-variable equations and inequalities.

Understand the relationship between zeros and factors of polynomials.

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

Add and subtract within 20.

Generate and analyze patterns.

Analyze patterns and relationships.

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

Work with equal groups of objects to gain foundations for multiplication.
problem_activity: Problem 1
How many?
[IMG]
Problem 2
Determine the value of the unknown in each equation below.
a.
$$a = 7 \times 8$$
b.
$$42 \div b =7$$
c.
$$49 = 7 \times c$$
d.
$$d\div 7 = 9$$
Problem 3
Here is the partially filled-in multiplication table from Lessons 1 and 6.
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text-align: center;"}, "strong": [{"_value": "7"}]}, {"_attributes": {"style": "background-color: rgb(153, 204, 255); text-align: center;"}, "strong": [{"_value": "8"}]}, {"_attributes": {"style": "background-color: rgb(153, 204, 255); text-align: center;"}, "strong": [{"_value": "9"}]}, {"_attributes": {"style": "background-color: rgb(153, 204, 255); text-align: center;"}, "strong": [{"_value": "10"}]}]}, {"td": [{"_attributes": {"style": "background-color: rgb(153, 204, 255); text-align: center;"}, "strong": [{"_value": "1"}]}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}, "_value": "1"}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}, "_value": "2"}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}, "_value": "3"}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}, "_value": "4"}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}, "_value": "5"}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}, "_value": "6"}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}, "_value": "7"}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}, "_value": "8"}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}, "_value": "9"}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}, "_value": "10"}]}, {"td": [{"_attributes": {"style": "background-color: rgb(153, 204, 255); text-align: center;"}, "strong": [{"_value": "2"}]}, {"_attributes": {"style": "text-align:center"}, "_value": "2"}, {"_attributes": {"style": "text-align:center"}, "_value": "4"}, {"_attributes": {"style": "text-align:center"}, "_value": "6"}, {"_attributes": {"style": "text-align:center"}, "_value": "8"}, {"_attributes": {"style": "text-align:center"}, "_value": "10"}, {"_attributes": {"style": "text-align:center"}, "_value": "12"}, {"_attributes": {"style": "text-align:center"}, "_value": "14"}, {"_attributes": {"style": "text-align:center"}, "_value": "16"}, {"_attributes": {"style": "text-align:center"}, "_value": "18"}, {"_attributes": {"style": "text-align:center"}, "_value": "20"}]}, {"td": [{"_attributes": {"style": "background-color: rgb(153, 204, 255); text-align: center;"}, "strong": [{"_value": "3"}]}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}, "_value": "3"}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}, "_value": "6"}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}, "_value": "9"}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}, "_value": "12"}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}, "_value": "15"}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}, "_value": "18"}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}, "_value": "21"}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}, "_value": "24"}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}, "_value": "27"}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}, "_value": "30"}]}, {"td": [{"_attributes": {"style": "background-color: rgb(153, 204, 255); text-align: center;"}, "strong": [{"_value": "4"}]}, {"_attributes": {"style": "text-align:center"}, "_value": "4"}, {"_attributes": {"style": "text-align:center"}, "_value": "8"}, {"_attributes": {"style": "text-align:center"}, "_value": "12"}, {"_attributes": {"style": "text-align:center"}, "_value": "16"}, {"_attributes": {"style": "text-align:center"}, "_value": "20"}, {"_attributes": {"style": "text-align:center"}, "_value": "24"}, {"_attributes": {"style": "text-align:center"}, "_value": "28"}, {"_attributes": {"style": "text-align:center"}, "_value": "32"}, {"_attributes": {"style": "text-align:center"}, "_value": "36"}, {"_attributes": {"style": "text-align:center"}, "_value": "40"}]}, {"td": [{"_attributes": {"style": "background-color: rgb(153, 204, 255); text-align: center;"}, "strong": [{"_value": "5"}]}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}, "_value": "5"}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}, "_value": "10"}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}, "_value": "15"}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}, "_value": "20"}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}, "_value": "25"}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}, "_value": "30"}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}, "_value": "35"}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}, "_value": "40"}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}, "_value": "45"}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}, "_value": "50"}]}, {"td": [{"_attributes": {"style": "background-color: rgb(153, 204, 255); text-align: center;"}, "strong": [{"_value": "6"}]}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}, "_value": "6"}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}, "_value": "12"}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}, "_value": "18"}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}, "_value": "24"}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}, "_value": "30"}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}, "_value": "36"}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}, "_value": "42"}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}, "_value": "48"}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}, "_value": "54"}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}, "_value": "60"}]}, {"td": [{"_attributes": {"style": "background-color: rgb(153, 204, 255); text-align: center;"}, "strong": [{"_value": "7"}]}, {"_attributes": {"style": "text-align:center"}, "_value": "7"}, {"_attributes": {"style": "text-align:center"}, "_value": "14"}, {"_attributes": {"style": "text-align:center"}, "_value": "21"}, {"_attributes": {"style": "text-align:center"}, "_value": "28"}, {"_attributes": {"style": "text-align:center"}, "_value": "35"}, {"_attributes": {"style": "text-align:center"}, "_value": "42"}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}, "_value": "70"}]}, {"td": [{"_attributes": {"style": "background-color: rgb(153, 204, 255); text-align: center;"}, "strong": [{"_value": "8"}]}, {"_attributes": {"style": "text-align:center"}, "_value": "8"}, {"_attributes": {"style": "text-align:center"}, "_value": "16"}, {"_attributes": {"style": "text-align:center"}, "_value": "24"}, {"_attributes": {"style": "text-align:center"}, "_value": "32"}, {"_attributes": {"style": "text-align:center"}, "_value": "40"}, {"_attributes": {"style": "text-align:center"}, "_value": "48"}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}, "_value": "80"}]}, {"td": [{"_attributes": {"style": "background-color: rgb(153, 204, 255); text-align: center;"}, "strong": [{"_value": "9"}]}, {"_attributes": {"style": "text-align:center"}, "_value": "9"}, {"_attributes": {"style": "text-align:center"}, "_value": "18"}, {"_attributes": {"style": "text-align:center"}, "_value": "27"}, {"_attributes": {"style": "text-align:center"}, "_value": "36"}, {"_attributes": {"style": "text-align:center"}, "_value": "45"}, {"_attributes": {"style": "text-align:center"}, "_value": "54"}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}, "_value": "90"}]}, {"td": [{"_attributes": {"style": "background-color: rgb(153, 204, 255); text-align: center;"}, "strong": [{"_value": "10"}]}, {"_attributes": {"style": "text-align:center"}, "_value": "10"}, {"_attributes": {"style": "text-align:center"}, "_value": "20"}, {"_attributes": {"style": "text-align:center"}, "_value": "30"}, {"_attributes": {"style": "text-align:center"}, "_value": "40"}, {"_attributes": {"style": "text-align:center"}, "_value": "50"}, {"_attributes": {"style": "text-align:center"}, "_value": "60"}, {"_attributes": {"style": "text-align:center"}, "_value": "70"}, {"_attributes": {"style": "text-align:center"}, "_value": "80"}, {"_attributes": {"style": "text-align:center"}, "_value": "90"}, {"_attributes": {"style": "text-align:center"}, "_value": "100"}]}]}]}]}
Add the new facts you encountered in this lesson to your multiplication table.


correct_option_index: 11

19