few_shots: Example:
Problem/activity:
Task
Cruz and Erica were both getting ready for soccer.
Cruz ran 1 lap around the school.
Erica ran 3 laps around the playground.
Erica said,
I ran more laps, so I ran farther.
Cruz said,
4 laps around the school is 1 mile, but it takes 12 laps around the playground to go 1 mile. My laps are much longer, so I ran farther.
Who is right? Draw a picture to help you explain your answer.


Mathematical concept/skill options: 
A. Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
B. Extend understanding of fraction equivalence and ordering.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
C. Use equivalent fractions as a strategy to add and subtract fractions.
D. Develop Understanding of fractions as numbers.
Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.
E. Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
F. Understand decimal notation for fractions, and compare decimal fractions.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.


Your response:
Thought: In this problem, students learn to recognize equivalent fractions. That is, three laps around the playground is 3/12 mile, which is equivalent to 1/4, which is one lap around the school.
Answer: B

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: im_task_000212

4
options: Understand the connections between proportional relationships, lines, and linear equations.

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

Analyze patterns and relationships.

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

Use the four operations with whole numbers to solve problems.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Use properties of operations to generate equivalent expressions.

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

Work with addition and subtraction equations.

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

Generate and analyze patterns.

Write expressions in equivalent forms to solve problems.

Represent and solve problems involving addition and subtraction.

Work with radicals and integer exponents.

Understand the relationship between zeros and factors of polynomials.

Gain familiarity with factors and multiples.

Represent and solve problems involving multiplication and division.

Solve equations and inequalities in one variable.

Use polynomial identities to solve problems.

Add and subtract within 20.

Represent and solve equations and inequalities graphically.

Create equations that describe numbers or relationships

Solve systems of equations.

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

Rewrite rational expressions.

Write and interpret numerical expressions.

Perform arithmetic operations on polynomials.

Represent and analyze quantitative relationships between dependent and independent variables.

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

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

Reason about and solve one-variable equations and inequalities.

Interpret the structure of expressions.

Multiply and divide within 100.

Solve real-life and mathematical problems using numerical and algebraic expressions and equations.
problem_activity: Problem 1
Explain how you know the expressions in Column A are equivalent to the expressions in Column B.
| **           Column A          ** | **           Column B          ** |
|-----------------------------------|-----------------------------------|
|           $${-3(x+4)}$$           |           $${-3x-12}$$            |
|           $${(4+x)+3}$$           |           $${x+(4+3)}$$           |
|           $${(x+4)-3}$$           |          $${-3+(x+4)}$$           |
Problem 2
Explain the properties of operations that were used to transform
$${a(x-y)}$$
to the equivalent expression,
$${-(ay-ax)}$$
.
Problem 3
If the expression
$${\frac{x}{2} + \frac{3}{4}}$$
is multiplied by
$$4$$
, the expression
$${{2x+3}}$$
results.
Is
$${{2x+3}}$$
an equivalent expression to
$${\frac{x}{2} + \frac{3}{4}}$$
?


correct_option_index: 3

31