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: Add and subtract within 20.

Create equations that describe numbers or relationships

Rewrite rational expressions.

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

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

Solve systems of equations.

Analyze patterns and relationships.

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

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

Reason about and solve one-variable equations and inequalities.

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

Solve equations and inequalities in one variable.

Represent and solve equations and inequalities graphically.

Represent and analyze quantitative relationships between dependent and independent variables.

Understand the relationship between zeros and factors of polynomials.

Write expressions in equivalent forms to solve problems.

Use polynomial identities to solve problems.

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

Gain familiarity with factors and multiples.

Apply and extend previous understandings of arithmetic to algebraic expressions.

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

Multiply and divide within 100.

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

Generate and analyze patterns.

Represent and solve problems involving addition and subtraction.

Work with addition and subtraction equations.

Use the four operations with whole numbers to solve problems.

Interpret the structure of expressions.

Represent and solve problems involving multiplication and division.

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

Use properties of operations to generate equivalent expressions.

Perform arithmetic operations on polynomials.

Work with radicals and integer exponents.

Write and interpret numerical expressions.
problem_activity: Warm-up
The purpose of this warm-up is for students to analyze symbolic statements about square roots and decide if they are true or not based on the meaning of the square root symbol.
Launch
Display one problem at a time. Tell students to give a signal when they have an answer and a strategy. After each problem, give students 1 minute of quiet think time and follow with a whole-class discussion.
Student Facing
Decide if each statement is true or false.
\(\left( \sqrt{5} \right)^2=5\)
\(\left(\sqrt{9}\right)^2 = 3\)
\(7 = \left(\sqrt{7}\right)^2\)
\(\left(\sqrt{10}\right)^2 = 100\)
\(\left(\sqrt{16}\right)= 2^2\)
Student Response
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Activity Synthesis
Poll students on their responses for each problem. Record and display their responses for all to see. If all students agree, ask 1 or 2 students to share their reasoning. If there is disagreement, ask students to share their reasoning until an agreement is reached.


correct_option_index: 32