options: Work with radicals and integer exponents.

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

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

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

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

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

Generate and analyze patterns.

Use the four operations with whole numbers to solve problems.

Add and subtract within 20.

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

Multiply and divide within 100.

Represent and analyze quantitative relationships between dependent and independent variables.

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

Gain familiarity with factors and multiples.

Analyze patterns and relationships.

Represent and solve problems involving multiplication and division.

Interpret the structure of expressions.

Rewrite rational expressions.

Use polynomial identities to solve problems.

Reason about and solve one-variable equations and inequalities.

Solve systems of equations.

Write expressions in equivalent forms to solve problems.

Represent and solve problems involving addition and subtraction.

Use properties of operations to generate equivalent expressions.

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

Write and interpret numerical expressions.

Understand the relationship between zeros and factors of polynomials.

Create equations that describe numbers or relationships

Work with addition and subtraction equations.

Solve equations and inequalities in one variable.

Perform arithmetic operations on polynomials.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Represent and solve equations and inequalities graphically.

Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.
problem_activity: Task
Bernardo and Silvia play the following game. An integer between 0
and 999, inclusive, is selected and given to Bernardo. Whenever
Bernardo receives a number, he doubles it and passes the result to
Silvia. Whenever Silvia receives a number, she adds 50 to it and
passes the result to Bernardo. The winner is the last person who
produces a number less than 1000. What is the smallest initial number that results in a win for Bernardo?


correct_option_index: 27