options: Apply and extend previous understandings of arithmetic to algebraic expressions.

Write and interpret numerical expressions.

Write expressions in equivalent forms to solve problems.

Reason about and solve one-variable equations and inequalities.

Represent and solve problems involving multiplication and division.

Rewrite rational expressions.

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

Represent and solve problems involving addition and subtraction.

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

Represent and solve equations and inequalities graphically.

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

Use properties of operations to generate equivalent expressions.

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

Interpret the structure of expressions.

Create equations that describe numbers or relationships

Represent and analyze quantitative relationships between dependent and independent variables.

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

Use polynomial identities to solve problems.

Add and subtract within 20.

Perform arithmetic operations on polynomials.

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

Understand the relationship between zeros and factors of polynomials.

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

Gain familiarity with factors and multiples.

Use the four operations with whole numbers to solve problems.

Multiply and divide within 100.

Generate and analyze patterns.

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

Solve equations and inequalities in one variable.

Work with radicals and integer exponents.

Solve systems of equations.

Analyze patterns and relationships.

Work with addition and subtraction equations.

Understand the connections between proportional relationships, lines, and linear equations.
problem_activity: Task
Most savings accounts advertise an annual interest rate, but they actually compound that interest at regular intervals during the year. That means that, if you own an account, you’ll be paid a portion of the interest before the year is up, and, if you keep that payment in the account, you’ll start earning interest on the interest you’ve already earned.
For example, suppose you put \$500 in a savings account that advertises 5% annual interest. If that interest is paid once per year, then your balance $B$ after $t$ years could be computed using the equation $B = 500(1.05)^t$, since you’ll end each year with 100% + 5% of the amount you began the year with.
On the other hand, if that same interest rate is compounded monthly, then you would compute your balance after $t$ years using the equation $$B=500\left(1+\frac{.05}{12}\right)^{12t}$$
Why does it make sense that the equation includes the term $\frac{.05}{12}$? That is, why are we dividing .05 by 12?
How does this equation reflect the fact that you opened the account with \$500?
What do the numbers 1 and $\frac{.05}{12}$ represent in the expression $\left(1+\frac{.05}{12}\right)$?
What does the “$12t$” in the equation represent?


correct_option_index: 13