options: Write expressions in equivalent forms to solve problems.

Apply and extend previous understandings of arithmetic to algebraic expressions.

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

Interpret the structure of expressions.

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

Work with radicals and integer exponents.

Create equations that describe numbers or relationships

Represent and solve problems involving addition and subtraction.

Use the four operations with whole numbers to solve problems.

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

Write and interpret numerical expressions.

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

Understand the relationship between zeros and factors of polynomials.

Represent and solve equations and inequalities graphically.

Multiply and divide within 100.

Rewrite rational expressions.

Analyze patterns and relationships.

Solve equations and inequalities in one variable.

Use properties of operations to generate equivalent expressions.

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

Generate and analyze patterns.

Represent and solve problems involving multiplication and division.

Use polynomial identities to solve problems.

Reason about and solve one-variable equations and inequalities.

Work with addition and subtraction equations.

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

Solve systems of equations.

Represent and analyze quantitative relationships between dependent and independent variables.

Perform arithmetic operations on polynomials.

Add and subtract within 20.

Gain familiarity with factors and multiples.

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

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

Understand and apply properties of operations and the relationship between addition and subtraction.
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: 3