Milk Carton Apartments

Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.

Solve real-world and mathematical problems by writing and solving equations of the form 𝘹 + 𝘱 = 𝘲 and 𝘱𝘹 = 𝘲 for cases in which 𝘱, 𝘲 and 𝘹 are all nonnegative rational numbers.

Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation 𝘥 = 65𝘵 to represent the relationship between distance and time.

Solve word problems leading to equations of the form 𝘱𝘹 + 𝘲 = 𝘳 and 𝘱(𝘹 + 𝘲) = 𝘳, where 𝘱, 𝘲, and 𝘳 are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?

Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.