Patterns & Algebraic Reasoning
Georgia Standards: 7.PAR.2: Use properties of operations, generate equivalent expressions and interpret the expressions to explain relevant situations.
7.PAR.3: Represent authentic situations using equations and inequalities with variables; solve equations and inequalities symbolically, using the properties of equality.
Expectations
Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
Rewrite an expression in different forms from a contextual problem to clarify the problem and show how the quantities in it are related.
Construct algebraic equations to solve practical problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Interpret the solution based on the situation.
Construct algebraic inequalities to solve problems, leading to inequalities of the form px + q > r, px + q < r, px + q ≤ r, or px + q ≥ r, where p, q, and r are specific rational numbers. Graph and interpret the solution based on the realistic situation that the inequalities represent.
Examples
A rectangle is twice as long as it is wide. One way to write an expression to find the perimeter would be w + w + 2w + 2w. Write the expression in two other ways.
If Madison and Brenda both get paid a wage of $11 per hour, but Madison was paid an additional $55 for overtime, the expression 11(M+B) + 55 may be more clearly interpreted as 11M+55+11B for purposes of understanding Brenda’s pay separated from Madison’s pay.
Vicky and Bob went to a store to buy school supplies. Vicky spent a total of $22 on school supplies. She spent $13 on a book and spent the rest of the money on notebooks. The store sells notebooks for $1.50 each. Without using a variable, determine the number of notebooks Vicky bought.
As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make and describe the solutions.