Unpacked Content
Knowledge
Students know:
- p(x + q) = px + pq, where p and q are specific rational numbers.
- When multiplying or dividing both sides of an inequality by a negative number, every term must change signs and the inequality symbol reversed.
- In the graph of an inequality, the endpoint will be a closed circle indicating the number is included in the solution set (≤ or ≥) or an open circle indicating the number is not included in the solution set ( ).
Skills
Students are able to:
- Use variables to represent quantities in a real-world or mathematical problem.
- Construct equations (px + q = r and p(x + q) = r) to solve problems by reasoning about the quantities.
- Construct simple inequalities (px + q > r or px + q ) to solve problems by reasoning about the quantities.
- Graph the solution set of an inequality.
Understanding
Students understand that:
- Real-world problems can be represented through algebraic expressions, equations, and inequalities.
- The inequality symbol reverses when multiplying or dividing both sides of an inequality by a negative number, and why.
Vocabulary
- Algebraic expressions
- Equations
- Inequalities
- Greater than
- Greater than or equal to
- less than
- less than or equal to
