Chapter 1
Number and Quantity
Course: Core Academic Skills For Educators Combined Test 5752
Subject: Core Academic Skills Educators Mathematics 5733
Chapter: Algebra
Writing equations or expressions to model problems is about translating a situation described in words into a mathematical form. An expression represents a single quantity using numbers, variables, and operations, while an equation shows a balance between two quantities. Modeling requires identifying variables, constants, and the relationships among them, then representing these relationships symbolically.
The skill is not just mechanical — it involves understanding the context, interpreting the language carefully, and checking whether the mathematical model reflects the real situation.
Distinction between equations and expressions
An expression shows a calculation but does not include an equal sign. Examples: 4x + 7, 3y² – 2y, 10(a + b).
An equation includes an equal sign and represents a statement of equality that can be solved for unknowns. Examples: 4x + 7 = 31, 3y² – 2y = 10, 10(a + b) = 50.