# 3.17 - Equivalent Relationships

The student will

• create equations to represent equivalent mathematical relationships.

### BIG IDEAS

• So that I can show that I understand what the equal symbol means
• So that I can balance equations by showing different ways to express the same values

### UNDERSTANDING THE STANDARD

• Mathematical relationships can be expressed using equations (number sentences).
• A number sentence is an equation with numbers (e.g., 6 + 3 = 9; or 6 + 3 = 4 + 5).
• The equal symbol (=) means that the values on either side are equivalent (balanced).
• The not equal (≠) symbol means that the values on either side are not equivalent (not balanced).
• An expression is a representation of a quantity.  It contains numbers, variables, and/or computational operation symbols.  It does not have an equal symbol (e.g., 5, 4 + 3, 8 - 2, 2 × 7).
• An equation is a mathematical sentence in which two expressions are equivalent. It consists of two expressions, one on each side of an 'equal' symbol (e.g., 5 + 3 = 8, 8 = 5 + 3 and 4 + 3 = 9 - 2).
• An equation can be represented using balance scales, with equal amounts on each side (e.g., 3 + 5 = 6 + 2).

### ESSENTIALS

The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to

• Identify and use the appropriate symbol to distinguish between expressions that are equal and expressions that are not equal (e.g., 256 - 13 = 220 + 23; 143 + 17 = 140 + 20;  457 + 100 ≠ 557 +100).
• Create equations to represent equivalent mathematical relationships (e.g., 4 × 3 = 14 - 2).

### KEY VOCABULARY

Updated: Aug 22, 2018