# 2.17 - Equality and Inequality

The student will

• demonstrate an understanding of equality through the use of the equal symbol and the use of the not equal symbol

### BIG IDEAS

• So that I can understand that mathematical sentences are equal
• So that I can understand that we all like to make things equal  and that dividing things into equal parts is an essential life skill

### UNDERSTANDING THE STANDARD

• 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).
• In order for students to develop the concept of equality, students need to see the = symbol used in various appropriate locations (e.g., 3 + 4 = 7 and 5 = 2 + 3).
• An equation (number sentence) is a mathematical statement representing two expressions that 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 a number balance scale, with equal amounts on each side (e.g., 3 + 5 = 6 + 2).
• An expression represents 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).  Students at this level are not expected to use the terms expression or variable.
• Manipulatives such as connecting cubes, counters, and number scales can be used to model equations.

### ESSENTIALS

The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to
• Identify the equal symbol (=) as the symbol used to indicate that the values on either side are equal

• Identify values and expressions that are not equal (e.g., 8 ≠ 9,  4 + 3 ≠ 8).
• Identify and use the appropriate symbol to distinguish between equal and not equal quantities (e.g., 9 + 24 = 10 + 23; 45 –  9 = 46 – 10; 15 + 16 ≠ 31 + 15).
• Use a model to represent the relationship of two expressions of equal value and two expressions that are not equivalent
• Identify values and expressions that are equal (e.g., 8 = 8,  8 = 4 + 4).

• Identify the not equal symbol (≠) as the symbol used to indicate that two values on either side are not equal.

### KEY VOCABULARY

Updated: Aug 22, 2018