# 1.15 - Equality

The student will

• demonstrate an understanding of equality through the use of the equal symbol.

### BIG IDEAS

• So that I know that the equal sign means that the expressions on either side have the same value, similar to a balanced scale.

### UNDERSTANDING THE STANDARD

 At this level, students should represent equality using objects, words, and symbols through the use of the equal symbol while inequality should be communicated primarily through words such as not equal, not equivalent, etc.Equality can be shown using a balance scale or a number balance.  An equation, such as 3 + 5 = 6 + 2, can be represented using a balance scale, with equal amounts on each side. 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). A common misunderstanding is that the equal symbol always means “the answer comes next.”  The equal symbol represents a balance between expressions.  The equal symbol means “is the same as” or “another name for” or “equal in value.”Inequalities such as 5 < 4 + 3 are not equations.  Equations must have the equal symbol (e.g., 5 + 6 = 11).Equations should be routinely modeled in conjunction with story problems.  Manipulatives such as connecting cubes and counters can be used to model equations.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). Students at this level are not expected to use the term expression.Solving missing addend problems and stories helps with the understanding of equality and use of the equal symbol (e.g., There are four red birds in the tree.  Some black birds fly to the tree.  Now there are six birds in the tree.  How many black birds flew to the tree?  4 +__ = 6)

### ESSENTIALS

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

• Describe the concept of equality.
• Identify equivalent values and represent equalities through the use of objects, words, and the equal (=) symbol.
• Identify and describe expressions that are not equal (e.g., 4 + 3 is not equal to 3 + 5).
• Recognize that equations can be used to represent the relationship between two expressions of equal value (e.g., 4 + 2 = 2 + 4 and 6 + 1= 4 + 3).
• Model an equation that represents the relationship of two expressions of equal value.

### KEY VOCABULARY

Updated: Aug 22, 2018