Student Actions

Teacher Actions

• Develop accurate and appropriate procedural fluency by appropriately using greater than, less than, and equal signs in equations and expressions.

• Develop strategies for problem solving by determining unknowns in number sentences in a variety of ways involving basic facts (addition/subtraction, multiplication/division).

• Develop a productive mathematical disposition by applying equivalent and non-equivalent expressions to real-world situations.

• Develop a deep and flexible conceptual understanding by identifying a mathematical expression which correctly represents a given real-world problem scenario.

• Facilitate meaningful mathematics discourse about the meaning of the equal sign as a comparative symbol, not an operational symbol.  

• Use and connect multiple representations of equivalent and non-equivalent expressions (manipulative and pictorial, as well as symbolic), in order to deepen student understanding of these expressions and the procedures for solving them.

• Elicit evidence of student thinking by asking students to explain and justify their reasoning as they interpret mathematical expressions.

• Use evidence of student thinking to assess progress toward key understandings and guide additional instruction.

Key Understandings

Misconceptions

• Symbols and letters can be used to represent numbers.

• The equal sign (=) means ‘the same as’, or ‘having the same value’; it is not an operational symbol.

• Real-world problem scenarios can be illustrated using mathematical expressions.

• By using knowledge of basic facts, and understandings of inverse operations, it is possible to find the value of unknowns, or variables, in both equivalent and non-equivalent expressions.

• There are rules that determine which number a letter stands for.
• For example, e = 5 because e is the fifth letter of the alphabet or y = 4 because y was 4 in the last number sentence.
• An inequality can be ‘reversed’ in the same way that an equation can.  For example, 5 + 2 = 7, 7 = 5 + 2.  Students may believe ‘5 + 2 < 9’ is the same as ‘9 < 5 + 2’.   
• An equal sign means "and the answer is." In this way, when they see an equal sign, they want to carry out the operation preceding it.
• For example, when asked what the △ represents in the equation 4 x 3 = △ x 2 they say 12. They need to think of the equal sign as meaning "is the same as."