Student Actions

Teacher Actions

• Develop Accurate and Procedural Fluency when given verbal phrases, translate into equations or inequalities by looking for words representing values and key operations.

• Develop Ability to Make Conjectures, Model, and Generalize when determining whether an equation or an inequality should be used to represent a given situation by examining the number of possible solutions in context to the situation.

• Productive Mathematical Disposition when writing an inequality from a word phrase, use real world examples to write out possible solutions to make meaning of what sign you should use. (Example:  You must be at least 16 to obtain a driver’s license. The student knows that the driver must be age 16 or any age higher (17, 18 , 19,etc…) making the inequality sign- greater than or equal to.)

• Develop Ability to Communicate Mathematically when graphing solutions to one variable equations and inequalities on a number line, discuss the meaning of an open circle versus a closed circle in context with a partner or class.

• Implement meaningful tasks that promote reasoning and problem solving by having students make a graphical organizer, such as a chart, to organize words that have operational or sign meanings (sum=addition, fewer than=<). Discuss real-world examples of when these keywords are used.

• Implement meaningful tasks that promote reasoning and problem solving by giving students a variety of situations and have them determine the number of possible solutions to aid in the development of when to to use an equation versus an inequality to represent to the solutions of a situation.

• Create mathematical meaning and connections when given graphed solutions on a number line, have students create real world situations that can be described with an equation or inequality that matches the graphs.                 

• Promote procedural fluency when teaching solutions to one-step equations, always show the graphical representation on a number line with a closed circle. This will make the closed circle vs open circle easier to understand when introducing inequalities.

                          

Key Understandings

Misconceptions

• Translate real world verbal representations and translate into equations and inequalities.

• Take real-world graphical representations and translate into equations and inequalities.

• Take real-world graphical representations and write a verbal description of a situation they may represent. 

• When writing solutions to inequalities, students will show that the answer is greater than 4, but then they will record their answer as 5 or greater. Students think the answer is the next whole number, ignoring all the numbers between 4 and 5 that are also part of the solution.

• The terms 'at least' and 'at most' sometimes cause confusion for students.

• The terms ‘is less than’ and ‘is greater than’ is confused with ‘less than’ and ‘greater than’. Some students do not realize the first set of terms are in an equation and the second set of terms are in an expression.