CCSS.Math.Content.8.EE.C.7a: Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).
CCSS.Math.Content.8.EE.C.7b: Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.
CCSS.Math.Content.HSA-REI.B.3: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
Solving equations is a foundational skill needed in pre-algebra and algebra. Being able to solve a variety of equations enables students to analyze functional relationships.
Students need practice in solving equations in order to develop fluency in uncovering unknown values.
In this sorting activity students analyze 12 equations to categorize them as true, never true, or sometimes true.
Equations that are always true have an infinite number of solutions and are known as identities.
Equations that are never true have no solutions and are known as contradictions.
Equations that are sometimes true have values for which they are true.
After sorting the equations there is a challenge activity in which an equation has a missing part. Students are asked to determine what the missing part would be if the equation had a specific solution. The challenge continues with asking what the missing part would be if the equation was always true, and then what would the missing part be if the equation was never true.
Last students are asked to create their own challenge equation with specific constraints.