CCSS.Math.Content.HSA-REI.B

CCSS.Math.Content.HSA-REI.B is a cluster heading. These are the individual standards under it.

• CCSS.Math.Content.HSA-REI.B.3

  Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

• CCSS.Math.Content.HSA-REI.B.4

  Solve quadratic equations in one variable.

• CCSS.Math.Content.HSA-REI.B.4a

  Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x - p)² = q that has the same solutions. Derive t...

• CCSS.Math.Content.HSA-REI.B.4b

  Solve quadratic equations by inspection (e.g., for x² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to ...

01

What Students Need to Do

Students isolate an unknown using valid inverse operations and keep each step equivalent to the original statement. They solve linear and quadratic equations, solve linear inequalities, show solution sets, and check results.

02

What Mastery Looks Like

Students choose efficient steps, keep both sides balanced, and explain why each transformation preserves the solution set. They represent inequality solutions correctly and check equation solutions in the original equation.

03

Common Misconceptions

Students may reverse an inequality sign without multiplying or dividing by a negative, or forget to reverse it when needed. They may apply an operation to only part of an expression, lose solutions when taking square roots, or accept extraneous answers.

04

How to Assess It

Give an exit ticket: solve 3(x - 2) ≤ -2x + 9 and x² - 5x = 14, then check each answer.

1. 01

   Use balance scales or algebra tiles to model 2x + 3 = 11, then record each physical move as an algebraic step.

2. 02

   Ask students to compare two worked solutions and write which steps preserve equivalence, which do not, and why.

3. 03

   Play an error-analysis relay where teams correct cards showing sign errors, distribution mistakes, missing roots, and extraneous solutions.

4. 04

   Give phone-plan costs and ask students to find when one plan becomes cheaper, then graph the solution on a number line.

• CCSS.Math.Content.8.EE.C.7

  Solve linear equations in one variable.

• CCSS.Math.Content.6.EE.B

  Reason about and solve one-variable equations and inequalities.