CCSS.Math.Content.HSA-REI.D

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

• CCSS.Math.Content.HSA-REI.D.10

  Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be...

• CCSS.Math.Content.HSA-REI.D.11

  Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); fin...

• CCSS.Math.Content.HSA-REI.D.12

  Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution ...

01

What Students Need to Do

Students graph both sides of an equation as separate functions and find where the graphs meet. For inequalities, they graph boundaries, test points, and identify shaded regions that satisfy all conditions.

02

What Mastery Looks Like

Students choose a useful scale and graph each relation accurately. They identify intersection values, shade correct regions, use solid or dashed boundaries correctly, and check answers in the original relation.

03

Common Misconceptions

Students may report the y-coordinate of an intersection instead of the x-coordinate that solves the equation. They may also use the wrong boundary line, shade the wrong side, or miss solutions because of a poor graphing window.

04

How to Assess It

On one set of axes, graph y = x + 2 and y = x². Give both x-values where the graphs meet, then shade where x² > x + 2.

1. 01

   Graph y = x² and y = 2x + 3 on separate transparencies, overlay them, and mark the intersections.

2. 02

   Write why the x-coordinate of an intersection solves f(x) = g(x), while the y-coordinate does not.

3. 03

   Match cards showing equations, graphs, intersection points, and solution sets, then explain each match to a partner.

4. 04

   Graph a business's cost and revenue functions, then identify and interpret the break-even point.

• CCSS.Math.Content.HSA-REI.B

  Solve equations and inequalities in one variable

• CCSS.Math.Content.2.OA.A

  Represent and solve problems involving addition and subtraction.

• CCSS.Math.Content.1.OA.A

  Represent and solve problems involving addition and subtraction.

• CCSS.Math.Content.6.EE.B

  Reason about and solve one-variable equations and inequalities.