7.10.B
The Standard
represent solutions for one-variable, two-step equations and inequalities on number lines
Texas Essential Knowledge and Skills for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students solve one-variable, two-step equations and inequalities. They show an equation’s solution as a point and an inequality’s solutions with an endpoint and a ray.
What Mastery Looks Like
- Students isolate the variable accurately and identify the boundary value. They graph an equation as one point and an inequality with the correct open or closed circle and ray direction.
Common Misconceptions
- Students may graph only the boundary point instead of the full inequality solution set. They often reverse the ray, confuse open and closed circles, or forget to reverse the inequality sign when dividing by a negative.
How to Assess It
- Give an exit ticket: solve and graph 3x - 5 = 7 and -2x + 3 ≤ 11. Ask students to label each endpoint and explain the ray direction.
Lesson moves
Ways to Teach It
Make a floor number line with tape; students solve cards, stand at equation solutions, and place rope rays for inequality solutions.
Display x = 3 and x > 3; ask students to write how the graphs differ and explain why.
Run a card match with equations, inequalities, solved forms, and number line graphs, then have pairs justify each match.
Use a phone plan with a fixed fee and per-gigabyte charge; students graph the data amounts that stay within a budget.
Keep exploring
Related Standards
- 7.11.A
model and solve one-variable, two-step equations and inequalities
- 6.9.B
represent solutions for one-variable, one-step equations and inequalities on number lines
- 6.9.A
write one-variable, one-step equations and inequalities to represent constraints or conditions within problems
- 7.10.A
write one-variable, two-step equations and inequalities to represent constraints or conditions within problems
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