7.11

Math7th Grade

Knowledge and Skills Statement (Standard Cluster)

The student applies mathematical process standards to solve one-variable equations and inequalities

Texas Essential Knowledge and Skills for Mathematics

Cluster contents

7.11 is a knowledge and skills statement. These are the student expectations under it.

Teacher's field guide

What Students Need to Do: Students write and solve two-step equations and inequalities with one variable. They test given values by substitution. They use triangle angle sums and angle relationships to write and solve equations.
What Mastery Looks Like: Students isolate the variable and keep both sides balanced. They substitute a given value and correctly decide whether the statement is true. They write equations from triangle and angle facts, then solve and check them.
Common Misconceptions: Students may undo operations in the wrong order or change only one side. They often forget to reverse an inequality sign after multiplying or dividing by a negative number. They may confuse supplementary, complementary, and vertical angle relationships.
How to Assess It: Use a four-item exit ticket: solve 3x - 5 = 16, solve -2x + 7 < 15, test x = 4 in 5x - 3 = 17, and write an equation for the third angle of a triangle with angles 48° and 67°.

Lesson moves

Use algebra tiles and inequality cards to build two-step problems, solve them, and show when the inequality sign must reverse.
Ask students to explain in writing why multiplying both sides by a negative number reverses an inequality sign.
Play Equation Check Relay: teams solve a card, test a proposed value, then pass the verified answer to the next student.
Give a floor-plan sketch with missing angles, and have students write and solve an equation for each unknown angle.

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