Maryland Math 8.AT.B.3.a
The Standard
- 8.AT.B.3
- Solve linear equations in one variable.
Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solution. Justify each example by showing how it can be rewritten in an equivalent equation in the form x=a, a=a, or a=b (where a and b are different rational numbers) and explaining what this form reveals about the solution.
Maryland College and Career Ready Standards for Mathematics (2025) · MAKE SENSE OF AND SOLVE EQUATIONS, INEQUALITIES, AND SYSTEMS OF EQUATIONS.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students write linear equations with one solution, every number as a solution, or no solution. They use equivalent steps to reach x = a, a = a, or a = b, then explain what each result means.
What Mastery Looks Like
- A student writes x + 3 = 8 and reduces it to x = 5. They also write 2x + 2 = 2x + 2 and 2x + 2 = 2x + 3. They reduce these to 2 = 2 and 2 = 3, then explain why one works for every number and the other works for none.
Common Misconceptions
- Students may read 2 = 2 as x = 2 instead of recognizing that every value of x works. They may treat 2 = 3 as a step to fix rather than proof that no value works.
How to Assess It
- Exit ticket: Write one equation that simplifies to x = 4, one to 2 = 2, and one to 2 = 3. Show the steps and state the solution set for each.
Lesson moves
Ways to Teach It
Build x + 2 = 5 and 2x + 2 = 2x + 3 with algebra tiles; remove matching tiles and describe what remains.
Compare 2x + 4 = 2(x + 2) and 2x + 4 = 2x + 5; explain why their solution sets differ.
Sort cards x + 3 = 7, x + 2 = x + 2, and x + 2 = x + 3; explain each final form.
Compare $5 plus $2 per mile with $9 plus $2 per mile; write an equation showing why these taxi fares never match.
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