Maryland Math 6.AT.C.8.b
The Standard
- 6.AT.C.8
- Solve problems in context by writing and solving equations and interpreting the solutions in context.
Write and solve one-step equations of the form x + p = q, x − p = q, px = q and x/p = q for cases in which p, q and x are all nonnegative rational numbers.
Maryland College and Career Ready Standards for Mathematics (2025) · REASON ABOUT AND SOLVE ONE-VARIABLE EQUATIONS AND INEQUALITIES
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students write an equation with one unknown from a word problem. They undo one operation to solve it, using whole numbers, fractions, or decimals. They check the answer in the original equation.
What Mastery Looks Like
- Given three equal shares totaling 2 1/4, a student writes 3x = 2 1/4 and finds x = 3/4. They solve x − 0.6 = 1.2 by adding 0.6, then check that 1.8 works.
Common Misconceptions
- Some students reverse the subtraction in x − p = q and subtract q from p. Others divide q by p when solving x/p = q, instead of multiplying.
How to Assess It
- Exit ticket: A ribbon has 3/4 meter cut off and 1 1/2 meters left. Write an equation for its original length, solve it, and check your answer.
Lesson moves
Ways to Teach It
Hide three quarter strips under a cup, place three more beside it, and balance against six strips; remove three from each side.
Ask pairs to explain, with a sketch, why x ÷ 3 = 1/2 gives x = 3/2, not 1/6.
Match cards x + 0.4 = 1.1, x − 1/3 = 1/2, 2x = 3, and x/4 = 3/8 to solutions.
Give students a recipe using 3/4 cup oats per batch and 3 cups total; have them write and solve for batch count.
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Related Standards
- 7.AT.C.8.a
Write equations of the form px + q = r and p(x + q) = r where p, q, and r are specific rational numbers.
- 6.AT.C.10.b
Write and solve one-step inequalities of the form x + p > q, x − p > q, px > q and x/p > q (using ≥, >, ≤, <) where p and q are nonnegative rational numbers.
- 7.AT.C.9.a
Write inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers.
- 8.NOS.B.4.a
Use square and cube roots symbols to represent solutions to equations of the form x² = p and x³ = p, where p is a positive rational number.
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