Maryland Math 7.AT.C.8.a
The Standard
- 7.AT.C.8
- Use variables to represent quantities and write and solve equations to model and reason about relationships in context.
Write equations of the form px + q = r and p(x + q) = r where p, q, and r are specific rational numbers.
Maryland College and Career Ready Standards for Mathematics (2025) · MODEL WITH AND SOLVE EQUATIONS AND INEQUALITIES.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students turn stories and diagrams into equations with one unknown. They decide whether an amount is added once or added to every group. They use fractions, decimals, and negative numbers when the situation calls for them.
What Mastery Looks Like
- A student writes 4x + 1.50 = 25.50 for four tickets with one order fee. They write 4(x + 1.50) = 30 when each ticket has that fee, and they say what x represents.
Common Misconceptions
- Students put a one-time fee inside parentheses, which charges it for every item. They may leave parentheses out when each item has its own fee. Negative amounts can also lose their signs when students write the equation.
How to Assess It
- Exit ticket: Write an equation for each case. Four tickets at x dollars each plus one $1.50 order fee cost $25.50; four tickets at x dollars each with a $1.50 fee per ticket cost $30.
Lesson moves
Ways to Teach It
Put an x card and two quarters in each of three cups; tell students the cups total $12 and have them write an equation.
Ask students why 3(x + 0.50) = 12 fits three cups with 50 cents in each, but 3x + 0.50 = 12 does not.
Give pairs story cards and equation cards, including 3x + 0.50 and 3(x + 0.50); have them match each story to an equation.
Show a taxi receipt with a $4 pickup fee and $2.50 per mile totaling $19; have students write an equation for the miles.
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Related Standards
- 6.AT.C.8.b
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.
- 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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