Seventh Grade · Math · week 21

Writing equations from word problems

Translate a word problem into a two-step equation of the form px + q = r, define the variable clearly, and solve it.

The hardest part of a word problem is usually not the solving -- it is the translating. Start by naming the variable in a full sentence, like "let x = the price of one notebook," before writing anything else.

Look for the repeated, per-item amount (that becomes the coefficient on x) and the extra flat amount (that gets added or subtracted). Once the equation is written, it solves exactly like last week.

📋 For the teacher
Teach it (10–15 min):
  • Insist on a full "let x = ..." sentence before any equation gets written -- it prevents confusion about what the answer even means.
  • Hunt for the per-unit rate (the coefficient) and the flat extra amount (the constant) separately in the story.
  • Once the equation is written, solving it is pure practice from last week -- treat translating and solving as two separate skills.
  • Have them answer in a full sentence at the end, like "each notebook costs $6," not just "x = 6."
Talk about it:
  • Why is writing "let x = ..." an important first step, even though it takes extra time?
  • How do you find the coefficient of x versus the constant in a word problem?
  • Why should the final answer be written as a full sentence?

Mastery looks like: They define a variable clearly, translate a word problem into a two-step equation, and solve it with a sentence answer.

Common stumbles: Writing the equation with the flat amount and per-unit amount swapped; giving a bare number as the final answer instead of a labeled sentence.

Homework for this lessonType it, write it with a stylus, or print it for pencil & paper.open →
Records attendance + 15 min of Math for this learner.
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