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🧩 High school math · Patterns & Algebra

High school algebra

Solve a formula for one letter the same way you solve an equation: undo each step, in reverse, on both sides. P = 2l + 2w. Take 2l from both sides: P − 2l = 2w. Divide by 2: w = (P − 2l) ÷ 2.

Worked example

The formula for the volume of a box is V = lwh. Which equation solves it for h?
Answer: h = V ÷ (lw)
Start with V = lwh and undo the operations around h in reverse order, doing the same thing to both sides each time. That gives h = V ÷ (lw). Test it with small numbers to be sure.

For grown-ups: HS Algebra: seeing structure, polynomials, rational expressions, creating equations, reasoning with equations (quadratics, systems). Below: three problems to try with the worked answers, and a free printable sheet. Children can practise the same skill as a game, with no sign-up and no ads.

  • CCSS A-SSE
  • CCSS A-APR
  • CCSS A-CED
  • CCSS A-REI
What this practises, for teachers

Practices hS Algebra: seeing structure, polynomials, rational expressions, creating equations, reasoning with equations (quadratics, systems) (A-SSE, A-APR, A-CED, A-REI). A printable sheet with its answer key, worked answers on the page, no accounts.

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For your class

🖨️ Printable sheet and key

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Try three

  1. The formula for simple interest is I = prt. Which equation solves it for t?
    Show the answer and how
    Answer: t = I ÷ (pr)
    Start with I = prt and undo the operations around t in reverse order, doing the same thing to both sides each time. That gives t = I ÷ (pr). Test it with small numbers to be sure.
  2. The formula for a line is y = mx + b. Which equation solves it for m?
    Show the answer and how
    Answer: m = (y − b) ÷ x
    Start with y = mx + b and undo the operations around m in reverse order, doing the same thing to both sides each time. That gives m = (y − b) ÷ x. Test it with small numbers to be sure.
  3. The formula for the area of a trapezoid is A = ½(a + b)h. Which equation solves it for a?
    Show the answer and how
    Answer: a = 2A ÷ h − b
    Start with A = ½(a + b)h and undo the operations around a in reverse order, doing the same thing to both sides each time. That gives a = 2A ÷ h − b. Test it with small numbers to be sure.

Before and after

Learn first: Two equations at once (8th)

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High school algebra (High school)

  1. The formula for the area of a rectangle is A = lw. Which equation solves it for w?
  2. The formula for the volume of a box is V = lwh. Which equation solves it for h?
  3. The formula for simple interest is I = prt. Which equation solves it for t?
  4. The formula for simple interest is I = prt. Which equation solves it for t?
  5. The formula for distance, rate and time is d = rt. Which equation solves it for r?
  6. The formula for speed that changes steadily is v = u + at. Which equation solves it for u?
  7. The formula for speed that changes steadily is v = u + at. Which equation solves it for u?
  8. The formula for the volume of a box is V = lwh. Which equation solves it for h?
  9. The formula for the area of a trapezoid is A = ½(a + b)h. Which equation solves it for a?
  10. The formula for the mean of three numbers is m = (a + b + c) ÷ 3. Which equation solves it for c?
  11. The formula for the volume of a box is V = lwh. Which equation solves it for h?
  12. The formula for the area of a trapezoid is A = ½(a + b)h. Which equation solves it for a?

Answer key

  1. w = A ÷ l
  2. h = V ÷ (lw)
  3. t = I ÷ (pr)
  4. t = I ÷ (pr)
  5. r = d ÷ t
  6. u = v − at
  7. u = v − at
  8. h = V ÷ (lw)
  9. a = 2A ÷ h − b
  10. c = 3m − a − b
  11. h = V ÷ (lw)
  12. a = 2A ÷ h − b

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