Ray's New Elementary Algebra · Art. 214 · Unit 7: Chapter VII: Quadratic equations

48. Problems producing quadratic equations

Goal: Your student sets up and solves word problems that lead to quadratics, and decides which root fits.

⏱ About 45 minutes · 7 steps

Open it at the Internet Archive ↗

You'll need

  • The book, open to the page
  • Pencil and plenty of paper (or a whiteboard)
  • A card to cover printed answers

What's in the book

Five worked problems (including the oranges, a number whose square plus 15 is 8 times itself, and dividing 24), a remark on negative roots, and exercises 6 to 20. Answers are printed.

The lesson, step by step

  1. Warm-up

    Solve x² − x = 20. (5 or −4.)

  2. Problem 1 together

    Read problem 1:

    1. What number is that, whose square diminished by the number itself, is equal to 20 ?

    Both 5 and −4 solve the equation. Read how Ray rewords the question so −4 fits too.

  3. Which root?

    Read problem 2 (oranges for 60 cents) and the Remark after it. Say: The positive root answers the question; the negative one answers a slightly different question.

  4. Guided practice

    4. Divide 24 into two such parts, that their product shall be 95.

    9. Find two numbers whose difference is 8, and whose product is 240. Ans. 12 and 20.

    Your student sets up and solves both. (The first gives 19 and 5.)

  5. Independent practice

    Exercises 6, 7, 10, 13, 14 and 16, then two or three of 11, 12, 15, 17 to 20.

  6. Check

    Read each answer back into the words of the problem, not just the equation.

  7. Wrap-up

    Ask your student to make up a "two numbers" problem with a quadratic equation for you.

Tip

In the orchard problem (14), drawing a small grid of rows and trees makes the equation obvious.

Answers to the book's problems

The book prints the answer after each exercise.

Worked out for this site from the scan. If a number in your copy differs, trust the book. Every answer is in the Key ↗.

@teddyrookbook GitHub