Ray's New Elementary Algebra · Arts. 18–38 · Unit 1: Chapter I: Fundamental rules

2. Signs, coefficients, powers and roots

Goal: Your student reads the signs = + − × ÷ > aloud correctly, and knows what a coefficient, an exponent and a root are.

⏱ About 40 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)

What's in the book

The principal signs of algebra one by one (equality, plus and minus, multiplication, division, inequality, infinity), then coefficients, powers and exponents, roots and the radical sign.

The lesson, step by step

  1. Warm-up

    Write 3 + 4 = 7 and 12 ÷ 3 > 2. Ask your student to read each aloud in words.

  2. Plus, minus and like signs

    Read Arts. 19 to 24.

    When a quantity has no sign prefixed, it is positive.

    Quantities having the same sign are said to have like signs; those having different signs, unlike signs.

    Write 5a − 3b + c. Ask: Which terms are positive? Which have like signs?

  3. Factors and the signs of multiplying and dividing

    Read Arts. 25 to 29.

    Factors are quantities that are to be multiplied together.

    SayIn algebra, ab means a times b. We leave out the times sign between letters.

    Ask your student to read aloud: a × b, ab, 3ab, a ÷ b.

  4. Coefficients

    Read Arts. 30 to 32.

    The Literal Coefficient of a quantity is a quantity by which it is multiplied.

    Write 5x, ax, 3ay. Ask: What is the coefficient of x in each? (5, a, 3a.) Point out that a letter with no number in front has coefficient 1.

  5. Powers and exponents

    Read Arts. 33 and 34.

    The Power of a quantity is the product arising from multiplying the quantity by itself one or more times.

    Saya³ means aaa, three a's multiplied. The small 3 is the exponent.

    Have your student write out a², a⁴ and x³ as products, then tell the difference between 3a and a³ using a = 2. (6 and 8.)

  6. Roots and the radical sign

    Read Arts. 35 to 38.

    The Root of a quantity is another quantity, some power of which equals the given quantity.

    Ask: What is the square root of 25? The cube root of 8? Show how the index sits over the radical sign for a cube root.

  7. Check and wrap-up

    Write 4a²b − 3x + √c. Your student names every sign, coefficient, exponent and radical in it, out loud.

Afterwards

Make flash cards: the sign on one side, how it is read on the other. Five minutes before the next session.

Tip

The mix-up to watch for is 3a versus a³. Testing both with a number (a = 2) settles it fast.

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