Ray's New Elementary Algebra · Arts. 145–152 · Unit 4: Chapter IV: Simple equations
24. What an equation is; the axioms
Goal: Your student can name the parts and kinds of equations, explain what "solve" and "verify" mean, and state the six axioms.
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
Equation, members, known and unknown quantities, degrees (simple, quadratic), identical, numerical and literal equations, solving and verifying, the root of an equation, and the six axioms. No exercises.
The lesson, step by step
Warm-up
Ask: What number take away 3 leaves 4? How did you know?
Equations and members
Read Arts. 145 to 147.
An Equation is an algebraic expression, stating the equality between two quantities
Write x − 3 = 4. Ask your student to name the first member and the second member.
Degrees and kinds
Read Arts. 148 and 149. Write 2x + 5 = 9, 4x² − 7 = 29, and 5 = 5. Your student names each: simple, quadratic, identical.
Solving and verifying
Read Arts. 150 and 151.
The Root of an equation is the value of its unknown quantity.
Solve x − 3 = 4 by adding 3 to both sides, then verify: 7 − 3 = 4.
The axioms
Read Art. 152 and the six axioms.
1. If, to two equal quantities, the same quantity be added, the sums will be equal.
Your student copies all six into the rule notebook, then says which axiom was used to solve x − 3 = 4. (Axiom 1.)
Wrap-up
Ask: If 3x = 12, which axiom lets you divide both sides by 3?
Tip
Picture a balance scale. Whatever you do to one pan, do to the other.