Ray's New Elementary Algebra · Art. 156 (problems 1–8) · Unit 4: Chapter IV: Simple equations
27. From words to equations
Goal: Your student turns a word problem into an equation by naming the unknown and writing what the problem says about it.
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
The two parts of solving a problem, the rule for forming the equation, and fully worked problems 1 to 8 (two numbers, father and son, a line 25 inches long, $68 shared, a cistern).
The lesson, step by step
Warm-up
Ask: If x is a number, how do you write three times it? Its third part? 5 more than it?
The two parts
Read Art. 156.
1. Expressing the conditions of the problem in algebraic language; that is, forming the equation.
2. Solving the equation, or finding the value of the unknown quantity.
SayThe first part is the hard one. That is what we practice today.
The rule
Denote the required quantity by one of the final letters of the alphabet; then, by means of signs, indicate the same operations that it would be necessary to make on the answer to verify it.
SayPretend you already know the answer. What would you do to check it? Write that with x.
Work problem 1 together
1. There are two numbers, the second of which is three times the first, and their sum is 48 ; what are the numbers?
Let x = the first; then 3x = the second; x + 3x = 48; x = 12, and 3x = 36. Check: 12 + 36 = 48.
Guided practice
Cover the solutions. Your student sets up problems 2 (father and son) and 5 (the line 25 inches long), then compares with the book's working.
Independent practice
Problems 3, 4, 6, 7 and 8: your student writes the equation first, solves it, verifies it, and only then reads the book's solution.
Wrap-up
Ask your student to make up a problem like problem 1, with different numbers, for you to solve.
Tip
Have your student write a "Let x = ..." line every time, in words. Most stuck moments come from not saying what x stands for.