Math 1 · Lesson 4 · part 4 of 4
Practice Problems
Try them, get help one step at a time, then print how it went.
Warm-up: the three moves
Four equations. For each one: rewrite first (Step 1), then add the opposite of the number added to x (if there is one), then multiply by the reciprocal of the coefficient on x. Type each move in its box, then check.
Every equation is the same three moves. Rewrite, add the opposite, multiply by the reciprocal. When a move has nothing to do, say so and go on.
Practice: try it, then get help one step at a time
Try each problem yourself first. Hint gives a nudge, Show next step shows one worked step at a time, Reveal answer checks, and Hide help / start over clears the card. Every problem here needs Step 1 for real: a subtraction to rewrite, a division sign to rewrite, or an invisible 1 to write in. Remember that a fraction like x4 is not a division: it is the coefficient 14 on x. The Step 1 rewrite is shown in this color; the number you add or multiply by in this color.
My results
Finished the practice? Print a page that shows each question, what you typed or chose, the correct answer, and how it went. Good for showing a teacher or keeping in a folder.
Exit ticket
On paper or an index card. Use the math word and the plain-English word.
- What is Step 1 of every equation, and why do you do it first?
- Solve 3x - 6 = 9. Show Step 1, then solve and check.
- Why do we do the same thing to both sides? One sentence.
- How is solving an equation the same idea as Lessons 1, 2, and 3? One sentence.
Check your exit ticket
- Step 1 is translate and reveal the invisible 1s: turn subtraction into adding the opposite and division into multiplying by the inverse, and show any hidden 1s. You do it first because the properties and the undo partners only work on addition and multiplication.
- Step 1: 3x - 6 = 3x + (-6). Add 6 to both sides: 3x = 15. Multiply by 13: x = 5. Check: 3 × 5 - 6 = 15 - 6 = 9.
- Any sentence about keeping the balance equal: an equation says two sides are equal, so if you change one side you must change the other the same way.
- Every step is one idea from Lessons 1 to 3: translate first (Lesson 3), then add an opposite to make 0 or multiply by a reciprocal to make 1 (Lessons 1 and 2).