Neft Teacher · Learn It

Unit 8 · Standard 6.AT.8

Understand Equations and Their Solutions

Lesson 8-1 · Learn It — how the math works

Why we're learning this

Detective Ruiz received a tip: 'A number of stolen gems plus 8 more equals 20 total gems.' She needs to write an equation to represent this clue before she can solve the case. How would you write this situation as an equation?

✱ Math Workbench

Learn It

How do I turn a word clue into an equation?

An equation is a math sentence with an equal sign (=). To write one, I pick a letter (a variable) for the unknown number and match the words to math symbols.

Picture itSee what the math looks like before you read about it

Detective Ruiz pins a clue to the case board: 'A number of stolen gems, plus 8 more found in the safe, equals 20 gems in all.'
Where you see this in real lifeDetective Ruiz pins a clue to the case board: 'A number of stolen gems, plus 8 more found in the safe, equals 20 gems in all.'

Watch me solve itI do — read one step at a time

The problem looks like this
A bar model: a bar for 20 split into an unknown part labelled n and a known part of 8. total = 20 n = ? 8 The unknown part and 8 together make 20.
  1. Clue: 'A number of stolen gems plus 8 more equals 20 total.'
  2. The is the number of gems. I let n stand for it.
  3. 'Plus 8 more' means + 8. 'Equals 20 total' means = 20.
  4. So my is n + 8 = 20.n + 8 = 20

Watch out — mistakes students make here

  • An equation is either true or false when a value is substituted — close does not make it a solution.
  • A number appearing in the equation is not automatically its solution; substitute and check.
  • The 14 were found in addition to Monday's, so they are added, not subtracted.

Try it with meWe do — you answer first, then check

Same steps, new numbers.

  1. New clue: 'A number plus 5 equals 9.' What is the ?
  2. We let n be the . What does 'plus 5' tell us to write?
  3. What does 'equals 9' tell us?
    Check this step
    Put it together:n + 5 = 9

On your ownYou do — solve this one by yourself

Before you start, remember:

  • Here is the from the clue: n + 5 = 9. A detective guesses n = 3.
  • the guess: replace n with 3 to get 3 + 5 = 9.
  • Is that statement true? 3 + 5 is 8, and 8 does not equal 9, so 3 is NOT a .
  • Revise the guess and test again until the statement is true. Which value makes it true, and how do you know it is the ?

Solve: A detective found some fingerprints on Monday and 14 more on Tuesday, for a total of 30. Which represents this?

My answer

Stuck? Open one hint at a time.

Hint 1

Monday's fingerprints are the unknown f. On Tuesday she found 14 MORE, and the two days together total 30.

Hint 2

'More' means the two amounts combine into one total. Combining to reach a total is addition, not multiplying or dividing.

Hint 3

Write it in story order: f (Monday) plus 14 (Tuesday) equals 30 (total). Which choice shows that sum?

Check my answer
✅ Answer: f + 14 = 30
The detective's Monday fingerprints (f) plus 14 more equals 30: f + 14 = 30.

Turn & TalkSay it out loud with a partner

Detective Ruiz's clue says 'a number of stolen gems plus 8 more equals 20 total.' How would you turn this clue into an , and what does each part stand for?

Try starting with:

  • The unknown is ___, so I write the variable ___.La incógnita es ___, así que escribo la variable ___.
  • My equation is ___ because 'plus 8' means ___ and 'equals 20' means ___.Mi ecuación es ___ porque 'más 8' significa ___ y 'es igual a 20' significa ___.
Use these wordsequationvariableequal signexpression