Grade 6 Mathematics · Unit 8: Equations & InequalitiesStandard 6.AT.8

Lesson 8.1Writing Equations

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can write an equation for a real situation and check whether a given value is a solution by substituting it.

Start hereWords for this lesson

Read each word before you begin. Say it out loud.

WordWhat it meansExample
EquationSpanish: Ecuación A math sentence with an equal sign showing both sides are the same. n + 8 = 20 means 'some number plus 8 equals 20'
VariableSpanish: Variable A letter that stands for a number that is unknown or can change. In n + 3 = 10, the letter n stands for the unknown number (n = 7)
Equal signSpanish: Signo igual The = sign, showing both sides are the same. 7 + 3 = 10 — both sides equal 10
ExpressionSpanish: Expresión A math phrase with numbers and letters, but no equal sign. n − 8
ConstantSpanish: Constante A fixed number in an expression or equation that does not change. In x + 7 = 12, the numbers 7 and 12 are constants; only x can change.
UnknownSpanish: Incógnita The value you are trying to find, usually shown with a variable. the n in n − 8 = 15

How it worksWorked examplewriting an equation, then testing a guess

These numbers are not on your problems. The steps are. Follow them with your own numbers.

A baker made 64 rolls. Some were sold, and 27 rolls were left. How many rolls were sold?

  1. Name the unknown: let r = the rolls sold. Rolls made − rolls sold = rolls left.
  2. Write the equation: 64 − r = 27.
  3. Estimate and test r = 35. That leaves 29 rolls, which is more than 27.
  4. Revise upward and test r = 37. That leaves exactly 27, so both sides match.

Answer: r = 37, so the baker sold 37 rolls.

Now you trySame steps, your turn

The steps are the same as the worked example. The numbers are yours. Do the work.

A tank held 52 liters. Some water leaked out, and 18 liters were left. How much leaked?

  1. Name the unknown: let k = the liters that .
  2. Write the equation: 52 − k = .
  3. Estimate and test k = 30. Liters left: . Too many or too few?
  4. Revise: try k = . Check that the left side equals .
Answer:liters that leaked

Say it and write itSentence starters

Finish each sentence out loud with a partner. Then use them in your writing.

  • The unknown in this problem is .
  • My equation is because .
  • I estimated , and my check showed .
  • I revised my guess because .

Word bank equationunknownestimateguesscheckrevisesubstitutesolutiontrueleft overtotalpart

Watch outA common mistake

A common mistake in Write Equations is writing subtraction and division clues in the wrong order — putting the number from the clue first instead of the variable first. For 'a number decreased by 8 equals 5,' students often write 8 − n = 5 instead of the correct n − 8 = 5; for 'a number divided by 4 equals 6,' they write 4 ÷ n (or 4n) instead of n / 4 = 6. Always start with the variable, then attach the operation in the order the words describe it, and check by substituting your answer back in.

Grade 6 Mathematics · Unit 8: Equations & InequalitiesStandard 6.AT.8

Lesson 8.1Writing Equations

Apply Day · Version ASupported practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can write an equation for a real situation and check whether a given value is a solution by substituting it.

  1. 1Complete each step, then write the final answer.

    Which value is a solution of n + 4 = 11: 6 or 7?

    Show your work

    Hint Replace n with 6, then with 7. Which one makes 11?

    Final answer:
  2. 2Complete each step, then write the final answer.

    Which value is a solution of n − 2 = 8: 6 or 10?

    Show your work

    Hint Replace n with each value. Subtract 2. Which one gives 8?

    Final answer:
  3. 3Complete each step, then write the final answer.

    Which value is a solution of n + 9 = 15: 5 or 6?

    Show your work

    Hint Replace n with each value. Which one makes the left side 15?

    Final answer:
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help
Grade 6 Mathematics · Unit 8: Equations & InequalitiesStandard 6.AT.8

Lesson 8.1Writing Equations

Apply Day · Version BCore practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can write an equation for a real situation and check whether a given value is a solution by substituting it.

  1. 1Complete each step, then write the final answer.

    Rosa tests n = 7 in n − 3 = 10. She writes 7 + 3 = 10 and says yes. Is she right? What is the solution: 7 or 13?

    Show your work
    Final answer:
  2. 2Complete each step, then write the final answer.

    Which value is a solution of 2.5 + n = 7: 4.5, 5.5, or 9.5?

    Show your work
    Final answer:
  3. 3Complete each step, then write the final answer.

    Which value is a solution of n + 6 = 21: 13, 15, or 27?

    Show your work
    Final answer:
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help
Grade 6 Mathematics · Unit 8: Equations & InequalitiesStandard 6.AT.8

Lesson 8.1Writing Equations

Apply Day · ChallengeExtension

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can write an equation for a real situation and check whether a given value is a solution by substituting it.

  1. 1Circle the letter of the best answer. Show how you know.

    Marisol tests values in the equation 7 + m = 23. Which value of m makes the equation true?

    1. Am = 9
    2. Bm = 16
    3. Cm = 23
    4. Dm = 30
    Show your work
  2. 2Complete each step, then write the final answer.

    Omar says n = 6 is a solution of n ÷ 3 = 18, because 18 ÷ 3 = 6. Which value is the real solution: 6, 21, or 54?

    Show your work
    Final answer:
  3. 3Complete each step, then write the final answer.

    Which value makes 8n = 56 true: 6, 7, or 48?

    Show your work
    Final answer:
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help