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

Lesson 8.18.1 Small Group · Group 2

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, explain what each part stands for, and build one for a situation I have not seen before.

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. x + 3 = 10
VariableSpanish: Variable A letter that stands for a number that is unknown or can change. the x in x + 3 = 10
Equal signSpanish: Signo igual The = sign, showing both sides are the same. =
ExpressionSpanish: Expresión A math phrase with numbers and letters, but no equal sign. 2x + 5 is an expression; it becomes an equation when you write 2x + 5 = 15
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. In n + 5 = 12, n is the unknown; you solve to find n = 7.

How it worksWorked examplechecking a solution by substituting

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

Jade wrote the equation m + 23 = 41 for a number puzzle. Is m = 18 a solution?

  1. Substitute: replace m with 18. The equation becomes 18 + 23 = 41.
  2. Do the arithmetic on the left side: 18 + 23 makes 41.
  3. Compare the two sides: 41 and 41. Both sides balance.
  4. The equation is true, so m = 18 is a solution.

Answer: Yes — m = 18 makes both sides equal 41, so it is a solution.

Now you trySame steps, your turn

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

A club wrote t + 14 = 31 for its total members. Is t = 17 a solution?

  1. Substitute: replace t with .
  2. Left side: + 14 =
  3. Compare the sides: left , right . Do they match?
  4. So t = 17 (is / is not) a solution.
Answer:Is t = 17 a solution? yes / no

Say it and write itSentence starters

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

  • I substituted for the variable and got .
  • The value (is / is not) a solution because .
  • An equation is true when both sides .
  • The variable stands for in this problem.

Word bank equationvariablesolutionsubstitutetruefalseequal signboth sidesbalancecheck

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 8.18.1 Small Group · Group 2

Group 2Challenge 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, explain what each part stands for, and build one for a situation I have not seen before.

  1. 1Complete each step, then write the final answer.
    ?35=
    Start with w gallons, lose 12, and 35 are left.

    A tank had some water. Then 12 gallons leaked out. Now 35 gallons are left. Write an equation. Is the solution 23 or 47?

    1. 1Let w be the gallons at the start. Write the equation.
    2. 2Test w = 23. What is 23 − 12?
    3. 3Test w = 47. What is 47 − 12?
    Final answer:
  2. 2Complete each step, then write the final answer.
    ?36=
    t tickets at $4 each cost $36.

    Tickets cost $4 each. Ray pays $36 for t tickets. Write an equation. Which value is the solution: 9, 32, or 40?

    1. 1Write the equation.
    2. 2Test t = 9. What is 4 × 9?
    3. 3Why are 32 and 40 not solutions? What mistake made them?
    Final answer:
  3. 3Complete 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:
  4. 4Complete each step, then write the final answer.

    Which value makes 7k = 63 true: 8, 9, or 56?

    Show your work
    Final answer:
  5. 5Complete each step, then write the final answer.

    Nia read some pages on Monday. On Tuesday she read 28 more. She read 75 pages in all. Write an equation. Is the solution 47 or 103?

    Show your work
    Final answer:
  6. 6Complete 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:

Explain your thinkingOmar picked 6 by dividing the numbers he saw. Why must you substitute a value to know if it is a solution?

ChallengeWrite your own problem

Write a new word problem that uses this lesson's idea. Then solve it and show every step.

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help