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

Lesson 8.18.1 Small Group · Group 1

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target With my small group, I can write an equation for a real situation and check whether a given value is a solution by substituting it — one step at a time, with support.

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 1

Group 1Supported practice

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

Learning target With my small group, I can write an equation for a real situation and check whether a given value is a solution by substituting it — one step at a time, with support.

  1. 1Complete each step, then write the final answer.
    ?15=
    Write the equation from the clue.

    Clue: "A number of marbles plus 6 more equals 15 total." Write an equation. Then test n = 9.

    1. 1Let n be the number of marbles. What does "plus 6 more" tell us to write?
    2. 2Put the parts together. What is the equation?
    3. 3Replace n with 9. What is 9 + 6?
    4. 4Are both sides equal? Is n = 9 a solution?
    Final answer:
  2. 2Complete each step, then write the final answer.
    ?10=
    Start with s stickers, take away 4, and 10 are left.

    Jada had some stickers. She gave away 4. Now she has 10 left. Write an equation. Is s = 6 a solution?

    1. 1Let s be the stickers at the start. Write the equation.
    2. 2Replace s with 6. What is 6 − 4?
    3. 3Is 2 equal to 10? Is s = 6 a solution?
    4. 4Now test s = 14. What is 14 − 4?
    Final answer:
  3. 3Complete each step, then write the final answer.

    Which value is a solution of n + 3 = 10: 6, 7, or 8?

    Show your work

    Hint Replace n with each number. Which one makes the left side equal 10?

    Final answer:
  4. 4Complete each step, then write the final answer.

    Which value is a solution of n + 18 = 47: 29, 31, or 65?

    Show your work

    Hint Put each value in place of n. Add 18. Which sum is exactly 47?

    Final answer:
  5. 5Complete each step, then write the final answer.
    ?30=
    Some cards plus 12 more make 30.

    Ben has some cards. He buys 12 more. Now he has 30 cards. Write an equation. Is the solution 18 or 42?

    Show your work

    Hint Let c be the cards at the start. Write c + 12 = 30. Then test each value.

    Final answer:
  6. 6Complete 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

    Hint Put 7 in place of n exactly as the equation is written. Is it − or +?

    Final answer:

Explain your thinkingWhy do you replace the letter with the number to check a solution? Use Rosa's mistake to explain.

Sentence starter To check, I replace ___ with ___. · A value is a solution when ___.

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