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

Lesson 8.78.7 Small Group · Group 1

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target With my small group, I can model and solve real-world problems using equations and inequalities — 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
ModelSpanish: Modelar To show a real-life situation with an equation or inequality. 'Twice a number is 18' → 2n = 18 — the equation models the words
EquationSpanish: Ecuación A math sentence with an equal sign showing both sides are the same. x + 8 = 15 — exactly one answer: x = 7
InequalitySpanish: Desigualdad A math sentence that compares two sides with <, >, ≤, or ≥. x + 5 > 12 — many answers: x = 8, 9, 10, ...
ReasonablenessSpanish: Razonabilidad Checking if your answer makes sense. If the problem asks for a number of people and you get x = −3, that is NOT reasonable
VariableSpanish: Variable A letter that stands for a number that is unknown or can change. “5 less than a number is 12” becomes x − 5 = 12, where x is the variable.
ConstraintSpanish: Restricción A limit in a problem that tells what values are allowed. “You can spend at most $20” is a constraint: cost ≤ 20.

How it worksWorked example

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

Clue: "A total divided equally among 4 people gave each person $85." Write and solve a model to find the total.

  1. Decide: equation or inequality?: exact total → equation
  2. Choose a letter and write the equation: t ÷ 4 = 85
  3. Multiply both sides by 4: t = 85 × 4 = 340
  4. Check that the answer makes sense: 340 ÷ 4 = 85 ✓
  5. t = 340. The total was $340.

Now you trySame steps, your turn

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

Clue: "The lookout earned less than $50." Write a model for the lookout's earnings.

Answer:

Say it and write itSentence starters

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

  • I use an equation when the problem says , but I use an inequality when the problem says because .

Word bank ModelEquationInequalityReasonablenessVariableConstraintequationinequalityequalat leastat mostmore than

Watch outA common mistake

A common mistake in Equations and Inequalities Problem Solving is matching the wrong model to a key phrase. For 'the getaway car held no more than 6 bags,' students often write the equation b = 6 instead of the inequality b ≤ 6, because they see one number and assume it must be exact. The same mistake happens in reverse: for 'the reward split equally among 5 people gave each $40,' students sometimes write the inequality 5p ≥ 40 instead of the equation 5p = 40, because 'split equally' sounds like it could mean a range. Before you submit, ask: does this phrase give one exact value (equation, =) or a limit/range (inequality, <, >, ≤, ≥)?

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

Lesson 8.78.7 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 model and solve real-world problems using equations and inequalities — one step at a time, with support.

  1. 1Complete each step, then write the final answer.
    Prize p$14$14$14$14$14p
    The prize p splits into 5 equal parts of $14.

    Clue: "5 friends shared a prize equally. Each friend got $14." Write and solve a model to find the prize p.

    1. 1Equation or inequality? How do you know?
    2. 2Write the model.
    3. 3Multiply both sides by 5. What is p?
    4. 4Is $70 reasonable? Check it.
    Final answer:
  2. 2Complete each step, then write the final answer.
    0102030$18 spentlimit
    How much more fits under $30?

    Clue: "A detective can spend at most $30 on lunch. She spent $18 on sandwiches." Write and solve a model for the amount d she can still spend.

    1. 1Equation or inequality? Which words tell you?
    2. 2Write the model.
    3. 3Subtract 18 from both sides. What is the most she can still spend?
    Final answer:
  3. 3Complete each step, then write the final answer.

    A shelf had some books. Then 9 more books were added. Now there are 25 books. Write and solve an equation. How many books were there at first?

    Show your work

    Hint There is one exact total, so use an equation. Write b + 9 = 25.

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

    A total divided equally among 6 people gave each person $42. What was the total?

    Show your work

    Hint Each person got an exact amount. Write t ÷ 6 = 42. Multiply both sides by 6.

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

    A team needs more than 60 points to win. They have 45 points now. Write and solve an inequality for the points p they still need. What is the boundary number?

    Show your work

    Hint "More than" is a limit, so use an inequality. Write 45 + p > 60.

    Final answer:
  6. 6Circle the letter of the best answer. Show how you know.

    Which situation needs an inequality, not an equation?

    1. AA bag can hold no more than 12 apples.
    2. BEach of 3 boxes holds exactly 12 eggs.
    3. C12 cookies were shared equally by 4 kids.
    4. DA pack of 12 pens costs $6.

    Hint Look for limit words like "at most," "at least," or "no more than."

    Show your work

Explain your thinkingHow do the words in a story tell you to use an equation or an inequality? Give one example of each.

Sentence starter I use an equation when ___. · I use an inequality when the words say ___.

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