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

Lesson 8.78.7 · Part II

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can model and solve real-world problems using equations and inequalities.

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.

Say it and write itSentence starters

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

Word bank ModelEquationInequalityReasonablenessVariableConstraint

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 · Part II

Apply Day · Version ASupported practice

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

Learning target I can model and solve real-world problems using equations and inequalities.

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

    A total divided equally among 2 people gave each person $35. What was the total?

    Show your work

    Hint Write t ÷ 2 = 35. Multiply both sides by 2.

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

    A cup holds at most 8 ounces. It has 5 ounces of juice. How many more ounces can you add at most?

    Show your work

    Hint "At most" is a limit. Write 5 + j ≤ 8.

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

    A total divided equally among 6 people gave each person $9. What was the total?

    Show your work

    Hint Write t ÷ 6 = 9. Multiply both sides by 6.

    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 8.78.7 · Part II

Apply Day · Version BCore practice

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

Learning target I can model and solve real-world problems using equations and inequalities.

  1. 1Circle 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.
    Show your work
  2. 2Complete each step, then write the final answer.

    Each shelf holds 18 books. A library has 250 books. Write and solve an inequality. How many shelves are needed?

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

    A total divided equally among 7 people gave each person $11. What was the total?

    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 8.78.7 · Part II

Apply Day · ChallengeExtension

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

Learning target I can model and solve real-world problems using equations and inequalities.

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

    A school van can carry at most 14 passengers. There are already 9 passengers on board. Let p be the number of additional passengers who can get on. Which inequality models this situation?

    1. A9 + p ≤ 14
    2. B9 + p ≥ 14
    3. C9 + p < 14
    4. Dp − 9 ≤ 14
    Show your work
  2. 2Complete each step, then write the final answer.

    A class needs at least $300 for a trip. They earn $12 for each car wash. Kim writes 12c = 300. Lee writes 12c ≥ 300. What is the least number of car washes they need?

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

    A box holds 24 cans. A store has 270 cans to pack. Write and solve an inequality. How many boxes are needed?

    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