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

Lesson 8.78.7 · Part II

Apply Day · Set BSecond form · new problems, same idea

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
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Learning target I can model and solve real-world problems using equations and inequalities.

Remember8.7 · Part II

Modeling Real-World Scenarios with Equations & Inequalities

  1. Define the variable and units in the scenario
  2. Look for keywords: 'equals/is' (=) vs 'at least/limit' (≥, ≤, >, <)
  3. Write the algebraic model, solve with inverse operations, and check in context

Words: Model (Modelar)Equation (Ecuación)Inequality (Desigualdad)Reasonableness (Razonabilidad)Variable (Variable)

Part 1Understand the ideamodels and meaning
  1. 1Circle the letter of the best answer. Show how you know.

    Which model is correct for: 'A number divided by 6 equals 7'?

    1. An / 6 = 7
    2. B6n = 7
    3. Cn − 6 = 7
    4. Dn + 6 = 7
    Show your work
Part 2Apply itreal-world problems
  1. 2Complete 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
    Final answer:
  2. 3Complete 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
    Final answer:
  3. 4Complete each step, then write the final answer.

    Tickets cost $7.50 each. Ray has $40. Write and solve an inequality. What is the greatest number of tickets he can buy?

    Show your work
    Final answer:
  4. 5Complete each step, then write the final answer.

    A suitcase can weigh at most 50 pounds. It has 34 pounds of clothes in it. Write and solve a model. How many more pounds can you add at most?

    Show your work
    Final answer:
  5. 6Complete each step, then write the final answer.

    A water tank holds at most 120 liters. It has 47.5 liters now. Write and solve a model. How many more liters can you add at most?

    Show your work
    Final answer:
  6. 7Complete each step, then write the final answer.

    A gym charges $20 to join, plus $15 each month. Sam can spend at most $140. Write and solve an inequality. How many months can he pay for?

    Show your work
    Final answer:
  7. 8Circle the letter of the best answer. Show how you know.

    A museum has some paintings. After adding 12, they have 45. Which equation models this?

    1. Ap + 12 = 45
    2. Bp − 12 = 45
    3. C12p = 45
    4. Dp / 12 = 45
    Show your work
  8. 9Circle the letter of the best answer. Show how you know.

    A detective needs more than 8 hours to finish the investigation. She has already worked 3 hours. Which inequality represents the additional hours h she needs?

    1. A3 + h > 8
    2. B3 + h = 8
    3. Ch > 3
    4. D8 + h > 3
    Show your work
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help