6.AT.8 Lesson 8-7-part2 Apply Day · Set B
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8.7 · Part II

Second Practice Form · Independent Application and Spiral Review

Equations and Inequalities Problem Solving · Model

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: 8.7 · Part II
1Modeling Real-World Scenarios with Equations & Inequalities
2The Structural Procedure
  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
3Mathematical Word Bank
  • Equations and Inequalities Problem Solving (Resolución de problemas con ecuaciones y desigualdades) — Use an equation for one exact value or an inequality for a range of values in a real situation.
  • Model (Modelar) — To show a real-life situation with an equation or inequality.
  • Equation (Ecuación) — A math sentence with an equal sign showing both sides are the same.
  • Inequality (Desigualdad) — A math sentence that compares two sides with <, >, ≤, or ≥.
  • Reasonableness (Razonabilidad) — Checking if your answer makes sense.
  • Variable (Variable) — A letter that stands for a number that is unknown or can change.
4Watch out
  • 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, <, >, ≤, ≥)?
SECTION 1 CONCEPTUAL UNDERSTANDING & VISUAL MODELS [Visual Modeling]
  1. 1 MULTIPLE CHOICE

    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
    ✏️ Workspace & Solution Steps
SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 2 MULTIPLE CHOICE

    (Lesson 8.5) Which graph represents x < 5?

    1. AOpen circle at 5, shaded left
    2. BClosed circle at 5, shaded left
    3. COpen circle at 5, shaded right
    4. DClosed circle at 5, shaded right
    ✏️ Workspace & Solution Steps
  2. 3 MULTIPLE CHOICE

    (Lesson 8.5) Which graph represents x ≥ 3?

    1. AClosed circle at 3, shaded right
    2. BOpen circle at 3, shaded right
    3. CClosed circle at 3, shaded left
    4. DOpen circle at 3, shaded left
    ✏️ Workspace & Solution Steps
  3. 4 MULTIPLE CHOICE

    Room 4: A locked drawer clue reads, 'Five identical evidence boxes weigh 60 pounds in all.' Solve 5w = 60 for each box's weight w.

    1. Aw = 12
    2. Bw = 55
    3. Cw = 300
    4. Dw = 65
    ✏️ Workspace & Solution Steps
  4. 5 MULTIPLE CHOICE

    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
    ✏️ Workspace & Solution Steps
  5. 6 MULTIPLE CHOICE

    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
    ✏️ Workspace & Solution Steps
SECTION 3 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 7 OPEN RESPONSE

    Create two word problems about the same situation: one that requires an equation and one that requires an inequality. Solve both and explain why the models are different.

    ✏️ Mathematical Justification & Response
📐 CER MATHEMATICAL PROOF MATRIX (CER 2.0) SMP.3 / Proof & Justification

Writing Task: Justify why your mathematical solution is accurate and complete.

C Claim
State your direct mathematical answer/claim with units.
E Evidence
Cite exact numbers, calculations, dimensions, or graph data.
R Reasoning
Explain the mathematical theorem, property, or definition connecting evidence to claim.
Student Mastery Self-Assessment:
1 · Need More Support
2 · Getting Closer
3 · Got It / Solid
4 · Master / Can Teach It