6.AT.8 Lesson 8-7-group1 🟡 Group 1 · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

8.7 Small Group · Group 1

Second Practice Form · Re-Teach, Homework or Retake · Same Standard, New Problems

Equations and Inequalities Problem Solving · Model · Procedural Fluency · Real-World Applications

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: Let's build it together — Should I model this problem with an equation or an inequality?
1'Equals' or 'exactly' points to an equation (=); 'at least, at most, more than, fewer than' points to an inequality.
  • To model means to write a real situation as math. I use an equation when there is one exact total, and an inequality when there is a limit or a range of allowed values. We'll walk through a worked example, try one together, then you'll try a few with hints right there when you need them.
2Worked Example — Watch me
  1. Clue: 'A total divided equally among 4 people gave each $85.'
  2. This has an exact total, so I use an equation. Let t be the total.
  3. Divided among 4 to get 85 means t ÷ 4 = 85, so t = 85 × 4 = 340.
  4. Check reasonableness: $340 split 4 ways is $85 each. That makes sense!
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 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 1 MULTIPLE CHOICE

    A student solved 4n = 52 and got n = 13. Is the answer reasonable if n represents the number of notebooks in a box?

    1. AYes — 13 notebooks per box is reasonable
    2. BNo — 13 is too many notebooks
    3. CNo — the answer should be 48
    4. DYes — but only if n is a fraction
    ✏️ Workspace & Solution Steps
  2. 2 MULTIPLE CHOICE

    Room 2: The vault keypad clue reads, 'A number of stolen coins plus 6 equals 14.' Solve x + 6 = 14 to find the code x.

    1. Ax = 8
    2. Bx = 20
    3. Cx = 6
    4. Dx = 2
    ✏️ Workspace & Solution Steps
  3. 3 MULTIPLE CHOICE

    Room 3: A sign warns, 'The safe holds at most 20 gold bars.' Which inequality models the number of bars x?

    1. Ax ≤ 20
    2. Bx ≥ 20
    3. Cx > 20
    4. Dx = 20
    ✏️ Workspace & Solution Steps
  4. 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
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 5 ERROR ANALYSIS

    Spot the Common Mistake

    1. 1Problem:A detective already found 8 fingerprints at the scene. After dusting more surfaces, she has 15 fingerprints in all. How many new fingerprints did she find?
    2. 2Model:x + 8 = 15
    3. 3Solve:x = 15 + 8 = 23
    4. 4Answer:23 new fingerprints.

    Which step contains the error? Explain the mathematical misconception and write the correct calculation below.

    ✏️ Corrected Mathematical Work & Explanation
  2. 6 ERROR ANALYSIS

    Level 2 Extension — The Final Door: Catch the Detective's Mistake

    1. 1Clue:Solve the keypad inequality 3x ≤ 18 to find how many bars x fit.
    2. 2Step 1:3x ≤ 18
    3. 3Step 2:Divide only the left side by 3: 3x ÷ 3 ≤ 18
    4. 4Step 3:x ≤ 18
    5. 5Answer:At most 18 bars fit.

    Which step contains the error? Explain the mathematical misconception and write the correct calculation below.

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

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

C Claim
Starter: My mathematical claim is that the solution is...
E Evidence
Starter: The evidence from the model/table demonstrates that...
R Reasoning
Starter: This proves my answer because the standard mathematical definition of...
Student Mastery Self-Assessment:
1 · Need More Support
2 · Getting Closer
3 · Got It / Solid
4 · Master / Can Teach It