6.AT.9 Lesson 8-4-group1 🟡 Group 1 · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

8.4 Small Group · Group 1

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

Visual Models · Write Inequalities · Inequality · Procedural Fluency

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: Let's build it together — How do I write an inequality from words?
1'At least' means ≥ and 'at most' means ≤; 'more than' means > and 'fewer/less than' means <.
  • An inequality compares two amounts using <, >, ≤, or ≥. I use one when many values are allowed, not just one. I pick a variable and match the words to the right symbol. 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: 'The suspect is at least 18 years old.'
  2. I let a stand for the age. 'At least 18' means 18 or more.
  3. 'At least' includes 18, so I use the symbol ≥.
  4. My inequality is a ≥ 18. So a could be 18, 19, 20, and up.
3Mathematical Word Bank
  • Write Inequalities (Escribir desigualdades) — Represent a range of possible values with <, >, ≤, or ≥.
  • Inequality (Desigualdad) — A math sentence that compares two sides with <, >, ≤, or ≥.
  • Greater than (Mayor que) — The > sign, showing one number is bigger.
  • Less than (Menor que) — The < sign, showing one number is smaller.
  • At least / At most (Al menos / A lo más) — 'At least' means ≥. 'At most' means ≤.
  • Variable (Variable) — A letter that stands for a number that is unknown or can change.
4Watch out
  • A common mistake in Write Inequalities is using a strict symbol (> or <) for a phrase that actually includes the boundary value. For 'the suspect is at least 18 years old,' students often write a > 18 instead of the correct a ≥ 18 — this wrongly excludes 18 itself, even though 'at least 18' means 18 counts as a match. The same error happens in reverse with 'at most': for 'the getaway bag holds at most 12 items,' students write n < 12 instead of n ≤ 12. Always ask: does the key phrase include the number ('at least,' 'at most,' 'no more than,' 'no fewer than' → use ≥ or ≤) or exclude it ('more than,' 'fewer than' → use > or <)?
SECTION 1 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 1 MULTIPLE CHOICE

    A parking garage charges if your stay is more than 2 hours. Which inequality represents times t that are charged?

    1. At > 2
    2. Bt ≥ 2
    3. Ct < 2
    4. Dt ≤ 2
    ✏️ Workspace & Solution Steps
  2. 2 MULTIPLE CHOICE

    A clue says the suspect carried at least 12 stolen gems. Which inequality shows the number g of gems?

    1. Ag ≥ 12
    2. Bg > 12
    3. Cg ≤ 12
    4. Dg < 12
    ✏️ Workspace & Solution Steps
  3. 3 MULTIPLE CHOICE

    A witness reports that fewer than 5 people entered the building. Which inequality shows the number n of people?

    1. An < 5
    2. Bn ≤ 5
    3. Cn > 5
    4. Dn ≥ 5
    ✏️ Workspace & Solution Steps
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 4 ERROR ANALYSIS

    Spot the Detective's Mistake

    1. 1Clue:The witness says the suspect is at least 16 years old.
    2. 2Choose a variable:Let a stand for the suspect's age.
    3. 3Write the inequality:a > 16

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

    ✏️ Corrected Mathematical Work & Explanation
  2. 5 ERROR ANALYSIS

    Crack the Inequality Error

    1. 1Clue:The report says no fewer than 9 witnesses saw the suspect.
    2. 2Choose a variable:Let w stand for the number of witnesses.
    3. 3Write the inequality:w < 9

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

    ✏️ Corrected Mathematical Work & Explanation
  3. 6 ERROR ANALYSIS

    Level 2 Extension — Catch the Symbol Mix-Up

    1. 1Clue:The suspect is at least 12 years on the force, where y is the years.
    2. 2Find the key phrase:'At least 12' means 12 is allowed and anything larger.
    3. 3Write the inequality:y > 12

    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