6.AT.9 Lesson 8-4-group2 🟣 Group 2 · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

8.4 Small Group · Group 2

Second Challenge Form · Non-Routine Extension · Same Standard, New Problems

Write Inequalities · Inequality · Procedural Fluency · Reasoning & Critique

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: Push further — How do I write an inequality from words?
1'At least' means ≥ and 'at most' means ≤; 'more than' means > and 'fewer/less than' means < — and you can say why it is true, and where it would stop being true.
  • You already can do this. So we go up a level, not up a number: find what is always true, show it a second way, and be ready to defend it with a reason instead of an answer.
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.
3Second Model — Try it together — then prove it
  1. Clue: 'A bag holds fewer than 10 items.' What does 'fewer than' mean?
  2. It means less than, and it does NOT include 10, so we use <.
  3. We let n be the number of items: n < 10.
  4. Now prove it: say why that move had to work at all — not just that it did.
  5. Sentence frame — convince a skeptic: "My method works because ___ . It would stop working if ___ ."
4Mathematical 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.
5Watch 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

    Which inequality represents: 'You must be at least 48 inches tall to ride'?

    1. Ah ≥ 48
    2. Bh > 48
    3. Ch < 48
    4. Dh ≤ 48
    ✏️ Workspace & Solution Steps
  2. 2 MULTIPLE CHOICE

    Which inequality represents: 'A store can hold no more than 75 people'?

    1. Ap ≤ 75
    2. Bp < 75
    3. Cp ≥ 75
    4. Dp > 75
    ✏️ Workspace & Solution Steps
  3. 3 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
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 4 ERROR ANALYSIS

    Fix our table's thinking

    1. 1The problem:Which inequality represents: 'A store can hold no more than 75 people'?
    2. 2A classmate at our table answered:p < 75

    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

    Find the Inequality Error

    1. 1Situation:No more than 25 students can join the field trip
    2. 2Identify key phrase:'No more than' means greater than
    3. 3Write inequality:s > 25

    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
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