6.AT.9 Lesson 8-4-part2 Apply Day · Practice
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

8.4 · Part II

Application Practice for Today's Problem

Write Inequalities · Inequality

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: 8.4 · Part II
1Writing & Representing Inequalities
2Strategy Model — step by step
  1. 'At least', 'minimum', 'no less than' translate to ≥ (greater than or equal to)
  2. 'At most', 'maximum', 'no more than' translate to ≤ (less than or equal to)
  3. 'More than' is >; 'Fewer than' / 'Less than' is <
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

    Which inequality represents: 'The speed limit is more than 25 mph'?

    1. As > 25
    2. Bs ≥ 25
    3. Cs < 25
    4. Ds = 25
    ✏️ Workspace & Solution Steps
  2. 2 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
  3. 3 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
  4. 4 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. 5 OPEN RESPONSE

    Write two different real-world situations: one that uses > and one that uses ≥. Explain why the situations need different symbols even though both mean 'bigger.'

    💬 Sentence Starter: Situation 1 (>): ___. This uses > because ___. Situation 2 (≥): ___. This uses ≥ because ___. The difference is that ≥ includes ___ while > does not.
    ✏️ 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
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