6.NOS.8 Lesson 7-4-group2 🟣 Group 2 · Challenge & Extension
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

7.4 Small Group · Group 2

Tier 1 Extension · Non-Routine Synthesis · Misconception Traps · Rigorous CER Proofs

Visual Models · Compare and Order Integers · Number line · Procedural Fluency

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: Push further — How do you compare and order integers?
1The number farther to the left is always less; the number farther to the right is always greater — 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. I will compare -7 and -5. They are both negative, so I look at the number line.
  2. -7 is 7 steps left of zero. -5 is only 5 steps left of zero.
  3. -7 is farther to the left, so -7 is the smaller number.
  4. I write -7 < -5. The open side of the symbol points to the bigger number, -5.
3Second Model — Try it together — then prove it
  1. Now let's compare -2 and 3. Which one is to the left on the number line? The -2 is left of zero.
  2. Which one is to the right? The 3 is right of zero.
  3. So which is greater, and what symbol do we use? 3 is greater, so -2 < 3.
  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
  • Compare and Order Integers (Comparar y ordenar enteros) — Use a number line to decide which integers are greater or less and place them in order.
  • Number line (Recta numérica) — A straight line where numbers are placed in order; numbers get smaller to the left and larger to the right.
  • Compare (Comparar) — To see if a number is bigger, smaller, or equal to another.
  • Order (Ordenar) — To arrange numbers by size, from least to greatest or greatest to least.
  • Greater than (Mayor que) — The > sign, showing one number is bigger.
  • Less than (Menor que) — The < sign, showing one number is smaller.
5Watch out
  • A common mistake in Compare and Order Integers is thinking that a negative number with a bigger digit is the bigger value — for example, believing -15 is greater than -8 because 15 is greater than 8. It's the opposite for negatives: the number farther to the left on the number line (farther from zero) is always the LESSER value, so -15 < -8. Before you submit, check your comparison against the number line, not just the digits.
SECTION 1 CONCEPTUAL UNDERSTANDING & VISUAL MODELS [Visual Modeling]
  1. 1 NUMBER LINE

    Plot these integers and write them in order from greatest to least: -8, 4, -3, 1, -1, 6

    ✏️ Workspace & Solution Steps
  2. 2 FILL TABLE

    Compare each pair of integers using < , > , or =.

    Integer AInteger BComparison (< , > , or =)
    -4
    -7
    0
    -1
    6
    ✏️ Scratchpad / Reasoning
SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 3 MULTIPLE CHOICE

    Four spots: -3 m, 2 m, -7 m, 0 m. Order them from least to greatest.

    1. A-7, -3, 0, 2
    2. B-3, -7, 0, 2
    3. C2, 0, -3, -7
    4. D-7, -3, 2, 0
    ✏️ Workspace & Solution Steps
  2. 4 MULTIPLE CHOICE

    Three buried chests sit at -9 m, -4 m, and -15 m below sea level. Which chest is at the GREATEST elevation (closest to the surface)?

    1. A-4 m
    2. B-9 m
    3. C-15 m
    4. DThey are equal
    ✏️ Workspace & Solution Steps
  3. 5 MULTIPLE CHOICE

    On the map, a sunken lantern is at -8 m and a coral shelf is at -3 m. Which symbol makes the comparison true: -8 ___ -3 ?

    1. A<
    2. B>
    3. C=
    4. D≥
    ✏️ Workspace & Solution Steps
SECTION 3 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 6 ERROR ANALYSIS

    Level 2 Extension — The Mis-Ranked Treasure Map

    1. 1Problem:Order the chest depths from least to greatest: -8 m and -15 m.
    2. 2Crew thinking:15 has bigger digits than 8, so -15 must be the bigger number. I'll list -8 first because it must be smaller.
    3. 3Crew answer:Least to greatest: -8, -15

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

    ✏️ Corrected Mathematical Work & Explanation
🗣️ MATHEMATICAL DISCOURSE & TALK MOVES SMP.3 / Construct Viable Arguments

Group Discussion Prompt: How does your visual model justify your mathematical solution?

🗣️ Partner A:
Partner A: "I modeled this by identifying the relationship and..."
👂 Partner B:
Partner B: "I agree with your step because the standard mathematical rule states..."
✍️ The Writing Revolution (TWR) · Sentence Expansion Because · But · So

Complete each sentence stem to demonstrate precise mathematical reasoning:

BECAUSE The mathematical model proves the solution because each step preserves quantitative equivalence.
BUT An estimate provides a quick benchmark, but an exact proof is required for precision.
SO The quantities follow the standard rule, so the final result is verified with certainty.
📐 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.
✍️ AUTHOR YOUR OWN EXTENSION CHALLENGE

Create an original multi-step word problem aligned to this standard. Include constraints, and write the complete step-by-step mathematical proof below.

✏️ Author Workspace & Complete Solution Key
Student Mastery Self-Assessment:
1 · Need More Support
2 · Getting Closer
3 · Got It / Solid
4 · Master / Can Teach It