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

7.4 Small Group · Group 2

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

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 MULTIPLE CHOICE

    Which statement is TRUE?

    1. A-3 > -1
    2. B-5 < -2
    3. C-4 > 0
    4. D-1 < -6
    ✏️ Workspace & Solution Steps
SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 2 MULTIPLE CHOICE

    Which integer is the LEAST: -3, 5, -8, 2, 0?

    1. A-8
    2. B-3
    3. C0
    4. D5
    ✏️ Workspace & Solution Steps
  2. 3 MULTIPLE CHOICE

    Three cities have temperatures of -12°F, -5°F, and 3°F. Which city is warmest?

    1. A3°F
    2. B-5°F
    3. C-12°F
    4. DThey are equal
    ✏️ Workspace & Solution Steps
SECTION 3 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 4 ERROR ANALYSIS

    Fix our table's thinking

    1. 1The problem:Three cities have temperatures of -12°F, -5°F, and 3°F. Which city is warmest?
    2. 2A classmate at our table answered:-12°F

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

    ✏️ Corrected Mathematical Work & Explanation
  2. 5 ERROR ANALYSIS

    Spot the Common Mistake

    1. 1Read:Order -8 and -15 from least to greatest.
    2. 2Attempt:The student wrote -8, -15, because 8 is smaller than 15.
    3. 3Check:-15 is farther left than -8 on the number line, so -15 is the least. The correct order is -15, -8.

    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 Comparison Error

    1. 1Problem:Compare -3 and -8. Which is greater?
    2. 2Student thinking:8 is bigger than 3, so -8 must be greater than -3
    3. 3Student answer:-8 > -3

    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