6.NOS.8 Lesson 7-4-group1 🟡 Group 1 · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

7.4 Small Group · Group 1

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

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

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: Let's build it together — 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.
  • To compare integers means to see which one is greater or less. On a number line, numbers get bigger as you go right and smaller as you go left. 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. 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.
3Mathematical 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.
4Watch 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 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 1 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
  2. 2 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
  3. 3 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
  4. 4 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 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 5 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
  2. 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
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