6.NOS.8 Lesson 7-3-group2 🟣 Group 2 · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

7.3 Small Group · Group 2

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

Visual Models · Integers and Absolute Value · Integer · Procedural Fluency

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: Push further — What is absolute value?
1Absolute value is a distance from zero, so it is never negative. It works the same for fractions and decimals as it does for whole numbers — 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 want to find the absolute value of -6, written |-6|.
  2. I find -6 on the number line. It sits 6 steps to the left of zero.
  3. Distance does not care about direction, so -6 is 6 units from zero.
  4. So |-6| = 6. Even though -6 is negative, its absolute value is positive 6.
3Second Model — Try it together — then prove it
  1. Now let's find |3|. Where is 3 on the number line? It is 3 steps to the right of zero.
  2. How far is it from zero? It is 3 units away.
  3. So |3| equals what? It equals 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
  • Integers and Absolute Value (Enteros y valor absoluto) — Integers are whole numbers and their opposites; absolute value is their distance from zero.
  • Integer (Número entero) — Whole numbers and their opposites, like -2, -1, 0, 1, 2.
  • Positive (Positivo) — A number bigger than zero, to the right of zero on a number line.
  • Negative (Negativo) — A number smaller than zero, to the left of zero on a number line.
  • Absolute value (Valor absoluto) — How far a number is from zero. It is never negative.
  • Opposite (Opuesto) — Two numbers the same distance from zero, on opposite sides, like 3 and -3.
5Watch out
  • A common mistake in Integers and Absolute Value is judging size by the digits alone instead of position on the number line — students think -8 is 'more' than -3 because 8 > 3, when really -8 sits farther left (colder, deeper, or lower) and is actually the SMALLER integer. Absolute value measures distance from zero and is always positive or zero, but that distance does not decide which integer is greater — only left-to-right order on the number line does. Before you submit, ask: am I comparing distance from zero (absolute value) or position on the number line (greater/less than)?
SECTION 1 CONCEPTUAL UNDERSTANDING & VISUAL MODELS [Visual Modeling]
  1. 1 MULTIPLE CHOICE

    Which statement about absolute value is TRUE?

    1. A|-4| = |4| because both are 4 units from zero
    2. B|-4| = -4 because the number is negative
    3. C|4| > |-4| because positive is always bigger
    4. D|-4| = 0 because negatives cancel out
    ✏️ Workspace & Solution Steps
SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 2 MULTIPLE CHOICE

    What is the absolute value of -9?

    1. A9
    2. B-9
    3. C0
    4. D1
    ✏️ Workspace & Solution Steps
  2. 3 MULTIPLE CHOICE

    Which number has the LEAST absolute value: −1.5, 0.75, −1/4, or 2?

    1. A−1/4
    2. B0.75
    3. C−1.5
    4. D2
    ✏️ Workspace & Solution Steps
SECTION 3 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 4 ERROR ANALYSIS

    Level 2 Extension — The Colder Temperature Mistake

    1. 1Mission:Captain Vega asks: which is colder, -8 degrees F or -2 degrees F?
    2. 2Crew member's reasoning:8 is bigger than 2, so -8 must be the warmer one.
    3. 3Crew member's answer:-2 degrees F is colder than -8 degrees F.

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

    ✏️ Corrected Mathematical Work & Explanation
  2. 5 ERROR ANALYSIS

    Fix our table's thinking

    1. 1The problem:On a frosty morning at the mountain cache, the thermometer reads -8 degrees. What is the absolute value of -8?
    2. 2A classmate at our table answered:-8

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

    ✏️ Corrected Mathematical Work & Explanation
  3. 6 ERROR ANALYSIS

    Confusing Opposite with Absolute Value

    1. 1Problem:Complete the table for the integer 9: find its absolute value and its opposite.
    2. 2Student's thinking:Absolute value and opposite both just make a number positive, so they should give the same answer as each other.
    3. 3Student's answer:Absolute value of 9 = 9, and opposite of 9 = 9.

    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