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

7.3 Small Group · Group 2

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

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 NUMBER LINE

    Plot these integers and circle pairs that have the same absolute value: -6, 6, -2, 2, -4, 4

    ✏️ Workspace & Solution Steps
  2. 2 FILL TABLE

    Complete the table with each integer's absolute value and its opposite.

    IntegerAbsolute ValueOpposite
    -7
    4
    -12
    0
    9
    ✏️ Scratchpad / Reasoning
SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 3 MULTIPLE CHOICE

    On a frosty morning at the mountain cache, the thermometer reads -8 degrees. What is the absolute value of -8?

    1. A8
    2. B-8
    3. C0
    4. D16
    ✏️ Workspace & Solution Steps
  2. 4 MULTIPLE CHOICE

    Two treasure sites report their temperatures: -5 degrees F at the Ice Cave and -2 degrees F at the Frozen Dock. Which site is COLDER?

    1. A-5 degrees F (Ice Cave)
    2. B-2 degrees F (Frozen Dock)
    3. CThey are the same
    4. DNeither is below zero
    ✏️ Workspace & Solution Steps
  3. 5 MULTIPLE CHOICE

    Captain Vega compares |-12| (a deep cave) and |7| (a hilltop). Which absolute value is GREATER?

    1. A|-12| because 12 > 7
    2. B|7| because 7 is positive
    3. CThey are equal
    4. D|-12| = -12, so |7| is greater
    ✏️ Workspace & Solution Steps
SECTION 3 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 6 OPEN RESPONSE

    A submarine is at -150 meters and a bird is flying at +150 meters. A student says the submarine is closer to sea level because -150 is less than 150. Is the student correct? Explain using absolute value.

    ✏️ Mathematical Justification & Response
🗣️ 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