6.NOS.8 Lesson 7-3-part2 Apply Day · Version A
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

7.3 · Part II

Supported Application · Guided Entry to Today's Problem

Integers and Absolute Value · Integer

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: 7.3 · Part II
1Absolute Value
2Strategy Model — step by step
  1. Absolute value represents distance on a number line, never direction
  2. Distance is always positive or zero: |-7| = 7 and |7| = 7
  3. Context: Magnitude of temperature, debt, elevation regardless of sign
3Mathematical 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.
4Watch 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)?
  1. 1 MULTIPLE CHOICE

    What is |−2.5|?

    1. A2.5
    2. B−2.5
    3. C0
    4. D25
    ✏️ Workspace & Solution Steps
  2. 2 MULTIPLE CHOICE

    What is |−3/4|?

    1. A3/4
    2. B−3/4
    3. C4/3
    4. D0
    ✏️ Workspace & Solution Steps
  3. 3 MULTIPLE CHOICE

    (Lesson 7.1) Badwater Basin is 86 meters below sea level, and sea level is 0. Which integer represents that elevation?

    1. A-86
    2. B86
    3. C0
    4. D-68
    ✏️ Workspace & Solution Steps
📐 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
6.NOS.8 Lesson 7-3-part2 Apply Day · Version B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

7.3 · Part II

On-Level Application · Standard Rigor

Integers and Absolute Value · Integer

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: 7.3 · Part II
1Absolute Value
2The Structural Procedure
  1. Absolute value represents distance on a number line, never direction
  2. Distance is always positive or zero: |-7| = 7 and |7| = 7
  3. Context: Magnitude of temperature, debt, elevation regardless of sign
3Mathematical 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.
4Watch 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

    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
  2. 3 MULTIPLE CHOICE

    What is |−3/4|?

    1. A3/4
    2. B−3/4
    3. C4/3
    4. D0
    ✏️ Workspace & Solution Steps
📐 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
6.NOS.8 Lesson 7-3-part2 Apply Day · Challenge
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

7.3 · Part II

Extension & Non-Routine Application

Integers and Absolute Value · Integer

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: 7.3 · Part II
1Absolute Value
2The Structural Procedure
  1. Absolute value represents distance on a number line, never direction
  2. Distance is always positive or zero: |-7| = 7 and |7| = 7
  3. Context: Magnitude of temperature, debt, elevation regardless of sign
3Mathematical 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.
4Watch 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 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 1 MULTIPLE CHOICE

    What is the value of |−12|?

    1. A12
    2. B−12
    3. C0
    4. D1/12
    ✏️ Workspace & Solution Steps
  2. 2 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
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 3 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
📐 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