6.NOS.6 Lesson 7-1-part2 Apply Day · Version A
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

7.1 · Part II

Supported Application · Guided Entry to Today's Problem

Integer · Opposite

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: 7.1 · Part II
1Integers & Opposites
2Strategy Model — step by step
  1. Integers: Positive whole numbers, negative whole numbers, and zero (..., -2, -1, 0, 1, 2, ...)
  2. Opposites: Numbers that are the same distance from 0 in opposite directions (e.g. -5 and 5)
  3. The opposite of the opposite of a number is the number itself: -(-a) = a
3Mathematical Word Bank
  • Integer (Número entero) — The counting numbers, their opposites, and 0.
  • Opposite (Opuesto) — A number that is the same distance from 0 as another number, but on the other side of 0.
  • Negative number (Número negativo) — A number less than 0, written with a − sign. On a number line it sits to the left of 0.
  • Positive number (Número positivo) — A number greater than 0. On a number line it sits to the right of 0.
  • Number line (Recta numérica) — A straight line where numbers are placed in order. It extends to the left of 0 to show values less than 0.
4Watch out
  • The most common mistake in this lesson is thinking that the opposite of a negative integer is still negative — for example, saying the opposite of -7 is -7, or that the opposite of -12 is -24. Opposites are the same DISTANCE from 0 but on OPPOSITE sides of 0, so taking an opposite always changes the direction and never changes the distance: the opposite of -7 is 7 and the opposite of -12 is 12. The one exception is 0, which is 0 units from itself and is therefore its own opposite. Before you submit, count the units from 0 and check that your answer is on the other side.
  1. 1 GUIDED FILL
    012345678910

    A diver is 4 feet below the surface. Write the integer, then its opposite.

    1. 1Below/lost/owed means negative: the integer is ___.
    2. 2The opposite sits the same distance from 0 on the other side: ___.
    3. 3Both are ___ units from zero, and here zero means the surface.
    Final answer:
  2. 2 GUIDED FILL
    012345678910

    The temperature is 6 degrees below zero. Write the integer, then its opposite.

    1. 1Below/lost/owed means negative: the integer is ___.
    2. 2The opposite sits the same distance from 0 on the other side: ___.
    3. 3Both are ___ units from zero, and here zero means zero degrees.
    Final answer:
  3. 3 GUIDED FILL
    012345678910

    A player loses 8 points. Write the integer, then its opposite.

    1. 1Below/lost/owed means negative: the integer is ___.
    2. 2The opposite sits the same distance from 0 on the other side: ___.
    3. 3Both are ___ units from zero, and here zero means no change in score.
    Final answer:
📐 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.6 Lesson 7-1-part2 Apply Day · Version B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

7.1 · Part II

On-Level Application · Standard Rigor

Integer · Opposite

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: 7.1 · Part II
1Integers & Opposites
2The Structural Procedure
  1. Integers: Positive whole numbers, negative whole numbers, and zero (..., -2, -1, 0, 1, 2, ...)
  2. Opposites: Numbers that are the same distance from 0 in opposite directions (e.g. -5 and 5)
  3. The opposite of the opposite of a number is the number itself: -(-a) = a
3Mathematical Word Bank
  • Integer (Número entero) — The counting numbers, their opposites, and 0.
  • Opposite (Opuesto) — A number that is the same distance from 0 as another number, but on the other side of 0.
  • Negative number (Número negativo) — A number less than 0, written with a − sign. On a number line it sits to the left of 0.
  • Positive number (Número positivo) — A number greater than 0. On a number line it sits to the right of 0.
  • Number line (Recta numérica) — A straight line where numbers are placed in order. It extends to the left of 0 to show values less than 0.
4Watch out
  • The most common mistake in this lesson is thinking that the opposite of a negative integer is still negative — for example, saying the opposite of -7 is -7, or that the opposite of -12 is -24. Opposites are the same DISTANCE from 0 but on OPPOSITE sides of 0, so taking an opposite always changes the direction and never changes the distance: the opposite of -7 is 7 and the opposite of -12 is 12. The one exception is 0, which is 0 units from itself and is therefore its own opposite. Before you submit, count the units from 0 and check that your answer is on the other side.
SECTION 1 CONCEPTUAL UNDERSTANDING & VISUAL MODELS [Visual Modeling]
  1. 1 MULTIPLE CHOICE

    Which statement about 0 is TRUE?

    1. A0 is an integer, and it is its own opposite
    2. B0 is a negative integer because it is not positive
    3. C0 is a positive integer because it has no negative sign
    4. D0 is not an integer at all
    ✏️ Workspace & Solution Steps
SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 2 MULTIPLE CHOICE

    Which list of integers is ordered from LEAST to GREATEST?

    1. A-8, -3, 0, 5
    2. B-3, -8, 0, 5
    3. C0, -3, -8, 5
    4. D5, 0, -3, -8
    ✏️ Workspace & Solution Steps
  2. 3 MULTIPLE CHOICE

    Badwater Basin is at -86 meters. Which elevation is FARTHER below sea level than Badwater Basin?

    1. A-120 meters
    2. B-40 meters
    3. C0 meters
    4. D86 meters
    ✏️ 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.6 Lesson 7-1-part2 Apply Day · Challenge
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

7.1 · Part II

Extension & Non-Routine Application

Integer · Opposite

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: 7.1 · Part II
1Integers & Opposites
2The Structural Procedure
  1. Integers: Positive whole numbers, negative whole numbers, and zero (..., -2, -1, 0, 1, 2, ...)
  2. Opposites: Numbers that are the same distance from 0 in opposite directions (e.g. -5 and 5)
  3. The opposite of the opposite of a number is the number itself: -(-a) = a
3Mathematical Word Bank
  • Integer (Número entero) — The counting numbers, their opposites, and 0.
  • Opposite (Opuesto) — A number that is the same distance from 0 as another number, but on the other side of 0.
  • Negative number (Número negativo) — A number less than 0, written with a − sign. On a number line it sits to the left of 0.
  • Positive number (Número positivo) — A number greater than 0. On a number line it sits to the right of 0.
  • Number line (Recta numérica) — A straight line where numbers are placed in order. It extends to the left of 0 to show values less than 0.
4Watch out
  • The most common mistake in this lesson is thinking that the opposite of a negative integer is still negative — for example, saying the opposite of -7 is -7, or that the opposite of -12 is -24. Opposites are the same DISTANCE from 0 but on OPPOSITE sides of 0, so taking an opposite always changes the direction and never changes the distance: the opposite of -7 is 7 and the opposite of -12 is 12. The one exception is 0, which is 0 units from itself and is therefore its own opposite. Before you submit, count the units from 0 and check that your answer is on the other side.
  1. 1 MULTIPLE CHOICE

    Badwater Basin sits 86 meters below sea level, where sea level is defined as 0. Which integer represents this elevation?

    1. A−86
    2. B86
    3. C0
    4. D−8.6
    ✏️ Workspace & Solution Steps
  2. 2 MULTIPLE CHOICE

    At 6 a.m. in Reykjavik the temperature was -12°C. At 2 p.m. it was the opposite of the 6 a.m. temperature, and at 11 p.m. it was the opposite of the 2 p.m. temperature. What were the temperatures at 2 p.m. and 11 p.m.?

    1. A12°C and -12°C
    2. B-12°C and 12°C
    3. C12°C and 24°C
    4. D0°C and 12°C
    ✏️ Workspace & Solution Steps
  3. 3 MULTIPLE CHOICE

    A football team starts at the line of scrimmage, which is 0. During one series they had a 10-yard loss, a 4-yard gain, a 3-yard loss, and a 21-yard gain. Where does the series leave them?

    1. A12 yards past the line of scrimmage
    2. B8 yards past the line of scrimmage
    3. C18 yards past the line of scrimmage
    4. D38 yards past the line of scrimmage
    ✏️ 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