6.NOS.6 Lesson 7-1-part2 Apply Day · Set B
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7.1 · Part II

Second Practice Form · Independent Application and Spiral Review

Integer · Opposite

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■ 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 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 1 GUIDED FILL
    012345678910

    An account is overdrawn by $10. 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 a balance of $0.
    Final answer:
  2. 2 GUIDED FILL
    012345678910

    A diver is 12 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:
  3. 3 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
  4. 4 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
  5. 5 MULTIPLE CHOICE

    Claim: “The opposite of a number is always negative.” Always, sometimes, or never true?

    1. ASometimes — it is negative only when the original number is positive
    2. BAlways — that is what taking the opposite does
    3. CNever — opposites are always positive
    4. DSometimes — it depends whether the number is a whole number
    ✏️ Workspace & Solution Steps
  6. 6 MULTIPLE CHOICE

    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
  7. 7 MULTIPLE CHOICE

    In Reykjavik the temperature was -9°C. What is the opposite of -9?

    1. A9
    2. B-9
    3. C0
    4. D-18
    ✏️ Workspace & Solution Steps
  8. 8 MULTIPLE CHOICE

    What is the opposite of 0?

    1. A0
    2. BA number written -0, which is less than 0
    3. CEvery negative number
    4. DZero has no opposite
    ✏️ Workspace & Solution Steps
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 9 OPEN RESPONSE

    Describe two different real-world situations that use negative integers. For each one, tell exactly what 0 means in that situation, write one negative integer it could produce, and explain what the opposite of that integer would mean in the same situation.

    ✏️ 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