6.NOS.6 Lesson 7-1-group1 🟡 Group 1 · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

7.1 Small Group · Group 1

Second Practice Form · Re-Teach, Homework or Retake · Same Standard, New Problems

Integer · Opposite · Procedural Fluency · Real-World Applications

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: Let's build it together — How do you use integers to describe quantities above and below zero?
1Pick what 0 means in the situation first. Then a quantity above 0 is a positive integer and a quantity below 0 is a negative integer, and its opposite is the same distance from 0 on the other side.
  • Counting numbers, their opposites, and 0 are integers. A negative integer is less than zero and is written with a − sign. Opposites are the same distance from 0, but on opposite sides of the number line. We'll walk through a worked example, try one together, then you'll try a few with hints right there when you need them.
2Worked Example — Watch me
  1. Badwater Basin is 86 meters below sea level, and sea level is defined as 0.
  2. Below 0 means a negative number, so I write the elevation as −86 meters.
  3. On a number line, I count 86 units to the LEFT of 0 and mark that point.
  4. The opposite of −86 is 86. Both are 86 units from 0, just on different sides.
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
  3. 4 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. 5 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
SECTION 3 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 6 ERROR ANALYSIS

    Spot the Mistake: Reykjavik's Temperature Swing

    1. 1Problem: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. What was the temperature at 2 p.m.?
    2. 2Student thinking:The opposite of a temperature should still be a cold temperature, so I keep the negative sign and just make the number bigger. That gives a temperature farther from 0.
    3. 3Student answer:The temperature at 2 p.m. was -24°C.

    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
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