6.NOS.6 Lesson 7-1-group1 🟡 Group 1 · Support & Scaffolding
MASTERY CHECK
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7.1 Small Group · Group 1

Tier 2 Intervention · Concrete-Representational-Abstract (CRA) · Dual-Language Anchors

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 FILL TABLE

    Write the integer that represents each situation. Remember to decide what 0 means first.

    SituationInteger
    A football play with a 12-yard loss
    A hiker 250 meters above sea level
    7 degrees below zero
    A submarine resting at the surface of the water
    ✏️ Scratchpad / Reasoning
  2. 2 DRAG SORT

    Sort each integer by which side of 0 it sits on when you graph it on a number line.

    Target Categories: Left of 0 (negative integer) Right of 0 (positive integer)
    SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
    1. 3 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
    2. 4 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
    3. 5 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 3 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
    1. 6 ERROR ANALYSIS

      Spot the Mistake: The Opposite of -7

      1. 1Problem:Name the opposite of -7.
      2. 2Student thinking:The number starts out negative, and taking the opposite of a negative number keeps it negative, so the answer stays on the left side of 0.
      3. 3Student answer:The opposite of -7 is -7.

      Which step contains the error? Explain the mathematical misconception and write the correct calculation below.

      ✏️ Corrected Mathematical Work & Explanation
    🗣️ 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
    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