6.NOS.6 Lesson 7-2-group1 🟡 Group 1 · Support & Scaffolding
MASTERY CHECK
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7.2 Small Group · Group 1

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

Visual Models · Rational Numbers on the Number Line · Rational number · Procedural Fluency

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: Let's build it together — How do you place rational numbers on a number line?
1To plot a rational number, find the two whole numbers it falls between, then split the space into equal parts.
  • A rational number is any number you can write as a fraction. This includes fractions, decimals, and integers. Many rational numbers fall between two whole numbers. 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. I will plot -2.5 on the number line.
  2. First, the whole numbers it falls between: -2.5 is between -2 and -3.
  3. The .5 means halfway, so I split the space between -2 and -3 in half.
  4. I place my dot exactly halfway between -2 and -3. That is -2.5.
3Mathematical Word Bank
  • Rational Numbers on the Number Line (Números racionales en la recta numérica) — Every rational number has one exact spot on the number line. Writing it as a fraction, a decimal, or an integer does not change where it sits.
  • Rational number (Número racional) — A number that can be written as a fraction of two integers, with a bottom number that is not zero.
  • Fraction (Fracción) — A number that shows part of a whole, like 3/4.
  • Decimal (Decimal) — A number with a dot, like 0.5, that shows a part less than one.
  • Number line (Recta numérica) — A straight line where numbers are placed in order; numbers get smaller to the left and larger to the right.
  • Equivalent (Equivalente) — Having the same value, just written a different way.
4Watch out
  • A common mistake in Rational Numbers on the Number Line is treating the numerator and denominator of a negative fraction as two separate whole numbers instead of one value between two integers — for example, plotting -3/4 by going to -3 and then counting 4 more units to the left, landing (incorrectly) at -7, instead of recognizing that -3/4 = -0.75, which sits between 0 and -1. Before you submit an answer, find the two whole numbers your value falls between, then split that space into equal parts.
SECTION 1 CONCEPTUAL UNDERSTANDING & VISUAL MODELS [Visual Modeling]
  1. 1 MATCHING GAME

    Match each fraction to its decimal equivalent.

    1. 1/2
    2. -3/4
    3. 1 1/4
    4. -2 1/2
    5. 3/10
    6. -1/5
    • A0.5
    • B-0.75
    • C1.25
    • D-2.5
    • E0.3
    • F-0.2
  2. 2 NUMBER LINE

    Plot these rational numbers: -1, 0.5, -0.5, 1, -1.5

    ✏️ Workspace & Solution Steps
SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 3 MULTIPLE CHOICE

    Which point is located between -1 and -2 on the number line?

    1. A-0.5
    2. B-1.5
    3. C-2.5
    4. D1.5
    ✏️ Workspace & Solution Steps
  2. 4 MULTIPLE CHOICE

    Which fraction is equivalent to 0.25?

    1. A1/4
    2. B1/2
    3. C2/5
    4. D1/3
    ✏️ Workspace & Solution Steps
  3. 5 MULTIPLE CHOICE

    Where is -3/4 located on the number line?

    1. ABetween 0 and -1
    2. BBetween -3 and -4
    3. CBetween -1 and -2
    4. DBetween 0 and 1
    ✏️ Workspace & Solution Steps
SECTION 3 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 6 ERROR ANALYSIS

    Spot the Mistake: Plotting 1.5

    1. 1Problem:Plot 1.5 on the number line.
    2. 2Student thinking:1.5 has a 1 and a 5, so I will plot it between 1 and 5.
    3. 3Student answer:Point plotted at about 3, halfway between 1 and 5.

    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