6.NOS.6 Lesson 7-2-group1 🟡 Group 1 · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

7.2 Small Group · Group 1

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

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 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 1 MULTIPLE CHOICE

    Which rational number is closest to 0 on the number line?

    1. A-1/4
    2. B0.5
    3. C-2
    4. D1.75
    ✏️ Workspace & Solution Steps
  2. 2 MULTIPLE CHOICE

    Which number is farthest to the LEFT on a number line?

    1. A-1
    2. B0
    3. C-4
    4. D2
    ✏️ Workspace & Solution Steps
  3. 3 MULTIPLE CHOICE

    What is the opposite of -3/4?

    1. A3/4
    2. B-3/4
    3. C4/3
    4. D0
    Rewrite each fraction
    Work it out
    Simplify
    1. 1Same size piecesCommon denominator first.
    2. 2OperateOnly then add or subtract.
    3. 3SimplifyDivide out common factors.
  4. 4 MULTIPLE CHOICE

    The first trail marker sits between 0 and 1. Which rational number belongs there?

    1. A3/4
    2. B1.5
    3. C-1/2
    4. D2
    ✏️ Workspace & Solution Steps
  5. 5 MULTIPLE CHOICE

    Order these three trail markers from least to greatest: -1.5, 0.5, -0.5.

    1. A-1.5, -0.5, 0.5
    2. B0.5, -0.5, -1.5
    3. C-0.5, -1.5, 0.5
    4. D-1.5, 0.5, -0.5
    ✏️ Workspace & Solution Steps
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 6 ERROR ANALYSIS

    Spot the Mistake: Plotting -2.25

    1. 1Problem:Plot -2.25 on the number line.
    2. 2Student thinking:It is negative, so I go past -2. The .25 is one quarter, so I count toward 0 (to the right) by a quarter unit and land between -2 and -1.
    3. 3Student answer:Point plotted at -1.75, between -2 and -1.

    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