6.NOS.6 Lesson 7-2-group2 🟣 Group 2 · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

7.2 Small Group · Group 2

Second Challenge Form · Non-Routine Extension · Same Standard, New Problems

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

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: Push further — 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 — and you can say why it is true, and where it would stop being true.
  • You already can do this. So we go up a level, not up a number: find what is always true, show it a second way, and be ready to defend it with a reason instead of an answer.
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.
3Second Model — Try it together — then prove it
  1. Now let's plot 0.75. Which two whole numbers is it between? It is between 0 and 1.
  2. What does 0.75 mean? It is 3/4 of the way from 0 to 1.
  3. So we split 0 to 1 into 4 equal parts and place the dot at the 3rd mark.
  4. Now prove it: say why that move had to work at all — not just that it did.
  5. Sentence frame — convince a skeptic: "My method works because ___ . It would stop working if ___ ."
4Mathematical 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.
5Watch 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

    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
  2. 2 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
  3. 3 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
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 4 ERROR ANALYSIS

    Fix our table's thinking

    1. 1The problem:Which rational number is closest to 0 on the number line?
    2. 2A classmate at our table answered:0.5

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

    ✏️ Corrected Mathematical Work & Explanation
  2. 5 OPEN RESPONSE

    A classmate says: 'The more digits after the decimal point, the smaller the number — look at 0.5 and 0.25.' Find a pair of numbers where that reasoning gives the WRONG answer, and write what is actually true. Where would each of your numbers sit on the number line?

    ✏️ Mathematical Justification & Response
  3. 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
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