6.NOS.3 Lesson 2-7-group2 🟣 Group 2 · Challenge & Extension
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

2.7 Small Group · Group 2

Tier 1 Extension · Non-Routine Synthesis · Misconception Traps · Rigorous CER Proofs

Divide Decimals · Dividend · Procedural Fluency · Reasoning & Critique

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: Push further — How do you divide with decimals?
1Move the decimal point the same number of places in BOTH the divisor and the dividend, put the point in the quotient straight above it, then repeat Divide → Multiply → Subtract → Bring Down — 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 want 18.9 ÷ 6.3. The divisor is 6.3, and long division needs a whole-number divisor.
  2. STEP 0 — MOVE THE POINT: I move the decimal point 1 place right in the divisor, so 6.3 becomes 63.
  3. I slide the decimal point 1 place to the right in the dividend too, so 18.9 becomes 189. Both points slid the same 1 place, so the answer does not change. The problem is now 189 ÷ 63.
  4. Now I write it the tall way — 63 into 189 — with the answer going on top of the bar and the answer's decimal point in the column directly above the dividend's point. Then I repeat the same four steps I always use: DIVIDE, MULTIPLY, SUBTRACT, BRING DOWN.
  5. DIVIDE: 63 does not fit into 1 or 18, so my first working number is 189. How many 63s fit into 189? Three. I write 3 above the 9.
  6. MULTIPLY: 3 × 63 = 189. I write it underneath.
  7. SUBTRACT: 189 − 189 = 0.
  8. BRING DOWN: there are no digits left to bring down, so the cycle is finished and the remainder is 0. 18.9 ÷ 6.3 = 3.
  9. I check by multiplying: 6.3 × 3 = 18.9. Correct — 3 pods can be filled.
3Second Model — Try it together — then prove it
  1. Let's do 8.4 ÷ 2.1. STEP 0 — MOVE THE POINT: how many places make 2.1 a whole number? (1 place, so 2.1 becomes 21.)
  2. Now slide the decimal point 1 place to the right in the dividend too. What does 8.4 become? (84, so the new problem is 84 ÷ 21.)
  3. DIVIDE: 84 ÷ 21 → 4. MULTIPLY: 4 × 21 = 84. SUBTRACT: 84 − 84 = 0. BRING DOWN: nothing is left, so 8.4 ÷ 2.1 = 4. Check: 2.1 × 4 = 8.4.
  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
  • Divide Decimals (Dividir decimales) — Find a quotient with decimals by sliding both decimal points right until the divisor is a whole number.
  • Dividend (Dividendo) — The total number being divided into equal groups (the number inside the division bracket).
  • Divisor (Divisor) — The number of equal groups you are dividing into (the number outside the division bracket).
  • Quotient (Cociente) — The answer when you divide.
  • Decimal Division Algorithm (Algoritmo de división decimal) — The steps for dividing decimals: slide the divisor's decimal point right until the divisor is a whole number, slide the dividend's point right the same number of places, then divide.
  • Equivalent division (División equivalente) — Multiplying both numbers by 10 or 100 gives the same answer.
5Watch out
  • A common mistake in Divide Decimals is moving the decimal point in the divisor but forgetting to move it the same number of places in the dividend. For example, in 6.4 ÷ 0.8 a student changes 0.8 to 8 but leaves the dividend as 6.4, then divides 6.4 ÷ 8 = 0.8 instead of moving both points to get 64 ÷ 8 = 8. A second version of this mistake happens when the divisor has two decimal places, like 0.12: students move both points only 1 place instead of 2, turning 9.6 ÷ 0.12 into 96 ÷ 1.2 instead of the correct 960 ÷ 12. Count the divisor's decimal places first, then move BOTH points that same number of places.
SECTION 1 CONCEPTUAL UNDERSTANDING & VISUAL MODELS [Visual Modeling]
  1. 1 FILL TABLE

    Solve each decimal division problem.

    Division ProblemQuotient
    9.6 ÷ 0.8
    15.6 ÷ 1.3
    24.5 ÷ 3.5
    5.76 ÷ 0.24
    11.34 ÷ 0.9
    ✏️ Scratchpad / Reasoning
  2. 2 MATCHING GAME

    Match each decimal division to its quotient.

    1. 7.2 ÷ 0.8
    2. 4.56 ÷ 0.6
    3. 13.2 ÷ 1.2
    4. 3.6 ÷ 0.12
    5. 10.5 ÷ 1.5
    6. 0.96 ÷ 0.8
    • A9
    • B7.6
    • C11
    • D30
    • E7
    • F1.2
SECTION 2 COMPUTATION & PROCEDURAL FLUENCY [Show Every Step]
  1. 3 MULTIPLE CHOICE

    What is 4.8 ÷ 0.6?

    1. A8
    2. B0.8
    3. C80
    4. D4.2
    ✏️ Workspace & Solution Steps
  2. 4 MULTIPLE CHOICE

    What is 15 ÷ 0.25?

    1. A60
    2. B6
    3. C1.5
    4. D0.6
    ✏️ Workspace & Solution Steps
SECTION 3 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 5 MULTIPLE CHOICE

    A ribbon is 7.2 meters long and is cut into 0.8-meter pieces. How many pieces are there?

    1. A9
    2. B8
    3. C7
    4. D10
    ✏️ Workspace & Solution Steps
  2. 6 MULTIPLE CHOICE

    Table 1's lunch bill is $15.00. Every sandwich costs $3.75. How many sandwiches did Table 1 order?

    1. A4 sandwiches
    2. B40 sandwiches
    3. C0.25 sandwiches
    4. D11.25 sandwiches
    ✏️ Workspace & Solution Steps
🗣️ 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
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.
✍️ AUTHOR YOUR OWN EXTENSION CHALLENGE

Create an original multi-step word problem aligned to this standard. Include constraints, and write the complete step-by-step mathematical proof below.

✏️ Author Workspace & Complete Solution Key
Student Mastery Self-Assessment:
1 · Need More Support
2 · Getting Closer
3 · Got It / Solid
4 · Master / Can Teach It