6.NOS.3 Lesson 2-7-group1 🟡 Group 1 · Support & Scaffolding
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

2.7 Small Group · Group 1

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

Divide Decimals · Dividend · Procedural Fluency · Reasoning & Critique

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: Let's build it together — How do you divide with decimals?
1Slide the decimal point the same number of places to the right in BOTH the divisor and the dividend. Write the answer's decimal point in the column directly above the dividend's point. Then repeat Divide → Multiply → Subtract → Bring Down.
  • Dividing splits a total into equal groups. When you divide by a decimal, first move the point to make the divisor a whole number — then run the same long-division cycle: divide, multiply, subtract, bring down. 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 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.
3Mathematical 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.
4Watch 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

    Rewrite each problem by making the divisor a whole number, then solve.

    OriginalMultiply Both ByNew ProblemQuotient
    4.5 ÷ 0.9
    3.6 ÷ 0.4
    ✏️ Scratchpad / Reasoning
  2. 2 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
SECTION 2 COMPUTATION & PROCEDURAL FLUENCY [Show Every Step]
  1. 3 MULTIPLE CHOICE

    What is 14.4 ÷ 1.2?

    1. A12
    2. B1.2
    3. C120
    4. D0.12
    ✏️ Workspace & Solution Steps
  2. 4 MULTIPLE CHOICE

    What is 3.78 ÷ 0.6?

    1. A6.3
    2. B63
    3. C0.63
    4. D0.063
    ✏️ Workspace & Solution Steps
  3. 5 MULTIPLE CHOICE

    What is 8.4 ÷ 0.7?

    1. A12
    2. B1.2
    3. C120
    4. D0.12
    ✏️ Workspace & Solution Steps
  4. 6 MULTIPLE CHOICE

    What is 15.6 ÷ 1.3?

    1. A12
    2. B1.2
    3. C120
    4. D13
    ✏️ 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
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