6.NOS.3 Lesson 2-12-group1 🟡 Group 1 · Support & Scaffolding
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

2.12 Small Group · Group 1

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

Multiply Decimals · Product · Procedural Fluency · Reasoning & Critique

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: Let's build it together — How do you multiply decimals?
1Multiply like whole numbers, then the product has the SAME total of decimal places as both factors combined.
  • To multiply decimals, you multiply the numbers as if there were no decimal points. Then you count the decimal places and put the point back in the answer. 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 4.5 × 12.60, the cost of 4.5 meters at $12.60 each.
  2. First I multiply without points, like whole numbers: 45 × 1260 = 56,700.
  3. Now I count decimal places: 4.5 has 1, and 12.60 has 2, so 1 + 2 = 3 decimal places.
  4. I put the point 3 places from the right in 56,700: that gives 56.700, or $56.70.
  5. I check with an estimate: 5 × $13 = $65, and $56.70 is close, so my answer is reasonable.
3Mathematical Word Bank
  • Multiply Decimals (Multiplicar decimales) — Find the product of decimals, then use place value to place the decimal point.
  • Product (Producto) — The answer when you multiply.
  • Decimal point (Punto decimal) — The dot that splits the whole number from the part after it.
  • Estimate (Estimar) — A close answer you get by rounding first.
  • Place value (Valor posicional) — What a digit is worth based on where it sits in a number.
  • Decimal places (Cifras decimales) — How many digits come after the decimal point.
4Watch out
  • A common mistake in Multiply Decimals is counting decimal places from only one factor instead of adding the decimal places from BOTH factors. For example, in 0.4 × 0.06, a student multiplies 4 × 6 = 24, then places the decimal point using just one factor's place count (1 place), writing 0.24 instead of the correct answer: 0.4 has 1 decimal place and 0.06 has 2 decimal places, for a total of 3, so 24 becomes 0.024. Before you submit, count the decimal places in EACH factor separately and add them together — that total is how many decimal places belong in your final answer.
SECTION 1 CONCEPTUAL UNDERSTANDING & VISUAL MODELS [Visual Modeling]
  1. 1 FILL TABLE

    Multiply as whole numbers, then place the decimal point.

    ProblemWhole Number ProductTotal Decimal PlacesFinal Answer
    2.5 × 4
    1.2 × 0.3
    6.1 × 0.5
    ✏️ Scratchpad / Reasoning
  2. 2 MATCHING GAME

    Match each expression to its product.

    1. 2.5 × 4
    2. 1.2 × 0.3
    3. 3.6 × 0.5
    4. 4.8 × 2.5
    5. 0.6 × 0.8
    6. 7.5 × 1.2
    • A10
    • B0.36
    • C1.8
    • D12
    • E0.48
    • F9
SECTION 2 COMPUTATION & PROCEDURAL FLUENCY [Show Every Step]
  1. 3 MULTIPLE CHOICE

    What is 3.4 × 2.6?

    1. A8.84
    2. B88.4
    3. C0.884
    4. D8.48
    Show each partial product, then add them
    1. 1SplitBreak one factor apart.
    2. 2MultiplyOne part at a time.
    3. 3AddAdd the parts.
  2. 4 MULTIPLE CHOICE

    What is 0.7 × 1.5?

    1. A1.05
    2. B10.5
    3. C0.105
    4. D1.50
    Show each partial product, then add them
    1. 1SplitBreak one factor apart.
    2. 2MultiplyOne part at a time.
    3. 3AddAdd the parts.
  3. 5 MULTIPLE CHOICE

    What is 5.3 × 4?

    1. A21.2
    2. B2.12
    3. C212
    4. D20.12
    Show each partial product, then add them
    1. 1SplitBreak one factor apart.
    2. 2MultiplyOne part at a time.
    3. 3AddAdd the parts.
SECTION 3 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 6 MULTIPLE CHOICE

    Which estimate is closest to 4.8 × 3.2?

    1. A5 × 3 = 15
    2. B4 × 3 = 12
    3. C5 × 4 = 20
    4. D48 × 32 = 1,536
    ✏️ 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