6.NOS.3 Lesson 2-12-group2 🟣 Group 2 · Challenge & Extension
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

2.12 Small Group · Group 2

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

Multiply Decimals · Product · Procedural Fluency · Reasoning & Critique

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: Push further — How do you multiply decimals?
1Multiply like whole numbers, then the product has the SAME total of decimal places as both factors combined — 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 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.
3Second Model — Try it together — then prove it
  1. Let's multiply 0.4 × 0.7. First multiply like whole numbers: what is 4 × 7? (28.)
  2. Now count decimal places: 0.4 has 1 and 0.7 has 1, so that is 2 places total.
  3. Put the point 2 places from the right in 28: 0.28. So 0.4 × 0.7 = 0.28.
  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
  • 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.
5Watch 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 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
  2. 2 FILL TABLE

    Complete each decimal multiplication.

    ProblemProduct
    6.4 × 3.5
    0.25 × 0.4
    8.3 × 2.1
    12.5 × 0.8
    ✏️ Scratchpad / Reasoning
SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 3 MULTIPLE CHOICE

    A customer orders 3 taco baskets at $4.25 each. What is the total before tax?

    1. A$12.75
    2. B$12.15
    3. C$1.275
    4. D$127.50
    ✏️ Workspace & Solution Steps
  2. 4 MULTIPLE CHOICE

    Each lemonade uses 0.6 of a cup of sugar, and sugar costs $0.40 per cup. How much sugar cost is in one lemonade? (0.6 × 0.4)

    1. A$0.24
    2. B$2.40
    3. C$0.024
    4. D$24.00
    per 1
  3. 5 MULTIPLE CHOICE

    The truck sells 2.5 pounds of fries, and each pound earns $1.20 in profit. What is the total profit? (2.5 × 1.2)

    1. A$3.00
    2. B$30.00
    3. C$0.30
    4. D$3.70
    Show each partial product, then add them
SECTION 3 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 6 ERROR ANALYSIS

    Level 2 Extension — Find the Cashier's Mistake

    1. 1Order:2 burrito bowls at $6.45 each: 2 × 6.45
    2. 2Multiply as whole numbers:2 × 645 = 1,290
    3. 3Count decimal places:6.45 has 2 decimal places → 2 total
    4. 4Place the decimal point:129.0, so the total is $129.00

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

    ✏️ Corrected Mathematical Work & Explanation
🗣️ 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