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

2.12 Small Group · Group 2

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

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 COMPUTATION & PROCEDURAL FLUENCY [Show Every Step]
  1. 1 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
  2. 2 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
SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 3 MULTIPLE CHOICE

    A car travels 55.5 miles per hour for 2.4 hours. How far does it go?

    1. A133.2 miles
    2. B13.32 miles
    3. C1,332 miles
    4. D57.9 miles
    per 1
SECTION 3 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 4 ERROR ANALYSIS

    Fix our table's thinking

    1. 1The problem:A car travels 55.5 miles per hour for 2.4 hours. How far does it go?
    2. 2A classmate at our table answered:1,332 miles

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

    ✏️ Corrected Mathematical Work & Explanation
  2. 5 ERROR ANALYSIS

    Spot the Common Mistake — Placing the Decimal Point

    1. 1Problem:1.5 × 2.4
    2. 2Multiply as whole numbers:15 × 24 = 360
    3. 3Count decimal places:1.5 has 1 decimal place and 2.4 has 1 decimal place → 2 total
    4. 4Place the decimal point:Move the point 2 places in 360 to get 0.36

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

    ✏️ Corrected Mathematical Work & Explanation
  3. 6 ERROR ANALYSIS

    Find Kai's Mistake

    1. 1Problem:2.4 × 3.15
    2. 2Multiply as whole numbers:24 × 315 = 7,560
    3. 3Count decimal places:2.4 has 1 decimal place, 3.15 has 2 decimal places → 2 total
    4. 4Place decimal:75.60

    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