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

2.12 Small Group · Group 1

Second Practice Form · Re-Teach, Homework or Retake · Same Standard, New Problems

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 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 1 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
    1. 1LabelWrite what each column is.
    2. 2Find per 1Divide to get one.
    3. 3ScaleMultiply up to what is asked.
    4. 4CheckDoes the size make sense?
  2. 2 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
  3. 3 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
    1. 1LabelWrite what each column is.
    2. 2Find per 1Divide to get one.
    3. 3ScaleMultiply up to what is asked.
    4. 4CheckDoes the size make sense?
  4. 4 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
    1. 1SplitBreak one factor apart.
    2. 2MultiplyOne part at a time.
    3. 3AddAdd the parts.
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 5 ERROR ANALYSIS

    Spot the Common Mistake — Counting Decimal Places

    1. 1Problem:0.3 × 0.6
    2. 2Multiply as whole numbers:3 × 6 = 18
    3. 3Count decimal places:0.3 has 1 decimal place and 0.6 has 1 decimal place → 1 total
    4. 4Place the decimal point:Move the point 1 place in 18 to get 1.8

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

    ✏️ Corrected Mathematical Work & Explanation
  2. 6 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
📐 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