6.NOS.3 Lesson 2-11-group2 🟣 Group 2 · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

2.11 Small Group · Group 2

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

Add and Subtract Decimals · Decimal · Procedural Fluency · Real-World Applications

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: Push further — How do you add and subtract decimals?
1Line up the decimal points, add zeros so each number has the same number of decimal places, then add or subtract one column at a time — 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. The tank has 128.75 liters. A shuttle adds 46.8 liters. I line up the decimal points and annex a zero: 46.80.
  2. I add: 128.75 + 46.80 = 175.55 liters.
  3. Now the thrusters use 19.35 liters, so I subtract: 175.55 − 19.35 = 156.20.
  4. The final fuel level is 156.20 liters. I check with estimation: about 130 + 47 − 19 = 158, which is close, so my answer is reasonable.
3Second Model — Try it together — then prove it
  1. Let's add 12.45 and 7.8. First, how do we write 7.8 with two decimal places? (7.80.)
  2. Line up the points and add the hundredths, then tenths, then ones. What do we get? (12.45 + 7.80 = 20.25.)
  3. So the sum is 20.25. The points stay lined up in the answer.
  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
  • Add and Subtract Decimals (Sumar y restar decimales) — Combine or find the difference between decimals by lining up equal place values.
  • Decimal (Decimal) — A number with a dot, like 0.5, that shows a part less than one.
  • Place value (Valor posicional) — What a digit is worth based on where it sits in a number.
  • Tenths (Décimas) — The first spot after the decimal point. It shows parts out of 10.
  • Hundredths (Centésimas) — The second spot after the decimal point. It shows parts out of 100.
  • Annex zeros (Agregar ceros) — Adding zeros at the end of a decimal so numbers line up evenly.
5Watch out
  • A common mistake in Add and Subtract Decimals is lining up the last digits (the right edges) of each number instead of lining up the decimal points — for example, adding 8.3 and 2.45 as if the 3 and the 5 belong in the same column. Before you add or subtract, add zeros so every number has the same number of decimal places (write 8.3 as 8.30), then check that the decimal points sit directly above one another.
SECTION 1 COMPUTATION & PROCEDURAL FLUENCY [Show Every Step]
  1. 1 MULTIPLE CHOICE

    What is 14.6 + 3.85?

    1. A18.45
    2. B18.35
    3. C17.45
    4. D18.55
    Line up the place values
SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 2 MULTIPLE CHOICE

    What is 20.3 − 7.48?

    1. A12.82
    2. B13.82
    3. C12.92
    4. D12.18
    Line up the place values
  2. 3 MULTIPLE CHOICE

    A student buys items costing $4.59, $12.75, and $3.80. What is the total cost?

    1. A$21.14
    2. B$20.14
    3. C$21.04
    4. D$21.24
    ✏️ Workspace & Solution Steps
SECTION 3 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 4 ERROR ANALYSIS

    Fix our table's thinking

    1. 1The problem:Case File: A supply log started the shift with $48.00 in the station snack fund. By the end, $31.27 had been spent. How much is left in the fund?
    2. 2A classmate at our table answered:$17.73

    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 Mistake — Subtracting Without a Placeholder

    1. 1Problem:Subtract 12.5 − 3.45
    2. 2Set up:Left 12.5 as one decimal place instead of annexing a zero
    3. 3Subtract:12.5 − 3.45 = 9.5
    4. 4Final answer:9.5

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

    ✏️ Corrected Mathematical Work & Explanation
  3. 6 ERROR ANALYSIS

    Find Tasha's Mistake

    1. 1Problem:15.7 − 8.36
    2. 2Set up:15.7 − 8.36
    3. 3Subtract:15.7 − 8.36 = 7.41
    4. 4Final answer:7.41

    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