5.NF.B.4 Lesson 1-2-group2 🟣 Group 2 · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

1.2 Small Group · Group 2

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

quantity · relationship · Procedural Fluency · Real-World Applications

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: Push further — Make sense, plan, check
1When we do math, we make sense of problems, develop a solution plan, check our progress, and try other strategies when we come to dead ends — 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 estimate the peas
  1. A bowl is full of peas — far too many to count one at a time. About how many peas are in the bowl?
  2. I do not count every pea — I look for a group I CAN count, like one small cluster of about 10.
  3. Then I ask how many of those clusters would cover the whole bowl. I count about 12.
  4. 12 clusters of about 10 is 12 × 10 = 120, so my estimate is about 120 peas — a reasoned answer, close enough to be useful.
3Second Model — Try it together — then prove it
  1. 76 = 100 + 5.76.
  2. 76 = 105 + 0.76.
  3. 76 = 110 − 4.24.
  4. 76 = 52.88 × 2, and 105.76 = 211.52 ÷ 2.
  5. Same number, five different breaks. Find one more of your own.
  6. Now prove it: say why that move had to work at all — not just that it did.
  7. Sentence frame — convince a skeptic: "My method works because ___ . It would stop working if ___ ."
4Mathematical Word Bank
  • quantity (cantidad) — An amount in a problem — a number with a meaning attached, like 540 meters.
  • relationship (relación) — How two quantities compare or connect to each other.
  • strategy (estrategia) — A plan for how to solve a problem before you start computing.
  • reasonable (razonable) — A solution that makes sense in the context of the problem.
  • persevere (perseverar) — To keep working on a problem, checking your progress and adjusting your plan when you get stuck.
5Watch out
  • Expecting a fraction of a number to be bigger than the number — 5/6 × 540 must be LESS than 540 because 5/6 is less than 1; only a fraction greater than 1, like 6/5, makes the product bigger.
SECTION 1 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 1 MULTIPLE CHOICE

    Which set shows FIVE different correct decompositions of 105.76?

    1. A100 + 5.76, 105 + 0.76, 110 − 4.24, 52.88 × 2, 211.52 ÷ 2
    2. B100 + 5.76, 105 + 7.6, 110 − 4.24, 52.88 × 2, 211.52 ÷ 2
    3. C100 + 5.76, 105 + 0.76, 110 + 4.24, 52.88 × 2, 211.52 ÷ 2
    4. D100 + 5.76, 105 + 0.76, 110 − 4.24, 52.88 × 3, 211.52 ÷ 2
    ✏️ Workspace & Solution Steps
  2. 2 MULTIPLE CHOICE

    A student has walked 2/3 of her route and has covered 14 blocks. How long is the whole route?

    1. A9 1/3 blocks
    2. B21 blocks
    3. C28 blocks
    4. D42 blocks
    ✏️ Workspace & Solution Steps
  3. 3 MULTIPLE CHOICE

    Claim: “Taking a fraction of a whole number always gives you a smaller number.” Always, sometimes, or never true?

    1. AAlways — a fraction is a part, and a part is smaller
    2. BNever — the answer is always larger
    3. CSometimes — only when the fraction is less than 1
    4. DSometimes — it depends on whether the whole number is even
    ✏️ Workspace & Solution Steps
  4. 4 MULTIPLE CHOICE

    The Tokyo building will be 6/5 as tall as One World Trade Center (540 meters). How tall will it be?

    1. A108 meters
    2. B432 meters
    3. C450 meters
    4. D648 meters
    Rewrite each fraction
    Work it out
    Simplify
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 5 ERROR ANALYSIS

    Fix our table's thinking

    1. 1The problem:You calculate 5/6 × 540 and get 650 meters. What does the checking step of your plan tell you?
    2. 2A classmate at our table answered:The answer is fine because 650 is a bigger number than 5/6

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

    ✏️ Corrected Mathematical Work & Explanation
  2. 6 OPEN RESPONSE

    Ana walked 1/2 of 24 blocks; Ben walked 3/4 of 20. Dana says: “3/4 is bigger than 1/2, so Ben walked farther.” Her conclusion is correct — but her reasoning is not. Explain why the reasoning fails, and give a route length for Ana that would make her conclusion wrong.

    ✏️ Mathematical Justification & Response
📐 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