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

    Without computing the exact heights, order the three new buildings from shortest to tallest. (London: 5/6 of 540 m, Rio de Janeiro: 9/10 of 540 m, Tokyo: 6/5 of 540 m.)

    1. ALondon, Rio de Janeiro, Tokyo
    2. BRio de Janeiro, London, Tokyo
    3. CTokyo, Rio de Janeiro, London
    4. DLondon, Tokyo, Rio de Janeiro
    ✏️ Workspace & Solution Steps
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 3 OPEN RESPONSE

    The lesson says we check on our progress toward a solution and adjust our plan as needed. Describe one way YOU can check on your progress while solving a problem.

    ✏️ Mathematical Justification & Response
  2. 4 OPEN RESPONSE

    A classmate says, "In math, only the final answer matters." Using this lesson, write what you would say back.

    ✏️ Mathematical Justification & Response
  3. 5 OPEN RESPONSE

    Write your own Comparing Walks problem: describe three people using only relationships (shorter than, longer than), so a reader can put them in order without any exact distances. Then give one set of values that fits.

    ✏️ Mathematical Justification & Response
  4. 6 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
📐 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