5.NBT.B.7 Lesson 1-3-group2 🟣 Group 2 · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

1.3 Small Group · Group 2

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

representation · tape diagram · Procedural Fluency · Real-World Applications

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: Push further — Visualize the problem, then choose a tool
1When we do math, we visualize and represent problems, use tools to show relationships among quantities, and make strategic decisions about which tool fits the problem — 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 coins
  1. A pile of coins is too big to count one at a time. About how many coins are in the pile?
  2. I do not count every coin — I find a small stack I CAN count, about 10 coins.
  3. Then I estimate how many stacks like that are in the pile. I count about 15.
  4. 15 stacks of about 10 is 15 × 10 = 150, so my estimate is about 150 coins — reasoned, not random.
3Second Model — Try it together — then prove it
  1. One tram ride takes 12.5 minutes, so 10 rides take 12.5 × 10 = 125 minutes and 50 rides take 12.5 × 50 = 625 minutes.
  2. The tram needs 50 rides to move 4,000 passengers, and 625 minutes is 625 ÷ 60 hours — about 10.42 hours.
  3. A tape diagram of 4,000 cut into equal rides shows WHY we divide, and the table shows how minutes grow with rides.
  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
  • representation (representación) — A picture, diagram, table, or equation that shows the mathematics in a situation.
  • tape diagram (diagrama de cintas) — A rectangle cut into equal parts that helps you visualize how a total breaks apart.
  • tool (herramienta) — Anything you choose to help you see relationships and solve a problem — a table, a diagram, a graph.
  • ordered pair (par ordenado) — Two numbers that go together, like a time and a number of trips, that you can plot as a point.
  • round trip (viaje de ida y vuelta) — A complete journey from the start, to the destination, and back to the start.
5Watch out
  • Converting minutes to hours by moving the decimal point — 625 minutes is NOT 6.25 hours. An hour is 60 minutes, so divide by 60: 625 ÷ 60 ≈ 10.42 hours.
SECTION 1 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 1 MULTIPLE CHOICE

    The 50 rides take 625 minutes. About how many HOURS is that?

    1. AAbout 10.42 hours
    2. BAbout 6.25 hours
    3. CAbout 62.5 hours
    4. DAbout 12.5 hours
    ✏️ Workspace & Solution Steps
  2. 2 MULTIPLE CHOICE

    How does the answer change for 2,000 passengers? Each ride carries 80 passengers and takes 12.5 minutes. How many MINUTES are needed?

    1. A312.5 minutes
    2. B31.25 minutes
    3. C3,125 minutes
    4. D300 minutes
    ✏️ Workspace & Solution Steps
  3. 3 MULTIPLE CHOICE

    One round trip takes 35 minutes. Using the table (35 → 1, 350 → 10, 525 → 15, 700 → 20), how many round trips does a tram car complete in 10 hours?

    1. A17 round trips
    2. B20 round trips
    3. C15 round trips
    4. D18 round trips
    ✏️ Workspace & Solution Steps
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 4 OPEN RESPONSE

    The lesson says we make strategic decisions about which tool to use. For the 10-hour round-trip question, would you choose a table of values, a coordinate plane, or an equation? Defend your choice.

    ✏️ Mathematical Justification & Response
  2. 5 OPEN RESPONSE

    Math is in YOUR world. Describe a real situation from your life that works like the tram problem — a total split into equal groups, or a time built from equal chunks — and show the math.

    ✏️ Mathematical Justification & Response
  3. 6 ERROR ANALYSIS

    Fix our table's thinking

    1. 1The problem:Apply — What Time Is It? The new year starts at midnight on January 1st. What time will it be 2,022 minutes after midnight?
    2. 2A classmate at our table answered:8:22 p.m. on January 1

    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