5.NBT.B.7 Lesson 1-3-group1 🟡 Group 1 · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

1.3 Small Group · Group 1

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

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

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: Let's build it together — 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.
  • The book opens with a warm-up — about how many coins are in the picture? — then rides an aerial tramway that must move 4,000 passengers. 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 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.
3Mathematical 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.
4Watch 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

    Each tram ride carries 80 passengers. How many rides are needed to transport 4,000 passengers?

    1. A50 rides
    2. B500 rides
    3. C320,000 rides
    4. D3,920 rides
    ✏️ Workspace & Solution Steps
  2. 2 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
  3. 3 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
  4. 4 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. 5 OPEN RESPONSE

    How can a tape diagram help you visualize the tram problem of moving 4,000 passengers?

    💬 Sentence Starter: My tape diagram shows ___ .<br>It helps because ___ .
    ✏️ Mathematical Justification & Response
  2. 6 OPEN RESPONSE

    The two tram problems both use the 35-minute or 12.5-minute ride times. How are the two problems the SAME, and how are they DIFFERENT?

    💬 Sentence Starter: They are the same because ___ .<br>They are different because ___ .
    ✏️ 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
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