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

1.3 Small Group · Group 2

Tier 1 Extension · Non-Routine Synthesis · Misconception Traps · Rigorous CER Proofs

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 CONCEPTUAL UNDERSTANDING & VISUAL MODELS [Visual Modeling]
  1. 1 FILL TABLE

    Each tram ride takes 12.5 minutes. Complete the table of total minutes.

    RidesExpressionTotal minutes
    10
    20
    50
    ✏️ Scratchpad / Reasoning
  2. 2 MATCHING GAME

    Match each tram question to the operation that answers it.

    1. Minutes for 40 rides (12.5 min each)
    2. Rides needed for 400 passengers (80 per ride)
    3. Hours in 625 minutes
    4. Passengers on 30 full rides
    • A40 × 12.5
    • B400 ÷ 80
    • C625 ÷ 60
    • D30 × 80
SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 3 MULTIPLE CHOICE

    The round trip is 5 miles. How far does a tram car travel in 5 round trips?

    1. A25 miles
    2. B10 miles
    3. C1 mile
    4. D50 miles
    ✏️ Workspace & Solution Steps
  2. 4 MULTIPLE CHOICE

    Apply — What Time Is It? The new year starts at midnight on January 1st. What time will it be 2,022 minutes after midnight?

    1. A9:42 a.m. on January 2
    2. B8:22 p.m. on January 1
    3. C9:42 a.m. on January 1
    4. D9:42 p.m. on January 2
    ✏️ Workspace & Solution Steps
  3. 5 MULTIPLE CHOICE

    How many rides would the tram need for 10,000 passengers, at 80 passengers per ride?

    1. A125 rides
    2. B1,250 rides
    3. C12.5 rides
    4. D250 rides
    per 1
SECTION 3 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 6 OPEN RESPONSE

    How does the answer change if the tram must transport 6,000 passengers? (Each ride carries 80 passengers and takes 12.5 minutes.) Show your steps.

    ✏️ Mathematical Justification & Response
✍️ The Writing Revolution (TWR) · Sentence Expansion Because · But · So

Complete each sentence stem to demonstrate precise mathematical reasoning:

BECAUSE The mathematical model proves the solution because each step preserves quantitative equivalence.
BUT An estimate provides a quick benchmark, but an exact proof is required for precision.
SO The quantities follow the standard rule, so the final result is verified with certainty.
📐 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.
✍️ AUTHOR YOUR OWN EXTENSION CHALLENGE

Create an original multi-step word problem aligned to this standard. Include constraints, and write the complete step-by-step mathematical proof below.

✏️ Author Workspace & Complete Solution Key
Student Mastery Self-Assessment:
1 · Need More Support
2 · Getting Closer
3 · Got It / Solid
4 · Master / Can Teach It