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

1.3 Small Group · Group 1

Tier 2 Intervention · Concrete-Representational-Abstract (CRA) · Dual-Language Anchors

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 CONCEPTUAL UNDERSTANDING & VISUAL MODELS [Visual Modeling]
  1. 1 DRAG SORT

    Sort each expression by whether it equals 125.

    Target Categories: Equals 125 Does NOT equal 125
    • 12.5 × 10
    • 1.25 × 100
    • 62.5 × 2
    • 12.5 × 100
    • 1.25 × 10
    • 12.5 + 10
  2. 2 FILL TABLE

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

    RidesExpressionTotal minutes
    10
    20
    50
    ✏️ Scratchpad / Reasoning
SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 3 MULTIPLE CHOICE

    One tram ride takes 12.5 minutes. How many minutes do 10 rides take?

    1. A125 minutes
    2. B22.5 minutes
    3. C1.25 minutes
    4. D1,250 minutes
    ✏️ Workspace & Solution Steps
  2. 4 MULTIPLE CHOICE

    Five Breaks: which of these is a correct way to decompose 12.5?

    1. A10 + 2.5
    2. B10 + 2.05
    3. C12 + 5
    4. D1 + 2.5
    ✏️ Workspace & Solution Steps
  3. 5 MULTIPLE CHOICE

    How many minutes do 50 tram rides take, at 12.5 minutes per ride?

    1. A625 minutes
    2. B62.5 minutes
    3. C600 minutes
    4. D6,250 minutes
    per 1
    1. 1LabelWrite what each column is.
    2. 2Find per 1Divide to get one.
    3. 3ScaleMultiply up to what is asked.
    4. 4CheckDoes the size make sense?
SECTION 3 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 6 OPEN RESPONSE

    About how many coins are in the picture in your book? Explain how you estimated WITHOUT counting every coin.

    💬 Sentence Starter: First I counted ___ .<br>Then I estimated about ___ because ___ .
    ✏️ 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
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