6.GR.4 Lesson 5-8-group1 🟡 Group 1 · Support & Scaffolding
MASTERY CHECK
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5.8 Small Group · Group 1

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

Surface Area of Pyramids · Pyramid · Procedural Fluency · Real-World Applications

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: Let's build it together — How do we find the surface area of a pyramid?
1Surface area of a pyramid = base area + the area of all the triangular lateral faces.
  • Surface area of a pyramid is the base area plus all the triangular side faces. A square pyramid has 1 square base and 4 triangular faces. Each triangle uses the slant height: ½ × base × slant height. 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
  1. My square pyramid has a 6 in. × 6 in. base and a slant height of 8 in.
  2. First the base area: 6 × 6 = 36.
  3. Now one triangular face: ½ × 6 × 8 = 24. A square pyramid has 4 of them, so 4 × 24 = 96.
  4. I add the base and the side faces: 36 + 96 = 132.
  5. So the total surface area is 132 in². I used the slant height (8) for the triangles, not the pyramid's height.
3Mathematical Word Bank
  • Surface Area of Pyramids (Área de superficie de pirámides) — The total area of a pyramid's base and triangular faces. Formula: SA = B + lateral area.
  • Pyramid (Pirámide) — A solid with a flat bottom and triangle sides that meet at one point on top.
  • Slant height (Altura inclinada (apotema)) — The height of a side triangle, measured along its slanted face.
  • Lateral face (Cara lateral) — A triangle side of a pyramid, not the bottom.
  • Base (Base) — The flat bottom of a pyramid.
  • Apex (Ápice) — The point at the top of a pyramid where the sides meet.
4Watch out
  • A common mistake in Surface Area of Pyramids is finding the four triangular lateral faces correctly (½ × base edge × slant height, times 4) and then stopping — forgetting to add the base area at the end. This leaves the total surface area too small by exactly the base's area. Before you submit, ask: 'Did I add the base area to the four lateral faces, or did I stop after the sides?'
SECTION 1 CONCEPTUAL UNDERSTANDING & VISUAL MODELS [Visual Modeling]
  1. 1 FILL TABLE

    Find the area of one lateral face for each pyramid.

    PyramidBase EdgeSlant HeightArea of One Face
    Pyramid 1
    Pyramid 2
    Pyramid 3
    ✏️ Scratchpad / Reasoning
  2. 2 DRAG SORT

    Put the steps in order for finding the surface area of a square pyramid (base edge 6, slant height 10).

    Target Categories: Group 1 Group 2
    • Find base area: 6 × 6 = 36
    • Find one lateral face: ½ × 6 × 10 = 30
    • Multiply by 4 faces: 4 × 30 = 120
    • Add base + lateral: 36 + 120
    • SA = 156 in²
SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 3 MULTIPLE CHOICE

    A square pyramid has a base edge of 5 in and a slant height of 7 in. What is the surface area?

    1. A95 in²
    2. B70 in²
    3. C95 in³
    4. D120 in²
    Formula
    Put the numbers in
    Work it out
    Answer with its unit
    1. 1Name itWhich measure is asked?
    2. 2Write the formulaBefore any numbers.
    3. 3SubstituteMatch each letter.
    4. 4Unitunits, sq units, or cubic?
  2. 4 MULTIPLE CHOICE

    How many lateral (triangular) faces does a square pyramid have?

    1. A4
    2. B3
    3. C5
    4. D6
    ✏️ Workspace & Solution Steps
  3. 5 MULTIPLE CHOICE

    What is the area of one triangular face with base 8 in and slant height 6 in?

    1. A24 in²
    2. B48 in²
    3. C14 in²
    4. D24 in³
    Formula
    Put the numbers in
    Work it out
    Answer with its unit
    1. 1Name itWhich measure is asked?
    2. 2Write the formulaBefore any numbers.
    3. 3SubstituteMatch each letter.
    4. 4Unitunits, sq units, or cubic?
SECTION 3 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 6 ERROR ANALYSIS

    Don't Forget the Base

    1. 1Box:Square pyramid: base edge = 5 in, slant height = 6 in
    2. 2One Triangular Face:½ × 5 × 6 = 15 in²
    3. 3Four Faces:4 × 15 = 60 in²
    4. 4Answer:SA = 60 in² (stopped after the four triangular faces)

    Which step contains the error? Explain the mathematical misconception and write the correct calculation below.

    ✏️ Corrected Mathematical Work & Explanation
🗣️ MATHEMATICAL DISCOURSE & TALK MOVES SMP.3 / Construct Viable Arguments

Group Discussion Prompt: How does your visual model justify your mathematical solution?

🗣️ Partner A:
Partner A: "I modeled this by identifying the relationship and..."
👂 Partner B:
Partner B: "I agree with your step because the standard mathematical rule states..."
✍️ 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