6.GR.4 Lesson 5-8-group2 🟣 Group 2 · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

5.8 Small Group · Group 2

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

Visual Models · Surface Area of Pyramids · Pyramid · Procedural Fluency

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: Push further — 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 — 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
  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.
3Second Model — Try it together — then prove it
  1. Now a smaller square pyramid: base 4 × 4, slant height 5. What is the base area?
  2. Right, 4 × 4 = 16. Now one triangular face: ½ × 4 × 5. What do you get?
  3. Yes, 10. Four faces is 4 × 10 = 40. Now add the base: 16 + 40. What is the surface area?
  4. Yes, SA = 56 in². Don't forget to add the base area!
  5. Now prove it: say why that move had to work at all — not just that it did.
  6. Sentence frame — convince a skeptic: "My method works because ___ . It would stop working if ___ ."
4Mathematical 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.
5Watch 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 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 1 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
  2. 2 MULTIPLE CHOICE

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

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

    A square pyramid has a base area of 49 cm² and a total lateral area of 84 cm². What is the surface area?

    1. A133 cm²
    2. B84 cm²
    3. C49 cm²
    4. D133 cm³
    Formula
    Put the numbers in
    Work it out
    Answer with its unit
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 4 ERROR ANALYSIS

    Fix our table's thinking

    1. 1The problem:A square pyramid has a base edge of 5 in and a slant height of 7 in. What is the surface area?
    2. 2A classmate at our table answered:120 in²

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

    ✏️ Corrected Mathematical Work & Explanation
  2. 5 ERROR ANALYSIS

    Did You Halve the Triangle?

    1. 1Box:Square pyramid: base edge = 8 in, slant height = 10 in
    2. 2Base Area:8 × 8 = 64 in²
    3. 3One Triangular Face:8 × 10 = 80 in² (forgot the ½)
    4. 4Answer:SA = 64 + 4 × 80 = 64 + 320 = 384 in²

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

    ✏️ Corrected Mathematical Work & Explanation
  3. 6 ERROR ANALYSIS

    Find the Surface Area Error

    1. 1Dimensions:Square pyramid: base edge = 10 in, slant height = 8 in
    2. 2Base Area:10 × 10 = 100 in²
    3. 3Lateral Area:½ × 10 × 8 = 40 in² (one face). Total lateral = 40 × 3 = 120 in²
    4. 4Answer:SA = 100 + 120 = 220 in²

    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