6.GR.4 Lesson 5-8-part2 Apply Day · Version A
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

5.8 · Part II

Supported Application · Guided Entry to Today's Problem

Surface Area of Pyramids · Pyramid

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: 5.8 · Part II
1Surface Area of Pyramids
2Strategy Model — step by step
  1. Calculate area of base polygon (square, rectangle, or triangle)
  2. Calculate area of each triangular face using ½ × base × slant height
  3. Add the base area and all triangular face areas together
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?'
  1. 1 MULTIPLE CHOICE

    (Lesson 5.7) What is the surface area of a rectangular prism with l = 5 cm, w = 4 cm, h = 3 cm?

    1. A47 cm²
    2. B60 cm²
    3. C94 cm²
    4. D94 cm³
    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. 2 MULTIPLE CHOICE

    (Lesson 5.7) How many faces does a triangular prism have?

    1. A3
    2. B4
    3. C5
    4. D6
    ✏️ Workspace & Solution Steps
📐 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
6.GR.4 Lesson 5-8-part2 Apply Day · Version B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

5.8 · Part II

On-Level Application · Standard Rigor

Surface Area of Pyramids · Pyramid

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: 5.8 · Part II
1Surface Area of Pyramids
2The Structural Procedure
  1. Calculate area of base polygon (square, rectangle, or triangle)
  2. Calculate area of each triangular face using ½ × base × slant height
  3. Add the base area and all triangular face areas together
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?'
  1. 1 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. A49 cm²
    2. B84 cm²
    3. C133 cm²
    4. D133 cm³
    Formula
    Put the numbers in
    Work it out
    Answer with its unit
  2. 2 MULTIPLE CHOICE

    Your first gift box is a square pyramid with a base edge of 7 in and a slant height of 9 in. How much wrapping paper (total surface area) covers it?

    1. A126 in²
    2. B144 in²
    3. C175 in²
    4. D175 in³
    Formula
    Put the numbers in
    Work it out
    Answer with its unit
  3. 3 MULTIPLE CHOICE

    Before adding the base, you need the area of just one triangular face of a gift box with base edge 8 in and slant height 5 in. What is it?

    1. A13 in²
    2. B20 in²
    3. C20 in³
    4. D40 in²
    Formula
    Put the numbers in
    Work it out
    Answer with its unit
📐 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
6.GR.4 Lesson 5-8-part2 Apply Day · Challenge
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

5.8 · Part II

Extension & Non-Routine Application

Surface Area of Pyramids · Pyramid

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: 5.8 · Part II
1Surface Area of Pyramids
2The Structural Procedure
  1. Calculate area of base polygon (square, rectangle, or triangle)
  2. Calculate area of each triangular face using ½ × base × slant height
  3. Add the base area and all triangular face areas together
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?'
  1. 1 MULTIPLE CHOICE

    A square pyramid has a base measuring 6 m by 6 m and four triangular faces, each with a base of 6 m and a slant height of 5 m. What is its surface area?

    1. A36 square meters
    2. B60 square meters
    3. C96 square meters
    4. D156 square meters
    Formula
    Put the numbers in
    Work it out
    Answer with its unit
📐 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