Neft Teacher Unit 10

📦

Surface Area of Pyramids

6.G.4 Lesson 10-5

My Math Notebook

Name:

Date:

Period:

I Can…

I can find the surface area of a pyramid by adding the base area and the lateral faces.

Reveal Math Grade 6 How to Use 6.G.4

📦 TIME CAPSULE

How to Use This Deck

▶Present

Click Present or press F11 for fullscreen. Use arrow keys to advance.

👩‍🏫Teacher cues

Blue boxes show exactly what to say, ask, and how long to spend.

👨‍🎓Student work

Text boxes, polls, and drag-sort save automatically in the browser.

📝Notes

Press N or click 📝 in the toolbar for pacing tips and answers.

🎮Activity link

Launch the full HTML activity for independent practice.

🖨️Print

File → Print or the print button for handout copies.

⏱️ Time: 30 sec — read aloud, then advance

Reveal Math Grade 6 Learning Targets 6.G.4

🎯 Content Objective / Objetivo de contenido

I can find the surface area of a pyramid by adding the base area and the lateral faces.

Reveal Math Grade 6 Agenda 6.G.4

📦 TIME CAPSULE

Today's Flow

1 Warm-Up 5m

2 Vocabulary 8m

3 I Do 5m

4 We Do 5m

5 Explore 8m

6 Practice 10m

7 Connect 5m

8 Exit Ticket 5m

Total pacing: ~45 min · Progress bar at top tracks your place

📦

Lesson Phase

LAUNCH

⏱ ~10 min

Reveal Math Grade 6 Warm-Up Hook 6.G.4

⏱️ 3 MIN · THINK-PAIR-SHARE

A square pyramid time capsule display has a square base and four triangular faces that meet at a point on top. To find its surface area, which parts do you need to measure?

pyramidbaselateral faceslant heightsurface area

Reveal Math Grade 6 CFU 1 6.G.4

📦 TIME CAPSULE

Check for Understanding #1

✋ CFU · THUMBS

❓ Ask: Can you restate the warm-up question in your own words?

⏱️ Time: 30 sec

Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.

Reveal Math Grade 6 Be Curious 6.G.4

Visual Prompt

Time Capsule Project

Your class is building a pyramid-shaped display to showcase the time capsule at the school entrance. The pyramid will be covered in gold leaf to make it shine. To figure out how much gold leaf you need, you must calculate the total surface area — the base plus all the triangular faces!

👁 I Notice...

🔹 How many faces does a square pyramid have?

🔹 What shape is the base? What shape are the side faces?

🔹 What is the difference between the height of the pyramid and the slant height?

💭 I Wonder...

🔹 Why do we use slant height instead of regular height for the triangular faces?

🔹 Would a taller pyramid always need more gold leaf than a shorter one?

Reveal Math Grade 6 Concept Launch 6.G.4

🎯 I can find the surface area of a pyramid by adding the base area and the lateral faces.

📦 TIME CAPSULE

Concept Launch

💡 How do we find the surface area of a pyramid?

👩‍🏫 Say: This is the big idea for today. Students should be able to repeat it by the end.

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.

Key Idea:

Surface area of a pyramid = base area + the area of all the triangular lateral faces.

Reveal Math Grade 6 I Do — Watch Me 6.G.4

Reveal Math Grade 6 I Do — Key Step 6.G.4

Reveal Math Grade 6 We Do — Together 6.G.4

Reveal Math Grade 6 CFU 2 6.G.4

📦 TIME CAPSULE

Check for Understanding #2

✋ CFU · THUMBS

❓ Ask: Can you explain what we did in the We Do example?

⏱️ Time: 30 sec

Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.

Reveal Math Grade 6 You Do — Your Turn 6.G.4

🎯 I can find the surface area of a pyramid by adding the base area and the lateral faces.

📦 TIME CAPSULE

Now it's your turn

👨‍🎓 Students: Work independently first, then check with a partner.

⏱️ Time: 5 min

1In the table below, find the area of one lateral face, then the total surface area of each pyramid display.

2Remember: total SA = base area + all the triangular faces.

🎮

Open the interactive HTML activity for full practice.

Launch Activity ↗

📚

Lesson Phase

VOCABULARY

⏱ ~8 min

Reveal Math Grade 6 Vocabulary 6.G.4

Term / Término	Meaning / Significado	Visual
Pyramid Pirámide	A solid with a flat bottom and triangle sides that meet at one point on top. Un sólido con un fondo plano y lados triangulares que se unen en un punto arriba.	Like the Great Pyramid of Giza — a square on the bottom, 4 triangles slanting up to a point
Slant height Altura inclinada (apotema)	The height of a side triangle, measured along its slanted face. La altura de un triángulo lateral, medida por su cara inclinada.	If you slide your finger from the bottom edge up the triangle face to the top point — that distance is the slant height
Lateral face Cara lateral	A triangle side of a pyramid, not the bottom. Un lado triangular de una pirámide, no el fondo.	A square pyramid has 4 lateral faces — one triangle for each side of the square base
Base Base	The flat bottom of a pyramid. El fondo plano de una pirámide.	A square pyramid sits on a square base; base area = side × side
Apex Ápice	The point at the top of a pyramid where the sides meet. El punto en la parte de arriba de una pirámide donde se unen los lados.	The pointy top of a pyramid — all the slanted edges connect here
Lateral area Área lateral	The total area of just the side triangles, not the bottom. El área total solo de los triángulos laterales, sin el fondo.	For a square pyramid: lateral area = 4 × (½ × base edge × slant height)

Pyramid: example vs. non-example

✓ A square base with four triangle sides meeting at a top pointIts triangular faces meet at one apex.

✗ A box with six rectangular facesThat is a rectangular prism, not a pyramid.

Reveal Math Grade 6 Which Word? 6.G.4

🎯 I can find the surface area of a pyramid by adding the base area and the lateral faces.

📦 TIME CAPSULE

Which Word Fits?

❓ CLOZE POLL

❓ Ask: Vote A B C D — then defend your choice.

A solid with a polygon base and triangular faces meeting at one point is a ___.

Use It In a Sentence

Reveal Math Grade 6 CFU 3 6.G.4

📦 TIME CAPSULE

Check for Understanding #3

✋ CFU · THUMBS

❓ Ask: Use one vocabulary word in a sentence about today's topic.

⏱️ Time: 30 sec

Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.

Reveal Math Grade 6 Turn & Talk 6.G.4

🎯 I can find the surface area of a pyramid by adding the base area and the lateral faces.

📦 TIME CAPSULE

Turn & Talk — Launch

🗣️ TURN & TALK

👩‍🏫 Say: Partner A shares first for 45 seconds, then Partner B.

👨‍🎓 Students: Turn to your elbow partner. Use the sentence stems.

⏱️ Time: 90 sec

A square pyramid time capsule display has a square base and four triangular faces that meet at a point on top. To find its surface area, which parts do you need to measure?

Sentence starters (tap to use):

✍️ I need the area of the ___ plus the areas of the ___ triangular faces.Necesito el área de la ___ más las áreas de las ___ caras triangulares.

✍️ The surface area is the ___ area plus the ___ faces.El área de superficie es el área de la ___ más las caras ___.

Stretch further:

➕ I use the slant height because it is the ___ of each triangular face.

➕ The vertical height would not work because ___.

WORD BANK:

pyramidbaselateral faceslant heightsurface area

90s

👂 Listen For

Students explain a square pyramid's surface area = base area + the four triangular lateral faces, and that you add every face together.

Extend: Why do you use the slant height, not the pyramid's vertical height, to find the area of each triangular face?

🔍

Lesson Phase

EXPLORE & PRACTICE

⏱ ~18 min

Reveal Math Grade 6 Visual Model 6.G.4

🎯 I can find the surface area of a pyramid by adding the base area and the lateral faces.

📦 TIME CAPSULE

Visual Modeling Workspace

Use the drawing tray below to annotate the visual model. Teacher: say "Click to reveal" on key steps.

Reveal Math Grade 6 Explore 6.G.4

📦 TIME CAPSULE

Explore Activity

Calculate the surface area of each pyramid display. SA = Base Area + Lateral Area. For each triangular face, use A = ½ × base × slant height.

10045180280lateralbasesurface areatriangularslant height

✍️ Explore Discourse

Display B has the largest surface area (280 in²). What contributes more to the total — the base or the lateral faces? Why?

For Display B, the base area is ___ in² and the total lateral area is 4 × ___ = ___ in². The ___ contribute(s) more because ___.

Reveal Math Grade 6 Whiteboard CFU 6.G.4

🎯 I can find the surface area of a pyramid by adding the base area and the lateral faces.

📦 TIME CAPSULE

Whiteboard Moment

🖊️ WHITEBOARD CFU

👨‍🎓 Students: On your whiteboard or paper, solve ONE quick problem using today's strategy. Hold it up when done.

⏱️ Time: 2 min

Show your work clearly. Be ready to explain your thinking to a partner.

Reveal Math Grade 6 Discuss Explore 6.G.4

🎯 I can find the surface area of a pyramid by adding the base area and the lateral faces.

📦 TIME CAPSULE

Turn & Talk — Explore

🗣️ TURN & TALK

👩‍🏫 Say: Partner A shares first for 45 seconds, then Partner B.

👨‍🎓 Students: Turn to your elbow partner. Use the sentence stems.

⏱️ Time: 90 sec

For Display A (square base 6×6, slant height 8), how did you combine the base area and the four triangular faces to get the total surface area?

Sentence starters (tap to use):

✍️ The base area is ___ × ___ = ___, and one triangular face is ½ × 6 × 8 = ___.El área de la base es ___ × ___ = ___, y una cara triangular es ½ × 6 × 8 = ___.

✍️ The total surface area is the base plus 4 × ___ = ___ in².El área total de superficie es la base más 4 × ___ = ___ in².

Stretch further:

➕ The pyramid with the larger slant height has ___ surface area because ___.

➕ The ___ area stays the same because slant height only affects ___.

WORD BANK:

pyramidbaselateral faceslant heightsurface area

90s

👂 Listen For

Students compute base = 36 in², one face = 24 in², four faces = 96 in², total SA = 132 in², distinguishing base from lateral faces.

Extend: Two pyramids have the same 8×8 base but different slant heights. How will their surface areas compare, and which part stays the same?

Reveal Math Grade 6 Practice A 6.G.4

🎯 I can find the surface area of a pyramid by adding the base area and the lateral faces.

📦 TIME CAPSULE

Practice Check A

📝 QUICK CHECK

❓ Ask: Give students 1 minute. Cold-call one student to defend their answer.

⏱️ Time: 2 min

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

✍️ Show Your Work

Explain why your answer is correct using today's vocabulary.

Teacher reveal: SA = Base Area + Lateral Area = 49 + 84 = 133 cm².

Reveal Math Grade 6 Practice B 6.G.4

🎯 I can find the surface area of a pyramid by adding the base area and the lateral faces.

📦 TIME CAPSULE

Practice Check B

📝 QUICK CHECK

❓ Ask: Partner discussion first, then vote.

⏱️ Time: 2 min

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

✍️ Show Your Work

Explain why your answer is correct using today's vocabulary.

Teacher reveal: Base: 5 × 5 = 25 in². Each lateral face: ½ × 5 × 7 = 17.5 in². Four faces: 4 × 17.5 = 70 in². SA = 25 + 70 = 95 in².

Reveal Math Grade 6 Net Fold Explorer 6.G.4

🎯 I can find the surface area of a pyramid by adding the base area and the lateral faces.

📦 TIME CAPSULE

Net Fold Explorer

📦 NET FOLD

👨‍🎓 Students: Work at your own pace. Check with a partner before we discuss.

⏱️ Time: 5 min

Complete the interactive activity using today's strategy.

✍️ Justify Your Thinking

Reveal Math Grade 6 Sort It Out 6.G.4

Sort each label into the correct box.

Card Bank — cut or drag these cards:

⠿Base 4×4, slant 5: SA = 56

⠿Base 6×6, slant 5: SA = 96

⠿Base 6×6, slant 8: SA = 132

⠿Base 10×10, slant 9: SA = 280

Category A

Category B

Reveal Math Grade 6 Error Analysis 6.G.4

⚠ Find the Surface Area Error

A classmate turned in the work below. One step has a mistake. Read every step, find it, name it, and fix it.

Student's work — read every step:

1 Dimensions Square pyramid: base edge = 10 in, slant height = 8 in

2 Base Area 10 × 10 = 100 in²

3 Lateral Area ½ × 10 × 8 = 40 in² (one face). Total lateral = 40 × 3 = 120 in²

4 Answer SA = 100 + 120 = 220 in²

Which step has the error?

Reveal Math Grade 6 Choice Board 6.G.4

Choose ONE option to show what you know — then do it in the workspace below.

I chose option — my work:

Reveal Math Grade 6 Think Write 6.G.4

Use evidence from today's lesson to complete each frame.

Frame 1 Explain the Rule

Today's key idea is: "Surface area of a pyramid = base area + the area of all the triangular lateral faces." — and it works because ___.

Frame 2 Because / But / So

Because Pyramid means ___, but a tricky part is ___, so I have to ___.

Frame 3 Catch the Mistake

A common mistake with Pyramid is ___. It happens because ___, and the fix is ___.

Frame 4 Prove It

I can prove my answer is correct by ___, using Slant height to check my work.

Reveal Math Grade 6 Because · But · So 6.G.4

✍️ TWR · WRITE 3 SENTENCES · 7 MIN

Sentence kernelSurface area of a pyramid = base area + the area of all the triangular lateral faces.

because

Give a reason

Surface area of a pyramid = base area + the area of all the triangular lateral faces. because ___

but

Name a tricky part

Surface area of a pyramid = base area + the area of all the triangular lateral faces. but ___

so

State what it means

Surface area of a pyramid = base area + the area of all the triangular lateral faces. so ___

Reveal Math Grade 6 Sentence Expansion 6.G.4

🌱 TWR · GROW THE KERNEL · 6 MIN

Sentence kernelToday we used Pyramid.

Answer these to add detail

What exactly?When?Where in real life?Why does it work?How did we use it?

Sentence starters (tap to use)

First, …For example, …This means that …In other words, …As a result, …I know this because …

Reveal Math Grade 6 Student Workspace 6.G.4

🎯 I can find the surface area of a pyramid by adding the base area and the lateral faces.

📦 TIME CAPSULE

Student Workspace

📊 FILL THE TABLE

👨‍🎓 Students: Complete the missing cells. Check with a partner before we discuss.

⏱️ Time: 5 min

Calculate the surface area of each pyramid display. SA = Base Area + Lateral Area. For each triangular face, use A = ½ × base × slant height.

Pyramid	Base Shape & Area	Number of Lateral Faces
Display A	Square: 6×6 = 36 in²	4
Display B	Square: 10×10 = 100 in²	4
Display C	Square: 8×8 = 64 in²	4
Display D	Triangle: ½×6×5.2 = 15.6 in²	3

✏️ Sketch Your Strategy

Reveal Math Grade 6 Differentiation 6.G.4

📦 TIME CAPSULE

Differentiation Paths

🎯 CHOOSE YOUR LEVEL

👩‍🏫 Say: Everyone works on the same math goal — pick the level of support that fits today.

⏱️ Time: 8–10 min independent or partner

🧩 Level 0 · Most support

Step-by-step with a worked model and sentence frames.

🌱 Level 1 · Support

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

🎯 Level 2 · Core

Core practice aligned to the standard.

🚀 Level 2+ · Enrichment

Extension with error analysis or multi-step reasoning.

Reveal Math Grade 6 Partner Activity 6.G.4

🎯 I can find the surface area of a pyramid by adding the base area and the lateral faces.

📦 TIME CAPSULE

Partner Activity

🤝 PARTNER WORK

📦 Materials: Whiteboards or paper, pencils, vocabulary reference cards

👨‍🎓 Students: Partner A solves, Partner B coaches. Switch roles on the next problem.

⏱️ Time: 6 min

Work with your partner on the practice problems at your differentiation path level. Explain each step using math vocabulary.

Reveal Math Grade 6 CFU 4 6.G.4

📦 TIME CAPSULE

Check for Understanding #4

✋ CFU · THUMBS

❓ Ask: Thumbs up if you and your partner agree on your answer.

⏱️ Time: 30 sec

Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.

Reveal Math Grade 6 Math in the Wild 6.G.4

🎯 I can find the surface area of a pyramid by adding the base area and the lateral faces.

📦 TIME CAPSULE

Real-World Connection

🌍 Math in the Wild

👩‍🏫 Say: Read the scenario. Ask: where else have you seen this kind of math?

A museum is building a square pyramid display case. The base edge is 3 feet and the slant height is 4 feet. The glass costs $12 per square foot.

34624288lateralsurface areaslant height

✍️ Connection Reasoning

How much will the glass for all 4 triangular sides cost? (The base is open — no glass needed.)

Each triangular face has area = ½ × ___ × ___ = ___ ft². Four faces: 4 × ___ = ___ ft². Cost: ___ × $12 = $___.

Reveal Math Grade 6 Discuss Connect 6.G.4

🎯 I can find the surface area of a pyramid by adding the base area and the lateral faces.

📦 TIME CAPSULE

Turn & Talk — Connect

🗣️ TURN & TALK

👩‍🏫 Say: Partner A shares first for 45 seconds, then Partner B.

👨‍🎓 Students: Turn to your elbow partner. Use the sentence stems.

⏱️ Time: 90 sec

A museum builds a square pyramid display case with base edge 3 ft and slant height 4 ft, and the base is open (no glass). Talk through how to find how much glass the 4 triangular sides need.

Sentence starters (tap to use):

✍️ Each triangular face has area ½ × ___ × ___ = ___ ft².Cada cara triangular tiene área ½ × ___ × ___ = ___ ft².

✍️ Four faces need ___ ft² of glass, and the base needs ___ because it is open.Cuatro caras necesitan ___ ft² de vidrio, y la base necesita ___ porque está abierta.

Stretch further:

➕ Leaving the base open means I use only the ___ area because ___.

➕ If the base needed glass, I would add ___ to the total.

WORD BANK:

pyramidbaselateral faceslant heightsurface area

90s

👂 Listen For

Students compute one face = ½ × 3 × 4 = 6 ft², four faces = 24 ft², and explain the open base is not counted, so only the lateral area matters.

Extend: How does leaving the base open change which formula you use, and how would the answer change if the base needed glass too?

✅

Lesson Phase

CLOSURE & REFLECT

⏱ ~8 min

Reveal Math Grade 6 Exit Ticket 6.G.4

Reflection

Today I learned that ___ because ___.

One thing I am still not sure about is ___.

Quick Exit Ticket

A square pyramid has a base edge of 6 in and a slant height of 5 in. What is the total surface area?

Reveal Math Grade 6 Goal Tracker 6.G.4

Reveal Math Grade 6 Bonus Check 6.G.4

🎯 I can find the surface area of a pyramid by adding the base area and the lateral faces.

📦 TIME CAPSULE

Bonus Exit Check

📝 QUICK CHECK

❓ Ask: Optional for early finishers.

⏱️ Time: 2 min

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

✍️ Show Your Work

Explain why your answer is correct using today's vocabulary.

Teacher reveal: A square pyramid has a square base and 4 triangular lateral faces — one for each side of the square.

Reveal Math Grade 6 Reflection 6.G.4

📦 TIME CAPSULE

Reflection & Self-Assessment

3 Things I learned:

2 Connections:

1 Question:

Self-Assessment:

Reveal Math Grade 6 Digital Activity 6.G.4

📦 TIME CAPSULE

Continue Learning

🎮

Launch the Full Interactive Activity

Students continue practice in the HTML lesson engine with auto-check, hints, and differentiation.

Open Lesson Activity ↗ Family Homework ↗

👩‍🏫 Say: Early finishers: open the activity. Everyone else: start homework tonight.

Reveal Math Grade 6 Family Connection 6.G.4

📦 TIME CAPSULE

Family Connection

Share tonight's family homework and discuss one vocabulary word at home.

Open Family Homework ↗

👩‍🏫 Say: Tell families: "Ask your student to teach you one thing from today's lesson."

Reveal Math Grade 6 Teacher Notes 6.G.4

📦 TIME CAPSULE

Teacher Notes

⏱️ Pacing Guide

Launch & vocab: 12 min
I Do / We Do / You Do: 15 min
Explore & practice: 15 min
Connect & closure: 8 min

Total: ~45 min

🎯 Listen For · Common Errors

• Students explain a square pyramid's surface area = base area + the four triangular lateral faces, and that you add every face together.

• Students compute base = 36 in², one face = 24 in², four faces = 96 in², total SA = 132 in², distinguishing base from lateral faces.

• Students compute one face = ½ × 3 × 4 = 6 ft², four faces = 24 ft², and explain the open base is not counted, so only the lateral area matters.

• Students identify the missing base area and state that total surface area = base area + all lateral (triangular) faces.

Common mistake: A common mistake in Surface Area of Pyramids is skipping the key idea: "Surface area of a pyramid = base area + the area of all the triangular lateral faces." — always check your work against this rule before you submit.

Reveal Math Grade 6 Answer Key 6.G.4

📦 TIME CAPSULE

Answer Key (Teacher Appendix)

Hide this slide during presentation or move to the end of your copy.

✓ Practice 1: 133 cm² — SA = Base Area + Lateral Area = 49 + 84 = 133 cm².

✓ Practice 2: 95 in² — Base: 5 × 5 = 25 in². Each lateral face: ½ × 5 × 7 = 17.5 in². Four faces: 4 × 17.5 = 70 in². SA = 25 + 70 = 95 in².

✓ Practice 3: 4 — A square pyramid has a square base and 4 triangular lateral faces — one for each side of the square.

✓ Practice 4: 24 in² — Area of a triangle = ½ × base × height = ½ × 8 × 6 = 24 in².

✓ Exit ticket: 96 in² — Base: 6 × 6 = 36 in². Each lateral face: ½ × 6 × 5 = 15 in². Four faces: 4 × 15 = 60 in². SA = 36 + 60 = 96 in². Surface area uses square units (in²).