Neft Teacher Unit 5

📐

Area of Triangles

6.G.1 Lesson 5-3-flagship

My Math Notebook

Name:

Date:

Period:

I Can…

I can find the area of a triangle using the formula A = ½ × base × height.

Reveal Math Grade 6 How to Use 6.G.1

📐 ARCHITECTURE FIRM

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.1

🎯 Content Objective / Objetivo de contenido

I can find the area of a triangle using the formula A = ½ × base × height.

Reveal Math Grade 6 Agenda 6.G.1

📐 ARCHITECTURE FIRM

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: ~50 min · Progress bar at top tracks your place

📐

Lesson Phase

LAUNCH

⏱ ~10 min

Reveal Math Grade 6 Warm-Up Hook 6.G.1

⏱️ 3 MIN · THINK-PAIR-SHARE

At the build site you survey a triangular garden bed with a base of 12 feet and a height of 8 feet. Which measurement is the height, and how is it different from the slanted side?

baseheightperpendicularareaformula

Reveal Math Grade 6 CFU 1 6.G.1

📐 ARCHITECTURE FIRM

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.1

Visual Prompt

Blueprint Review

Your architecture firm is designing a park with triangular garden beds. The client wants to know exactly how much soil to order, which means calculating the area of each triangular section. The first garden has a base of 12 feet and a height of 8 feet.

👁 I Notice...

🔹 What shape are the garden beds?

🔹 What measurements do we need to find the area?

🔹 How is the area of a triangle related to the area of a rectangle?

💭 I Wonder...

🔹 Why do we divide by 2 when finding the area of a triangle?

🔹 Does it matter which side we call the base?

Reveal Math Grade 6 Concept Launch 6.G.1

🎯 I can find the area of a triangle using the formula A = ½ × base × height.

📐 ARCHITECTURE FIRM

Concept Launch

💡 How do we find the area of a triangle?

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

A triangle has three sides. The base is one side, and the height is the straight-up (perpendicular) distance from the base to the top corner.

Key Idea:

Area of a triangle = ½ × base × height. A triangle is exactly half of a rectangle with the same base and height.

Reveal Math Grade 6 I Do — Watch Me 6.G.1

Reveal Math Grade 6 I Do — Key Step 6.G.1

Reveal Math Grade 6 We Do — Together 6.G.1

Reveal Math Grade 6 CFU 2 6.G.1

📐 ARCHITECTURE FIRM

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.1

🎯 I can find the area of a triangle using the formula A = ½ × base × height.

📐 ARCHITECTURE FIRM

Now it's your turn

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

⏱️ Time: 5 min

1Next you will plot the triangle on a grid and see how it fits inside a rectangle.

2Remember: multiply base × height, then take half.

🎮

Open the interactive HTML activity for full practice.

Launch Activity ↗

📚

Lesson Phase

VOCABULARY

⏱ ~8 min

Reveal Math Grade 6 Vocabulary 6.G.1

Term / Término	Meaning / Significado	Visual
Base Base	A side of the triangle you use to find the area. Un lado del triángulo que usas para hallar el área.	If the bottom of a triangle is 10 cm, then b = 10 cm in the formula A = ½ × b × h
Height Altura	The straight-up distance from the base to the top corner. La distancia recta desde la base hasta la esquina de arriba.	A dashed vertical line from the top point straight down to the base at a 90° angle
Area Área	How much space is inside a flat shape. Cuánto espacio hay dentro de una figura plana.	A triangle with b = 8 and h = 6 has area = ½ × 8 × 6 = 24 sq units
Perpendicular Perpendicular	Two lines that meet to make a square corner (90 degrees). Dos líneas que se unen formando una esquina recta (90 grados).	The corner of a book or a door frame meets at exactly 90°
Composite figure Figura compuesta	A shape made by putting two or more simple shapes together. Una figura formada al juntar dos o más figuras simples.	A house shape = a rectangle (walls) + a triangle (roof)
Formula Fórmula	A math rule written with symbols. Una regla matemática escrita con símbolos.	A = ½ × b × h means Area equals one-half times base times height

Perpendicular: example vs. non-example

✓ Two lines meeting at a 90° anglePerpendicular lines form a right angle.

✗ Two lines that never meetThose are parallel lines, not perpendicular.

Reveal Math Grade 6 Which Word? 6.G.1

🎯 I can find the area of a triangle using the formula A = ½ × base × height.

📐 ARCHITECTURE FIRM

Which Word Fits?

❓ CLOZE POLL

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

The side of a triangle used as the bottom for measuring area is the ___.

Use It In a Sentence

Reveal Math Grade 6 CFU 3 6.G.1

📐 ARCHITECTURE FIRM

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.1

🎯 I can find the area of a triangle using the formula A = ½ × base × height.

📐 ARCHITECTURE FIRM

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

At the build site you survey a triangular garden bed with a base of 12 feet and a height of 8 feet. Which measurement is the height, and how is it different from the slanted side?

Sentence starters (tap to use):

✍️ The height is the ___ distance from the base to the top corner.La altura es la distancia ___ desde la base hasta la esquina de arriba.

✍️ It is different from the slanted side because ___.Es diferente del lado inclinado porque ___.

Stretch further:

➕ It ___ matter which side is the base because ___.

➕ No matter which base I choose, the area is the same since ___.

WORD BANK:

baseheightperpendicularareaformula

90s

👂 Listen For

Students identify the height as the perpendicular (straight-up, 90-degree) distance from the base to the opposite vertex, not the slanted side.

Extend: Does it matter which side of the triangular panel you call the base? Justify your thinking using the formula A = 1/2 x b x h.

🔍

Lesson Phase

EXPLORE & PRACTICE

⏱ ~18 min

Reveal Math Grade 6 Visual Model 6.G.1

🎯 I can find the area of a triangle using the formula A = ½ × base × height.

📐 ARCHITECTURE FIRM

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.1

📐 ARCHITECTURE FIRM

Explore Activity

Plot the vertices of a triangle with base 12 and height 8.

halfbaseheight4896rectangle1/2

✍️ Explore Discourse

The triangle fits inside a 12 × 8 rectangle. How does the triangle's area compare to the rectangle's area?

The area of the triangle is ___ the rectangle because A = 1/2 × ___ × ___ = ___ square feet.

Reveal Math Grade 6 Whiteboard CFU 6.G.1

🎯 I can find the area of a triangle using the formula A = ½ × base × height.

📐 ARCHITECTURE FIRM

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.1

🎯 I can find the area of a triangle using the formula A = ½ × base × height.

📐 ARCHITECTURE FIRM

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

Your triangular panel (base 12, height 8) fits inside a 12 by 8 rectangle. Why do we divide by 2 to find the triangle's area before cutting the glass?

Sentence starters (tap to use):

✍️ A triangle is half of a ___ with the same base and height.Un triángulo es la mitad de un ___ con la misma base y altura.

✍️ So the area is 1/2 times 12 times 8, which equals ___.Entonces el área es 1/2 por 12 por 8, que es ___.

✍️ The rectangle's area is ___, so the triangle is ___.El área del rectángulo es ___, entonces el triángulo es ___.

Stretch further:

➕ They ___ have the same base and height because ___.

➕ A counterexample is a triangle with base ___ and height ___, which also gives ___.

WORD BANK:

baseheightareaperpendicularformula

90s

👂 Listen For

A strong answer states the triangle is half of the 12 x 8 = 96 rectangle, so the panel area is 48 sq ft, and connects the 1/2 to that halving.

Extend: Two glass panels both have area 48 sq ft. Must they have the same base and height? Justify or give a counterexample.

Reveal Math Grade 6 Practice A 6.G.1

🎯 I can find the area of a triangle using the formula A = ½ × base × height.

📐 ARCHITECTURE FIRM

Practice Check A

📝 QUICK CHECK

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

⏱️ Time: 2 min

A triangular sail has an area of 30 sq m and a height of 12 m. What is its base?

✍️ Show Your Work

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

Teacher reveal: 30 = ½ × b × 12 → 30 = 6b → b = 5 m.

Reveal Math Grade 6 Practice B 6.G.1

🎯 I can find the area of a triangle using the formula A = ½ × base × height.

📐 ARCHITECTURE FIRM

Practice Check B

📝 QUICK CHECK

❓ Ask: Partner discussion first, then vote.

⏱️ Time: 2 min

What is the area of a triangle with base 10 cm and height 6 cm?

✍️ Show Your Work

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

Teacher reveal: A = ½ × b × h = ½ × 10 × 6 = 30 square centimeters.

Reveal Math Grade 6 Area Grid Shading 6.G.1

🎯 I can find the area of a triangle using the formula A = ½ × base × height.

📐 ARCHITECTURE FIRM

Area Grid Shading

📐 GRID SHADE

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

⏱️ Time: 5 min

✍️ Justify Your Thinking

Reveal Math Grade 6 Sort It Out 6.G.1

On your blueprint, sort each segment of the triangular sign into the correct column: the perpendicular height you use in the formula, or a side you do NOT use as the height.

Card Bank — cut or drag these cards:

⠿A dashed line from the top corner straight down to the base at a 90° angle

⠿The perpendicular distance from the base up to the opposite vertex

⠿A slanted side that leans from the base up to the top corner

⠿The longest slanted edge of the triangle

⠿The base sitting flat along the bottom

Perpendicular height (use this)

Not the height

Reveal Math Grade 6 Error Analysis 6.G.1

⚠ Find Dana's Mistake

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 Problem Find the area of a triangle with base 10 ft and height 7 ft.

2 Write the formula A = ½ × b × h

3 Substitute A = ½ × 10 × 7

4 Multiply A = 10 × 7 = 70

5 Final answer A = 70 sq ft

Which step has the error?

Reveal Math Grade 6 Choice Board 6.G.1

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.1

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

Frame 1 Explain the Rule

Today's key idea is: "Area of a triangle = ½ × base × height. A triangle is exactly half of a rectangle with the same base and height." — and it works because ___.

Frame 2 Because / But / So

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

Frame 3 Catch the Mistake

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

Frame 4 Prove It

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

Reveal Math Grade 6 Because · But · So 6.G.1

✍️ TWR · WRITE 3 SENTENCES · 7 MIN

Sentence kernelArea of a triangle = ½ × base × height. A triangle is exactly half of a rectangle with the same base and height.

because

Give a reason

Area of a triangle = ½ × base × height. A triangle is exactly half of a rectangle with the same base and height. because ___

but

Name a tricky part

Area of a triangle = ½ × base × height. A triangle is exactly half of a rectangle with the same base and height. but ___

so

State what it means

Area of a triangle = ½ × base × height. A triangle is exactly half of a rectangle with the same base and height. so ___

Reveal Math Grade 6 Sentence Expansion 6.G.1

🌱 TWR · GROW THE KERNEL · 6 MIN

Sentence kernelToday we used Base.

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.1

🎯 I can find the area of a triangle using the formula A = ½ × base × height.

📐 ARCHITECTURE FIRM

Student Workspace

📊 FILL THE TABLE

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

⏱️ Time: 5 min

Plot the vertices of a triangle with base 12 and height 8.

Column A	Column B

✏️ Sketch Your Strategy

Reveal Math Grade 6 Differentiation 6.G.1

📐 ARCHITECTURE FIRM

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

What is the area of a triangle with base 10 cm and height 6 cm?

🎯 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.1

🎯 I can find the area of a triangle using the formula A = ½ × base × height.

📐 ARCHITECTURE FIRM

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.1

📐 ARCHITECTURE FIRM

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.1

🎯 I can find the area of a triangle using the formula A = ½ × base × height.

📐 ARCHITECTURE FIRM

Real-World Connection

🌍 Math in the Wild

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

A homeowner wants to paint one triangular wall of an A-frame cabin. The wall has a base of 20 feet and a height of 14 feet. One can of paint covers 50 square feet.

140area1/220143canstriangle

✍️ Connection Reasoning

How many cans of paint does the homeowner need?

The wall's area is ___ sq ft because A = 1/2 × ___ × ___. She needs ___ cans because ___ ÷ 50 = ___.

Reveal Math Grade 6 Discuss Connect 6.G.1

🎯 I can find the area of a triangle using the formula A = ½ × base × height.

📐 ARCHITECTURE FIRM

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

At the client review, the homeowner paints a triangular A-frame wall with base 20 ft and height 14 ft; one can covers 50 sq ft. Talk through how many cans the budget needs.

Sentence starters (tap to use):

✍️ The wall's area is 1/2 times 20 times 14, which equals ___ square feet.El área de la pared es 1/2 por 20 por 14, que es ___ pies cuadrados.

✍️ She needs ___ cans because ___ divided by 50 equals ___.Necesita ___ latas porque ___ entre 50 es ___.

Stretch further:

➕ She must round up to ___ cans because ___.

➕ The leftover paint covers about ___ sq ft, since ___.

WORD BANK:

trianglebaseheightareaformula

90s

👂 Listen For

Students compute area = 140 sq ft, then 140 / 50 = 2.8, and reason she must round up to 3 cans to cover the whole wall.

Extend: Why can't the budget order exactly 2.8 cans? Explain what rounding up means in this real situation and how it changes the leftover paint.

✅

Lesson Phase

CLOSURE & REFLECT

⏱ ~8 min

Reveal Math Grade 6 Exit Ticket 6.G.1

Reflection

Today I learned that ___ because ___.

One thing I am still not sure about is ___.

Quick Exit Ticket

A triangle has a base of 11 inches and a height of 8 inches. What is its area?

Reveal Math Grade 6 Goal Tracker 6.G.1

Reveal Math Grade 6 Bonus Check 6.G.1

🎯 I can find the area of a triangle using the formula A = ½ × base × height.

📐 ARCHITECTURE FIRM

Bonus Exit Check

📝 QUICK CHECK

❓ Ask: Optional for early finishers.

⏱️ Time: 2 min

A triangle has an area of 24 sq ft and a base of 8 ft. What is the height?

✍️ Show Your Work

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

Teacher reveal: 24 = ½ × 8 × h → 24 = 4h → h = 6 ft.

Reveal Math Grade 6 Reflection 6.G.1

📐 ARCHITECTURE FIRM

Reflection & Self-Assessment

3 Things I learned:

2 Connections:

1 Question:

Self-Assessment:

Reveal Math Grade 6 Digital Activity 6.G.1

📐 ARCHITECTURE FIRM

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.1

📐 ARCHITECTURE FIRM

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.1

📐 ARCHITECTURE FIRM

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: ~50 min

🎯 Listen For · Common Errors

• Students identify the height as the perpendicular (straight-up, 90-degree) distance from the base to the opposite vertex, not the slanted side.

• A strong answer states the triangle is half of the 12 x 8 = 96 rectangle, so the panel area is 48 sq ft, and connects the 1/2 to that halving.

• Students compute area = 140 sq ft, then 140 / 50 = 2.8, and reason she must round up to 3 cans to cover the whole wall.

• Listen for students naming a specific strategy tied to 6.G.1 — not just "I multiplied." They should connect steps to the key idea.

Common mistake: A common mistake in Area of Triangles is skipping the key idea: "Area of a triangle = ½ × base × height. A triangle is exactly half of a rectangle with the same base and height." — always check your work against this rule before you submit.

Reveal Math Grade 6 Answer Key 6.G.1

📐 ARCHITECTURE FIRM

Answer Key (Teacher Appendix)

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

✓ Practice 1: 5 m — 30 = ½ × b × 12 → 30 = 6b → b = 5 m.

✓ Practice 2: 30 sq cm — A = ½ × b × h = ½ × 10 × 6 = 30 square centimeters.

✓ Practice 3: 6 ft — 24 = ½ × 8 × h → 24 = 4h → h = 6 ft.

✓ Practice 4: 42 sq ft — A = ½ × 14 × 6 = ½ × 84 = 42 sq ft.

✓ Exit ticket: 44 sq in — A = 1/2 × 11 × 8 = 1/2 × 88 = 44 square inches.