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Area Adventures • Sequence • Lenny.com

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Area Adventures

A foundational two-lesson 3rd-grade math sequence introducing area through unit square tiling and multiplication of side lengths, structured with explicit whiteboard scripts and guided notes for substitute teachers.

SMSamantha McBath

Tiled Area Foundations

Substitute-ready lesson introducing area through tiling and counting unit squares without gaps or overlaps, featuring explicit whiteboard drawing scripts and scaffolded student notes.

Multiplying Side Lengths

Substitute-ready lesson connecting square tiling arrays to side lengths and the rectangle area formula (length × width) through explicit whiteboard modeling and real-world application.

Area Adventures

A foundational two-lesson 3rd-grade math sequence introducing area through unit square tiling and multiplication of side lengths, structured with explicit whiteboard scripts and guided notes for substitute teachers.

SMSamantha McBath

Tiled Area Sub Guide

Substitute Teacher Guide • No-Tech Whiteboard Plan

Lesson 1: Finding Area of Tiled Shapes

Duration & Grade 60 Minutes • Grade 3 Math

Sub Note (First Time Learning Area): Connect today's lesson directly to the multiplication arrays students mastered in the last unit! A tiled rectangle is simply an array made of solid square tiles with no gaps and no overlaps. Everything is taught directly on the whiteboard!

1. Hook & Vocab

10 Mins (00-10)

2. I Do (Whiteboard)

15 Mins (10-25)

3. We Do (Guided)

15 Mins (25-40)

4. You Do & Exit

20 Mins (40-60)

1

Warm-Up & Hook: From Dot Arrays to Area! (10 Min)

Say to Class: "Pencils down for 2 minutes and look at the board. In our last unit, we mastered arrays for multiplication! Look at the left side of the board: I drew 3 rows of 4 dots. How many dots total? Call it out!" (Students: "12! 3 × 4 = 12!")

Draw & Bridge to Area: "Exactly! Now look at what I draw right next to it: instead of separate round dots, what if each spot is a square tile touching edge-to-edge? It makes 3 rows of 4 square tiles! Just like an array, but with no gaps and no overlaps. That covers the entire inside of a flat shape! Measuring how many square tiles cover a shape is called AREA!"

Direct Vocab Fill-In: Have students open their handout to Key Vocabulary. Write these 2 definitions on the board for students to copy:

Area: The amount of flat space a shape covers, measured in square units.
Unit Square: A square with side lengths of 1 unit.

Draw on Board (Left)

Last Unit: Dot Array

● ● ● ●
● ● ● ●
● ● ● ●

3 rows of 4 = 12 dots

Today: Tile Array (Area)

Area = 12 square units

Takes ~45 seconds to sketch!

2

Explicit Modeling: I Do (15 Min)

Problem 1: Tiled Rectangle (3 rows of 5) Matches Student Note Problem 1

Say: "Watch how I find the area. I could count one by one: 1, 2, 3... up to 15. But mathematicians find smarter ways. Let's look at the rows like an array!"

Action: Point to each row across. "Row 1 has 5 squares. Row 2 has 5 squares. Row 3 has 5 squares. That is 3 groups of 5! 5 + 5 + 5 = 15. Or 3 × 5 = 15."

Rule to Chant with Class: "We never just write 15! We write 15 SQUARE UNITS because each tile is a square unit!"

Board Layout #1:

[ 3 rows of 5 tiles ]
5 + 5 + 5 = 15
3 × 5 = 15

Area = 15 square units

Problem 2: Non-Rectangular Shape (L-Shape: Top 3, Bottom 2x5 = 10) Matches Student Note Problem 2

Say: "What if the shape is NOT a normal rectangle? Don't panic! We break it into sections. Look at the top step: 3 tiles. Look at the bottom block: 2 rows of 5 = 10 tiles. Total: 3 + 10 = 13 square units!"

Board Layout #2:

Top: 3 tiles
Bottom: 10 tiles
Total: 3 + 10 = 13

Area = 13 square units

Area Adventures • Lesson 1 Sub Guide Page 1 of 2 (Turn for We Do & You Do Plans)

Lesson 1: We Do, You Do & Class Closure

Teacher Script Continued

3

Guided Practice: We Do (15 Min)

We Do 1: 2 × 4 Rectangle

Sub Prompt: "Look at Problem 1 in your 'We Do' column. Put your finger on the top row. How many squares in that row? (Class: 4!) How many rows? (Class: 2!)"

Call-and-Response: Write on board: 2 rows of 4 = 8. Prompt students: "What unit must we write?" Have all students whisper to their hand: "square units!"

We Do 2: L-Shape Comparison

Sub Prompt: "Look at We Do 2. How many squares in the tall column? (Class: 3!) How many squares on the right? (Class: 2!) Total? (5 square units)."

Key Teaching Point: Ask: "Does a shape have to be a rectangle to have an area?" (Class: NO! Any flat shape covered by squares has area!)

3-Minute All-Class Check (Slates or Fingers Up):

Draw a quick 4 × 4 grid on the board. Say: "Show me on your whiteboards (or fingers): What is the area? Don't forget the label!" Look for: 16 square units. If anyone writes just 16, tap your chin and say: "16 what? Elephants? Pencils? Square units!"

4

Independent Practice & Exit Ticket (20 Min)

Step 1: Partner Work (8 Min): Have students complete Problems 4–7 on page 2 of their handout with their desk partner. Circulate the room and look for neat counting checkmarks.

Step 2: Silent Independent Work (7 Min): Students complete Problems 8–10 independently.

Step 3: Exit Ticket (5 Min): Direct students to the bottom Exit Ticket box. Absolute silence for 5 minutes. Collect the papers before lining up!

Common Sub Pitfalls:

Mistake 1: Forgetting "square units" and writing only the number. Praise students who write the unit!

Mistake 2: Counting the boundary lines instead of the square tiles. Remind them: "We count the square tiles covering the shape, not the edges!"

Wrap-Up / Teacher Script (Last 2 Minutes):

"Class, today you conquered area! You learned that area measures how much flat space a shape covers using unit squares. Tomorrow, you're going to learn an incredible math secret—a shortcut that lets you find the area without counting each square one-by-one!"

Sub Quick Checklist:

✔ Supplies: Dry erase markers for board, pencils for students.

✔ Accommodations: Pair struggling readers with strong peers for word problems.

✔ Early Finishers: Have them draw a shape with an area of exactly 18 square units.

✔ Turn In: Collect all student packets for regular teacher review.

Area Adventures • Lesson 1 Sub Guide Page 2 of 2

Tiled Area Student Notes

3rd Grade Math • Unit 3: Lesson 1

Finding Area of Tiled Shapes

Name:

Date:

🎯 Learning Target: I can find the area of shapes by counting unit squares with no gaps and no overlaps.

Speedy Fact Fluency: 2 Minutes!

1. 6 × 4 = ____

2. 7 × 3 = ____

3. 9 × 2 = ____

4. 6 × 8 = ____

5. 7 × 6 = ____

6. 9 × 5 = ____

7. 6 × 2 = ____

8. 7 × 9 = ____

9. 6 × 5 = ____

10. 7 × 4 = ____

✎

Key Vocabulary (Fill In With Teacher)

1. Area

The amount of flat space a shape covers, measured in square units.

2. Unit Square

A square that is exactly 1 unit long on every side.

3. The Tiling Rule

Tiles must cover the shape completely with NO gaps and NO overlaps!

I DO

Watch Teacher Model on the Whiteboard

Follow along and copy notes neatly

Problem 1: Find the area of this tiled rectangle.

• Count by ones: Total squares = _______

• Count by rows: _____ rows of _____ = _____

• Multiplication: _____ × _____ = _____

Area = ___________ square units

Problem 2: Non-rectangular shape (Count by sections!)

• Top section: _______ unit squares

• Bottom section: _______ unit squares

• Add sections: _______ + _______ = _______

Area = ___________ square units

Problem 3: Can two different shapes have the same area?

• Shape A (3 rows of 4) = _____ sq units | Shape B (6 rows of 2) = _____ sq units

Do they have the same area? [ YES / NO ] Because: both cover 12 unit squares!

Turn page for We Do and Independent Practice Page 1 of 2

Lesson 1: Practice & Exit Ticket

Unit 3: Tiled Area

WE DO

Let's Try Together as a Class

1. Find the area of this rectangle:

Rows: ______

Each row: ______

Area = ______ square units

2. Find the area of this step figure:

Tall part: ______

Side part: ______

Area = ______ square units

YOU DO

Independent Practice (Show All Work)

3. Find the area:

Count rows or count by ones.

Tiled Area Answer Key

Teacher & Substitute Reference

Lesson 1: Answer Key & Rubric

Unit 3: Tiled Area

Grade 3 Math Solutions

Fluency Sprint Solutions:

1. 6 × 4 = 24

2. 7 × 3 = 21

3. 9 × 2 = 18

4. 6 × 8 = 48

5. 7 × 6 = 42

6. 9 × 5 = 45

7. 6 × 2 = 12

8. 7 × 9 = 63

9. 6 × 5 = 30

10. 7 × 4 = 28

Vocabulary Fill-Ins:

Area: The amount of flat space a shape covers, measured in square units.
Unit Square: A square that is exactly 1 unit long on every side.
Tiling Rule: Tiles must cover the shape completely with no gaps and no overlaps.

I DO Problems (Page 1)

Prob 1: Count by ones: 15 | Rows: 3 rows of 5 = 15 | Equation: 3 × 5 = 15 | Area = 15 square units

Prob 2 (L-Shape): Top: 3 sq units | Bottom: 10 sq units | Total: 3 + 10 = 13 square units

Prob 3: Shape A = 12 sq units | Shape B = 12 sq units | Same area? YES (Both cover 12 square units despite different side lengths).

WE DO Problems (Page 2)

1. Rectangle (2×4): 2 rows of 4 = 8. Area = 8 square units.

2. Step Figure: Tall part = 2 sq units, side part = 2 sq units. Total: Area = 4 square units.

YOU DO Practice (Page 2)

3. Square (3×3): 3 rows of 3 = 9. Area = 9 square units.

4. Rectangle (2×5): 2 rows of 5 = 10. Area = 10 square units.

5. Cross / Plus Shape: Center column 3 + left 1 + right 1 = 5. Area = 5 square units.

4 rows of 5 = 4 × 5 = .

Multiply Area Sub Guide

Substitute Teacher Guide • No-Tech Whiteboard Plan

Lesson 2: Area by Multiplying Side Lengths

Duration & Grade 60 Minutes • Grade 3 Math

Sub Objective: Today students make the big leap from counting squares to the Area Formula: \(\text{Area} = \text{length} \times \text{width}\). Connect this to their knowledge of arrays! Model each problem step-by-step on the whiteboard.

1. Hook & Shortcut

10 Mins (00-10)

2. I Do (Whiteboard)

15 Mins (10-25)

3. We Do (Guided)

15 Mins (25-40)

4. You Do & Exit

20 Mins (40-60)

1

Warm-Up & Hook: The Tile Race (10 Min)

Say to Class: "Ms. Chen wants to tile her bathroom floor. It is 8 feet long and 6 feet wide. Look at the board: Student A is counting 48 tiny tiles one-by-one. Student B just smiled and wrote: \(8 \times 6 = 48\)! Who will finish first?"

Turn & Talk (30 seconds): "Tell your partner: Did they get the same answer? Why?"

Whiteboard Anchor to Write: Write in big letters at the top center of the board:

★ The Area Formula: \(\text{Area} = \text{length} \times \text{width}\) (or \(A = l \times w\)) ★

Explain: Length is the longer side; Width is the shorter side. Multiplying gives the exact same total as counting!

Draw on Board (Left)

Bathroom Floor: 8 ft × 6 ft

Student A: 1, 2, 3... 48 (Slow!)
Student B: 8 × 6 = 48 sq ft!

Chant together: "Length times Width!"

2

Explicit Modeling: I Do (15 Min)

Problem 1: Proving Both Methods on a 4 × 3 Rectangle Matches Student Note Problem 1

Say: "Watch me prove that counting and multiplying always give the same answer. First, let's count: 12 unit squares. Now, let's use our new formula: Length is 4. Width is 3. 4 × 3 = 12! Both give 12 square units!"

Explain the Connection: "Why does it work? A rectangle is an array! 3 rows with 4 in each row is 3 groups of 4: \(3 \times 4 = 12\)!"

Board Layout #1:

Method 1: Count = 12 sq units
Method 2: Formula
A = length × width
A = 4 × 3 = 12

Area = 12 square units

Problem 2: Rectangle With No Grid (7 ft × 5 ft Garden) Matches Student Note Problem 2

Say: "Notice this rectangle has NO grid lines inside. Do we need to draw 35 little squares? NO! We have the formula: Step 1: Write \(A = l \times w\). Step 2: Plug in numbers: \(A = 7 \times 5\). Step 3: Multiply: 35! Step 4: Write unit: 35 square feet!"

Multiply Area Student Notes

3rd Grade Math • Unit 3: Lesson 2

Finding Area by Multiplying

Name:

Date:

🎯 Learning Target: I can find the area of a rectangle by multiplying the side lengths: \(\text{Area} = \text{length} \times \text{width}\).

Speedy Fact Fluency: 2 Minutes!

1. 8 × 4 = ____

2. 8 × 7 = ____

3. 8 × 2 = ____

4. 8 × 9 = ____

5. 8 × 5 = ____

6. 8 × 3 = ____

7. 8 × 8 = ____

8. 8 × 6 = ____

9. 8 × 1 = ____

10. 8 × 10 = ____

★ The Rectangle Area Formula ★

Area = length × width (\(A = l \times w\))

• Length: The longer side of the rectangle.

• Width: The shorter side of the rectangle.

• Units: Always label square units (sq ft, sq in, sq m, sq cm)!

I DO

Watch Teacher Model on the Whiteboard

Follow along and copy notes neatly

Problem 1: Show that BOTH methods give the same answer!

Method 1: Count Squares

Counted tiles = _______

Area = _______ sq units

Method 2: Use Formula

\(\text{Area} = \text{length} \times \text{width}\)

\(\text{Area} = \) ____ × ____ = ____

Area = _______ sq units

Why it works: 3 rows with 4 tiles in each row is 3 groups of 4: \(3 \times 4 = 12\)!

4 units

3 units

Problem 2: Rectangular garden (7 ft long by 5 ft wide)

Length = _______ feet | Width = _______ feet

\(\text{Area} = \text{length} \times \text{width}\)

\(\text{Area} = \) _______ × _______ = _______

Area = ___________ square feet

7 feet

5 feet

Garden

Problem 3: Working Backwards (Area = 24 square units)

What multiplication pairs equal 24? ____ × ____ = 24 or ____ × ____ = 24

Turn page for We Do and Independent Practice Page 1 of 2

Lesson 2: Practice & Exit Ticket

Unit 3: Multiplying Side Lengths

WE DO

Let's Try Together as a Class

1. Notebook: 11 inches long, 8 inches wide

Write formula, plug in numbers, solve:

Area = length × width

Area = ______ × ______

Area = ______ square inches

Multiply Area Answer Key

Teacher & Substitute Reference

Lesson 2: Answer Key & Rubric

Unit 3: Multiplying Area

Grade 3 Math Solutions

Fluency Sprint Solutions (8s Facts):

1. 8 × 4 = 32

2. 8 × 7 = 56

3. 8 × 2 = 16

4. 8 × 9 = 72

5. 8 × 5 = 40

6. 8 × 3 = 24

7. 8 × 8 = 64

8. 8 × 6 = 48

9. 8 × 1 = 8

10. 8 × 10 = 80

The Core Mathematical Rule:

Area = length × width (or Area = width × length due to commutative property)

Units must always be squared: square inches (sq in), square feet (sq ft), square meters (sq m), or square units.

I DO Problems (Page 1)

Prob 1 (4×3): Counted tiles = 12 | Formula = 4 × 3 = 12 | Area = 12 square units.

Prob 2 (7×5 Garden): Length = 7 ft, Width = 5 ft | \(7 \times 5 = 35\) | Area = 35 square feet.

Prob 3 (Area = 24): Accept any factor pairs: 4 × 6 = 24, 3 × 8 = 24, 2 × 12 = 24, or 1 × 24 = 24.

WE DO Problems (Page 2)

1. Notebook (11 in × 8 in): \(\text{Area} = 11 \times 8 = 88\). Area = 88 square inches.

2. Classroom Rug (6 × 9): \(\text{Area} = 6 \times 9 = 54\). Area = 54 square units.

YOU DO Practice (Page 2)

3. Poster (8 ft × 4 ft): \(8 \times 4 = 32\). Area = 32 square feet.

4. Carpet (9 m × 7 m): \(9 \times 7 = 63\). Area = 63 square meters.

5. Comparison: Rect A: \(7 \times 4 = 28\); Rect B: \(6 \times 5 = 30\). Larger: Rectangle B.

6. Missing Side: \(? \times 4 = 16 \rightarrow\) Length = 4 units.

Exit Ticket Solution & Rubric

1. Formula: \(\text{Area} = \text{length} \times \text{width}\) (or \(A = l \times w\))

Area = _____ sq units

4. Find the area:

Count rows or count by ones.

Area = _____ sq units

5. Cross / Plus shape:

Count every unit square carefully.

Area = _____ sq units

6. Missing Tiles Puzzle:

A rectangle has 4 rows. Each row has 5 tiles. What is the total area?

Area = _____ sq units

Lesson 1 Exit Ticket: 5-Minute Quick Check

Do this on your own!

1. Find the area of the rectangle on the right.

Area = square units

2. Explain how you counted or calculated your answer:

Unit 3: Area of Tiled Shapes • Student Notes Page 2 of 2

6. Missing Tiles Puzzle:

20 square units

Exit Ticket Solution & Rubric

Answer: Area = 12 square units (Rectangle is 4 rows of 3 tiles, or 4 × 3 = 12).

Explanation Acceptable Samples:
• "I counted 4 rows of 3 squares which equals 12."
• "I skip counted by 3s: 3, 6, 9, 12."
• "I counted all the unit squares one-by-one."

Exit Ticket 2-Point Quick Rubric:

2 Points (Mastery): Correct answer of 12 with label "square units" and valid counting or multiplication explanation.

1 Point (Approaching): Correct number (12) but forgot "square units", OR minor counting error (e.g., 11 or 13) with clear strategy.

0 Points (Needs Reteach): Incorrect answer without strategy, counted outside edges instead of square tiles, or blank.

Area Adventures • Lesson 1 Teacher Reference Complete Solutions

Board Layout #2:

Length = 7 ft, Width = 5 ft
Area = length × width
Area = 7 × 5 = 35

Area = 35 square feet

Area Adventures • Lesson 2 Sub Guide Page 1 of 2 (Turn for We Do & Independent Practice)

Lesson 2: We Do, You Do & Class Closure

Teacher Script Continued

3

Guided Practice: We Do (15 Min)

We Do 1: Notebook (11 in × 8 in)

Sub Prompt: "Read Problem 1 with me: 'A rectangular notebook is 11 inches long and 8 inches wide.' Draw a rectangle with me on your paper. Label the top 11 in and the side 8 in."

Step-by-Step Call: "What is the formula? (Class: Area = length × width!) What is 11 × 8? (Class: 88!) What is the unit? (Class: square inches!)"

We Do 2: Rug (6 units × 9 units)

Sub Prompt: "Look at Problem 2. Dimensions are 6 units by 9 units. What equation do we write?"

Commutative Property Tip: Ask: "If Maya wrote 9 × 6 and Leo wrote 6 × 9, are they both right? YES! In multiplication, order doesn't change the product. Area = 54 square units!"

3-Minute Whiteboard Check (Before Letting Them Work Alone):

Write on board: "A rectangle has length = 5 units and width = 4 units." Say: "Hold up your whiteboards with: 1) The formula, 2) The math, 3) The answer with units!" Look for: \(\text{Area} = 5 \times 4 = 20\text{ square units}\). Praise fast accurate work!

4

Independent Practice & Exit Ticket (20 Min)

Step 1: Partner Work (8 Min): Students complete Problems 3–5 on page 2. Partners can verify each other's multiplication facts.

Step 2: Silent Independent Work (7 Min): Students complete Problems 6–7 on their own.

Step 3: Exit Ticket (5 Min): Direct students to the bottom Exit Ticket box. Remind them to show both the multiplication sentence and the correct unit label.

Common Sub Pitfalls:

Adding Instead of Multiplying: Some students will do \(7 + 5 = 12\) instead of \(7 \times 5 = 35\). Remind them: "Area is rows TIMES columns!"

Wrong Units: Forgetting "square" (writing "feet" instead of "square feet").

Wrap-Up / Teacher Script (Last 2 Minutes):

"Class, look how far you've come! In Lesson 1, we counted every single square unit. Today, you mastered the mathematical shortcut: Area equals length times width. You can now calculate the area of a rug, a classroom, or even a soccer field without counting single tiles!"

Sub Quick Checklist:

✔ Supplies: Whiteboards/markers (or scratch paper) for quick-check.

✔ Differentiation: Allow multiplication charts for students who struggle with 7s and 8s facts.

✔ Early Finishers: Have them find all rectangles with an area of 24 square units.

✔ Turn In: Collect all packets with Exit Tickets completed.

Area Adventures • Lesson 2 Sub Guide Page 2 of 2

2. Classroom Rug: 6 units by 9 units

Write the multiplication equation:

Area = length × width

Area = ______ × ______

Area = ______ square units

YOU DO

Independent Practice (Show All Work)

3. Rectangular Poster:

8 feet long and 4 feet wide. What is the area?

Calculation: _____ × _____ = _____

Area = _____ square feet

4. Classroom Carpet:

9 meters long and 7 meters wide. What is the area?

Calculation: _____ × _____ = _____

Area = _____ square meters

5. Comparison Challenge:

Which rectangle has the larger area?

• Rectangle A: 7 units × 4 units = ____ sq units

• Rectangle B: 6 units × 5 units = ____ sq units

Larger Rectangle: Rectangle ____

6. Missing Side Length:

A rectangle has an area of 16 square units and a width of 4 units. What is its length?

Equation: _____ × 4 = 16

Length = _____ units

Lesson 2 Exit Ticket: 5-Minute Quick Check

Do this on your own!

A rectangular playground sandbox is 8 feet long and 5 feet wide.

1. Write the formula:

2. Show multiplication:

Area = square feet

8 feet

Sandbox

5 feet wide

Unit 3: Finding Area by Multiplying • Student Notes Page 2 of 2

2. Math: \(8 \times 5 = 40\)

Answer: Area = 40 square feet

Exit Ticket 2-Point Quick Rubric:

2 Points (Mastery): Correct answer of 40 with label "square feet" (or sq ft) and clearly written multiplication formula \(8 \times 5 = 40\).

1 Point (Approaching): Calculated 40 but wrote "feet" instead of "square feet", OR correct formula with minor multiplication slip.

0 Points (Needs Reteach): Added side lengths instead of multiplying (\(8 + 5 = 13\)), or incorrect with no formula shown.

Area Adventures • Lesson 2 Teacher Reference Complete Solutions

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