Grade 3 Mathematics

Big Idea: Key Concept

Area is the amount of space inside a shape. We measure area by counting how many unit squares fit inside. For rectangles, we can multiply the length by the width to find the area quickly. A unit square is a square with sides of 1 unit. If a rectangle is 4 units long and 3 units wide, we can fit 4 × 3 = 12 unit squares inside it. Area is measured in square units like square centimeters (cm²) or square inches (in²).

🧪 Interactive
Simulation

Worked Example:

Problem: A garden is 8 feet long and 6 feet wide. What is the area?

Identify the shape: This is a rectangle with length = 8 ft and width = 6 ft

Write the formula: Area = length × width

Substitute the values: Area = 8 × 6

Calculate: 8 × 6 = 48

Answer: The area is 48 square feet (ft²)

(B) Basic Practice

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Problem 1 Apply ★ [8 pts]

A rectangle is 4 cm long and 6 cm wide. What is the area?

A. 24 cm²

B. 10 cm²

C. 20 cm²

D. 28 cm²

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Problem 2 Apply ★ [8 pts]

A square has sides of 5 inches. What is the area?

A. 20 in²

B. 25 in²

C. 15 in²

D. 10 in²

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Problem 3 Apply ★★ [10 pts]

A rectangle is 7 meters long and 3 meters wide. What is the area?

A. 10 m²

B. 14 m²

C. 21 m²

D. 24 m²

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Problem 4 Apply ★ [8 pts]

Count the unit squares. What is the area of this rectangle?

A. 12 square units

B. 10 square units

C. 15 square units

D. 18 square units

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Problem 5 Apply ★★ [10 pts]

Which rectangle has the largest area? Rectangle A: 3 × 8, Rectangle B: 4 × 5, Rectangle C: 2 × 9

A. Rectangle B

B. Rectangle C

C. Rectangle A

D. They are all equal

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Problem 6 Apply ★★ [12 pts]

A bedroom floor is 9 feet long and 8 feet wide. How many square feet of carpet are needed to cover the floor?

A. 17 ft²

B. 64 ft²

C. 72 ft²

D. 81 ft²

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Problem 7 Apply ★★★ [12 pts]

An L-shaped figure is made of two rectangles. The first is 5 × 3 and the second is 4 × 3. What is the total area?

A. 18 square units

B. 22 square units

C. 24 square units

D. 27 square units

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Problem 8 Apply ★★★ [12 pts]

A rectangle has an area of 28 cm². If the length is 7 cm, what is the width?

A. 3 cm

B. 6 cm

C. 5 cm

D. 4 cm

(D) Advanced Challenge (Higher-Order Thinking)

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Problem 9 Apply ★★★ [14 pts]

Three gardens have these dimensions: Garden A is 6 × 5, Garden B is 6 × 4, and Garden C is 8 × 3. Which two gardens have the same area?

A. Gardens B and C

B. Gardens A and B

C. Gardens A and C

D. No two gardens have the same area

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Problem 10 Apply ★★★★ [14 pts]

Sam wants to build a rectangular sandbox with an area of 36 square feet. Which dimensions could Sam use?

A. 5 ft × 7 ft

B. 6 ft × 6 ft

C. 3 ft × 10 ft

D. 4 ft × 8 ft

(E) Mini Quiz - Check Your Understanding!

Mini Quiz

E1. A rectangle is 3 cm long and 8 cm wide. What is the area?

A. 24 cm²

B. 11 cm²

C. 16 cm²

D. 28 cm²

E2. A square has an area of 16 square inches. What is the length of each side?

A. 8 in

B. 4 in

C. 6 in

D. 2 in

E3. A poster is 10 inches long and 7 inches wide. What is the area?

A. 17 in²

B. 34 in²

C. 70 in²

D. 77 in²

Self-Reflection

How did you feel about this topic?
Confident / Okay / Confused - Circle one

What is one thing you must remember?

Problem-Solving Strategy (4-Step Process)

Challenge Problem: A farmer has a rectangular field that is 12 meters long and 9 meters wide. He wants to plant tomatoes in half of the field. What is the area of the tomato section?

1. Understand:

2. Plan:

3. Execute:

4. Check:

(F) Answer Key & Detailed Explanations

#	Answer	Type	Solution
1	A	Apply	final_step: Area = 24 cm². Answer: A step_1: Length = 4 cm, Width = 6 cm step_2: Area = 4 × 6 = 24
2	B	Apply	final_step: Area = 25 in². Answer: B step_1: Side = 5 inches step_2: Area = 5 × 5 = 25
3	C	Apply	final_step: Area = 21 m². Answer: C step_1: Length = 7 m, Width = 3 m step_2: Area = 7 × 3 = 21
4	A	Apply	final_step: Area = 12 square units. Answer: A step_1: Count rows: 3 rows. Count columns: 4 columns step_2: Total squares = 3 × 4 = 12
5	C	Apply	final_step: Rectangle A has the largest area (24). Answer: C step_1: Rectangle A: 3 × 8 = 24. Rectangle B: 4 × 5 = 20. Rectangle C: 2 × 9 = 18 step_2: Compare: 24 > 20 > 18
6	C	Apply	final_step: Need 72 ft² of carpet. Answer: C step_1: Length = 9 ft, Width = 8 ft step_2: Area = 9 × 8 = 72
7	D	Apply	final_step: Total area = 27 square units. Answer: D step_1: First rectangle: 5 × 3 = 15 step_2: Second rectangle: 4 × 3 = 12 step_3: Total area = 15 + 12 = 27
8	D	Apply	final_step: Width = 4 cm. Answer: D step_1: Area = 28 cm², Length = 7 cm step_2: Width = Area ÷ Length = 28 ÷ 7 = 4
9	A	Apply	final_step: Gardens B and C both have area 24. Answer: A step_1: Garden A: 6 × 5 = 30. Garden B: 6 × 4 = 24. Garden C: 8 × 3 = 24 step_2: Compare: Garden A = 30, Garden B = 24, Garden C = 24
10	B	Apply	final_step: Only 6 × 6 = 36. Answer: B step_1: Check each option: A) 5 × 7 = 35 (no). B) 6 × 6 = 36 (yes!). C) 3 × 10 = 30 (no). D) 4 × 8 = 32 (no).

(G) Mini Quiz Answers

Multiple Choice:

E1. A

E2. B

E3. C

Self-Reflection:

I feel pretty good about finding area. One thing I must remember is to multiply length times width, not add them. I also need to write 'square units' or cm² to show it's area, not just a regular number.

Problem-Solving Strategy (4-Step):

1. Understand: We need to find the total area of an L-shaped figure made of two rectangles. The first rectangle is 5 × 3 and the second is 4 × 3. We must find each area separately, then add them together.

2. Plan: First, calculate the area of the first rectangle (5 × 3). Second, calculate the area of the second rectangle (4 × 3). Finally, add both areas together.

3. Execute: Step 1: First rectangle: Area = 5 × 3 = 15 square units. Step 2: Second rectangle: Area = 4 × 3 = 12 square units. Step 3: Total area = 15 + 12 = 27 square units.

4. Check: Verify: 5 × 3 = 15 (correct). 4 × 3 = 12 (correct). 15 + 12 = 27 (correct). The L-shape is made of these two parts, so the total is 27 square units.

(H) Error Analysis Notebook (Growth Mindset Tool)

Problem #	My Score	Error Type	What I Learned / How to Improve
#9	0/15	Concept	"I forgot to check my answer. Next time I will verify my solution."

Error Types: Concept (개념), Procedure (절차), Calculation (계산), Reading (문제 이해), Careless (실수)

(I) Review Schedule

Review this worksheet on these dates for maximum retention:

Today (Initial Learning)
Tomorrow (Day 2)
Day 3 (Short-term consolidation)
Week 28 (1 week later)
Month 1 (Long-term retention)

Why this works: Ebbinghaus forgetting curve research shows spaced repetition increases retention by 200%+

학부모 가이드 (Parent Guide)

넓이
아이에게 'How many small squares can fit inside this shape?'라고 물어보며 넓이의 개념을 설명해주세요.
집 안의 방이나 카펫을 예시로 'How much space does this cover?'라고 물어보세요.
종이를 가로세로로 나누며 'What happens when we multiply the length and width?'라고 물어보세요.
블록이나 타일을 이용해 'Can you build a rectangle and count how many blocks you used?'라고 놀이로 연습해보세요.

Learning Objectives (What You'll Master Today)

(A) Mathematical Concepts - Self-Learning Guide

Big Idea: Key Concept

How-To Methods

Key Formula/Rule:

Worked Example:

Why This Matters

(B) Basic Practice

(C) Problem Solving (Real-World Applications)

(D) Advanced Challenge (Higher-Order Thinking)

(E) Mini Quiz - Check Your Understanding!

Mini Quiz

Problem-Solving Strategy (4-Step Process)

(F) Answer Key & Detailed Explanations

(G) Mini Quiz Answers

(H) Error Analysis Notebook (Growth Mindset Tool)

(I) Review Schedule

학부모 가이드 (Parent Guide)