Grade 3 · Measurement & Data · MAT-03-MD-013
Compare Area and Perimeter
Represent compare area and perimeter with words, symbols, diagrams, or models appropriate to Grade 3.
Learning objectives
What you should be able to do
- Represent compare area and perimeter with words, symbols, diagrams, or models appropriate to Grade 3.
- Solve problems involving compare area and perimeter accurately and explain why the method works.
- Check results for reasonableness using a second representation, inverse relationship, benchmark, or property when appropriate.
Prerequisite check
Make sure the foundation is ready.
Checks conceptual readiness before new Grade 3 reasoning.
Checks whether prior skills are available for use, not only recalled by name.
Learn
Build the idea from meaning, not memorization.
Meaning of Compare Area and Perimeter
Area and perimeter measure different attributes, so one can change while the other stays the same.
A reliable reasoning strategy
For each figure, calculate area in square units and perimeter in linear units, then compare the pairs.
Representations that should agree
Rectangles can share an area but have different perimeters, or share a perimeter but have different areas. A correct model, equation, verbal explanation, or diagram should preserve the same quantities and relationships.
How to check the result
Check whether the answer fits the quantities, units, and structure of the problem. Use a second representation or inverse relationship when available, and explain what would make an answer unreasonable.
Interactive math lab
Change it. See what stays true.
Geometry Explorer
- build a model
- change one quantity
- predict before calculating
- explain why the result changes
Worked examples
Twenty different ways to see the concept work.
For a 4 by 4 rectangle, find both area and perimeter.
Area: 4 × 4 = 16; perimeter parts: 2 × 4 = 8; 2 × 4 = 8; 8 + 8 = 16Area measures the interior in square units; perimeter measures boundary length.
For a 5 by 6 rectangle, find both area and perimeter.
Area: 5 × 6 = 30; perimeter parts: 2 × 5 = 10; 2 × 6 = 12; 10 + 12 = 22Area measures the interior in square units; perimeter measures boundary length.
For a 6 by 3 rectangle, find both area and perimeter.
Area: 6 × 3 = 18; perimeter parts: 2 × 6 = 12; 2 × 3 = 6; 12 + 6 = 18Area measures the interior in square units; perimeter measures boundary length.
For a 7 by 5 rectangle, find both area and perimeter.
Area: 7 × 5 = 35; perimeter parts: 2 × 7 = 14; 2 × 5 = 10; 14 + 10 = 24Area measures the interior in square units; perimeter measures boundary length.
For a 8 by 2 rectangle, find both area and perimeter.
Area: 8 × 2 = 16; perimeter parts: 2 × 8 = 16; 2 × 2 = 4; 16 + 4 = 20Area measures the interior in square units; perimeter measures boundary length.
For a 3 by 4 rectangle, find both area and perimeter.
Area: 3 × 4 = 12; perimeter parts: 2 × 3 = 6; 2 × 4 = 8; 6 + 8 = 14Area measures the interior in square units; perimeter measures boundary length.
For a 4 by 6 rectangle, find both area and perimeter.
Area: 4 × 6 = 24; perimeter parts: 2 × 4 = 8; 2 × 6 = 12; 8 + 12 = 20Area measures the interior in square units; perimeter measures boundary length.
For a 5 by 3 rectangle, find both area and perimeter.
Area: 5 × 3 = 15; perimeter parts: 2 × 5 = 10; 2 × 3 = 6; 10 + 6 = 16Area measures the interior in square units; perimeter measures boundary length.
For a 6 by 5 rectangle, find both area and perimeter.
Area: 6 × 5 = 30; perimeter parts: 2 × 6 = 12; 2 × 5 = 10; 12 + 10 = 22Area measures the interior in square units; perimeter measures boundary length.
For a 7 by 2 rectangle, find both area and perimeter.
Area: 7 × 2 = 14; perimeter parts: 2 × 7 = 14; 2 × 2 = 4; 14 + 4 = 18Area measures the interior in square units; perimeter measures boundary length.
For a 8 by 4 rectangle, find both area and perimeter.
Area: 8 × 4 = 32; perimeter parts: 2 × 8 = 16; 2 × 4 = 8; 16 + 8 = 24Area measures the interior in square units; perimeter measures boundary length.
For a 3 by 6 rectangle, find both area and perimeter.
Area: 3 × 6 = 18; perimeter parts: 2 × 3 = 6; 2 × 6 = 12; 6 + 12 = 18Area measures the interior in square units; perimeter measures boundary length.
For a 4 by 3 rectangle, find both area and perimeter.
Area: 4 × 3 = 12; perimeter parts: 2 × 4 = 8; 2 × 3 = 6; 8 + 6 = 14Area measures the interior in square units; perimeter measures boundary length.
For a 5 by 5 rectangle, find both area and perimeter.
Area: 5 × 5 = 25; perimeter parts: 2 × 5 = 10; 2 × 5 = 10; 10 + 10 = 20Area measures the interior in square units; perimeter measures boundary length.
For a 6 by 2 rectangle, find both area and perimeter.
Area: 6 × 2 = 12; perimeter parts: 2 × 6 = 12; 2 × 2 = 4; 12 + 4 = 16Area measures the interior in square units; perimeter measures boundary length.
For a 7 by 4 rectangle, find both area and perimeter.
Area: 7 × 4 = 28; perimeter parts: 2 × 7 = 14; 2 × 4 = 8; 14 + 8 = 22Area measures the interior in square units; perimeter measures boundary length.
For a 8 by 6 rectangle, find both area and perimeter.
Area: 8 × 6 = 48; perimeter parts: 2 × 8 = 16; 2 × 6 = 12; 16 + 12 = 28Area measures the interior in square units; perimeter measures boundary length.
For a 3 by 3 rectangle, find both area and perimeter.
Area: 3 × 3 = 9; perimeter parts: 2 × 3 = 6; 2 × 3 = 6; 6 + 6 = 12Area measures the interior in square units; perimeter measures boundary length.
For a 4 by 5 rectangle, find both area and perimeter.
Area: 4 × 5 = 20; perimeter parts: 2 × 4 = 8; 2 × 5 = 10; 8 + 10 = 18Area measures the interior in square units; perimeter measures boundary length.
For a 5 by 2 rectangle, find both area and perimeter.
Area: 5 × 2 = 10; perimeter parts: 2 × 5 = 10; 2 × 2 = 4; 10 + 4 = 14Area measures the interior in square units; perimeter measures boundary length.
Practice
Guided practice with hints
01For a 4 by 4 rectangle, find both area and perimeter.
Hint: For each figure, calculate area in square units and perimeter in linear units, then compare the pairs.
Answer: Area 16 square units; perimeter 16 units
02For a 5 by 6 rectangle, find both area and perimeter.
Hint: For each figure, calculate area in square units and perimeter in linear units, then compare the pairs.
Answer: Area 30 square units; perimeter 22 units
03For a 6 by 3 rectangle, find both area and perimeter.
Hint: For each figure, calculate area in square units and perimeter in linear units, then compare the pairs.
Answer: Area 18 square units; perimeter 18 units
04For a 7 by 5 rectangle, find both area and perimeter.
Hint: For each figure, calculate area in square units and perimeter in linear units, then compare the pairs.
Answer: Area 35 square units; perimeter 24 units
05For a 8 by 2 rectangle, find both area and perimeter.
Hint: For each figure, calculate area in square units and perimeter in linear units, then compare the pairs.
Answer: Area 16 square units; perimeter 20 units
06For a 3 by 4 rectangle, find both area and perimeter.
Hint: For each figure, calculate area in square units and perimeter in linear units, then compare the pairs.
Answer: Area 12 square units; perimeter 14 units
Practice
Independent practice
01For a 6 by 4 rectangle, find both area and perimeter.
Answer: Area 24 square units; perimeter 20 units
02For a 7 by 6 rectangle, find both area and perimeter.
Answer: Area 42 square units; perimeter 26 units
03For a 8 by 3 rectangle, find both area and perimeter.
Answer: Area 24 square units; perimeter 22 units
04For a 3 by 5 rectangle, find both area and perimeter.
Answer: Area 15 square units; perimeter 16 units
05For a 4 by 2 rectangle, find both area and perimeter.
Answer: Area 8 square units; perimeter 12 units
06For a 5 by 4 rectangle, find both area and perimeter.
Answer: Area 20 square units; perimeter 18 units
07For a 6 by 6 rectangle, find both area and perimeter.
Answer: Area 36 square units; perimeter 24 units
08For a 7 by 3 rectangle, find both area and perimeter.
Answer: Area 21 square units; perimeter 20 units
Common mistakes
Learn to catch the error, not just the answer.
Calculate each attribute separately and keep its units visible.
Reconnect the answer to compare area and perimeter and verify that the model, calculation, and label describe the same quantity.
Applications & challenge
Use the idea beyond a single exercise.
Applications
- Compare design options with the same floor space or boundary length.
- Use compare area and perimeter to interpret or solve a Grade 3 situation with quantities, diagrams, measurements, or data.
Challenge problems
For a 8 by 4 rectangle, find both area and perimeter.
Area 32 square units; perimeter 24 units
For a 3 by 6 rectangle, find both area and perimeter.
Area 18 square units; perimeter 18 units
For a 4 by 3 rectangle, find both area and perimeter.
Area 12 square units; perimeter 14 units
For a 5 by 5 rectangle, find both area and perimeter.
Area 25 square units; perimeter 20 units
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 4
Game mode
Compare Area and Perimeter Challenge
Solve and explain Grade 3 problems involving compare area and perimeter without relying on answer guessing.
Practice
Mastery check
01For a 4 by 4 rectangle, find both area and perimeter.
Answer: Area 16 square units; perimeter 16 units
02For a 5 by 6 rectangle, find both area and perimeter.
Answer: Area 30 square units; perimeter 22 units
03For a 6 by 3 rectangle, find both area and perimeter.
Answer: Area 18 square units; perimeter 18 units
04For a 7 by 5 rectangle, find both area and perimeter.
Answer: Area 35 square units; perimeter 24 units
05For a 8 by 2 rectangle, find both area and perimeter.
Answer: Area 16 square units; perimeter 20 units
06For a 3 by 4 rectangle, find both area and perimeter.
Answer: Area 12 square units; perimeter 14 units
07For a 4 by 6 rectangle, find both area and perimeter.
Answer: Area 24 square units; perimeter 20 units
08For a 5 by 3 rectangle, find both area and perimeter.
Answer: Area 15 square units; perimeter 16 units
Terminology
Words to know
- linear unit
- A unit of length used for perimeter.
- square unit
- A unit of area used for surface measure.
Continue learning
Connected concepts
Curriculum references
Standards and instructional references
California Common Core State Standards for Mathematics — Grade 3, 3.MD.8
Primary standards alignment for Compare Area and Perimeter.2023 Mathematics Framework for California Public Schools
Instructional emphasis on reasoning, representations, problem solving, and equitable access.