Grade 3 · Geometry · MAT-03-GEO-002
Partition Shapes into Equal-Area Fractions
Represent partition shapes into equal-area fractions with words, symbols, diagrams, or models appropriate to Grade 3.
Learning objectives
What you should be able to do
- Represent partition shapes into equal-area fractions with words, symbols, diagrams, or models appropriate to Grade 3.
- Solve problems involving partition shapes into equal-area fractions 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 Partition Shapes into Equal-Area Fractions
Partitioning a shape into equal-area regions creates a fraction model in which each region is a unit fraction of the whole.
A reliable reasoning strategy
Verify the regions have equal area, count the total regions, and name each region as 1/b of the whole.
Representations that should agree
Geometry and fractions meet because equal-area parts can have different shapes but still represent equal fractional 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.
Equal-Share Lab
Keep the whole fixed and change how many equal shares it contains.
- build a model
- change one quantity
- predict before calculating
- explain why the result changes
Worked examples
Twenty different ways to see the concept work.
A shape is partitioned into 3 regions of equal area. What fraction of the whole is one region?
One equal region is 1/3 of the whole.Equal-area partitions define unit fractions.
A shape is partitioned into 4 regions of equal area. What fraction of the whole is one region?
One equal region is 1/4 of the whole.Equal-area partitions define unit fractions.
A shape is partitioned into 6 regions of equal area. What fraction of the whole is one region?
One equal region is 1/6 of the whole.Equal-area partitions define unit fractions.
A shape is partitioned into 8 regions of equal area. What fraction of the whole is one region?
One equal region is 1/8 of the whole.Equal-area partitions define unit fractions.
A shape is partitioned into 2 regions of equal area. What fraction of the whole is one region?
One equal region is 1/2 of the whole.Equal-area partitions define unit fractions.
A shape is partitioned into 3 regions of equal area. What fraction of the whole is one region?
One equal region is 1/3 of the whole.Equal-area partitions define unit fractions.
A shape is partitioned into 4 regions of equal area. What fraction of the whole is one region?
One equal region is 1/4 of the whole.Equal-area partitions define unit fractions.
A shape is partitioned into 6 regions of equal area. What fraction of the whole is one region?
One equal region is 1/6 of the whole.Equal-area partitions define unit fractions.
A shape is partitioned into 8 regions of equal area. What fraction of the whole is one region?
One equal region is 1/8 of the whole.Equal-area partitions define unit fractions.
A shape is partitioned into 2 regions of equal area. What fraction of the whole is one region?
One equal region is 1/2 of the whole.Equal-area partitions define unit fractions.
A shape is partitioned into 3 regions of equal area. What fraction of the whole is one region?
One equal region is 1/3 of the whole.Equal-area partitions define unit fractions.
A shape is partitioned into 4 regions of equal area. What fraction of the whole is one region?
One equal region is 1/4 of the whole.Equal-area partitions define unit fractions.
A shape is partitioned into 6 regions of equal area. What fraction of the whole is one region?
One equal region is 1/6 of the whole.Equal-area partitions define unit fractions.
A shape is partitioned into 8 regions of equal area. What fraction of the whole is one region?
One equal region is 1/8 of the whole.Equal-area partitions define unit fractions.
A shape is partitioned into 2 regions of equal area. What fraction of the whole is one region?
One equal region is 1/2 of the whole.Equal-area partitions define unit fractions.
A shape is partitioned into 3 regions of equal area. What fraction of the whole is one region?
One equal region is 1/3 of the whole.Equal-area partitions define unit fractions.
A shape is partitioned into 4 regions of equal area. What fraction of the whole is one region?
One equal region is 1/4 of the whole.Equal-area partitions define unit fractions.
A shape is partitioned into 6 regions of equal area. What fraction of the whole is one region?
One equal region is 1/6 of the whole.Equal-area partitions define unit fractions.
A shape is partitioned into 8 regions of equal area. What fraction of the whole is one region?
One equal region is 1/8 of the whole.Equal-area partitions define unit fractions.
A shape is partitioned into 2 regions of equal area. What fraction of the whole is one region?
One equal region is 1/2 of the whole.Equal-area partitions define unit fractions.
Practice
Guided practice with hints
01A shape is partitioned into 3 regions of equal area. What fraction of the whole is one region?
Hint: Verify the regions have equal area, count the total regions, and name each region as 1/b of the whole.
Answer: 1/3
02A shape is partitioned into 4 regions of equal area. What fraction of the whole is one region?
Hint: Verify the regions have equal area, count the total regions, and name each region as 1/b of the whole.
Answer: 1/4
03A shape is partitioned into 6 regions of equal area. What fraction of the whole is one region?
Hint: Verify the regions have equal area, count the total regions, and name each region as 1/b of the whole.
Answer: 1/6
04A shape is partitioned into 8 regions of equal area. What fraction of the whole is one region?
Hint: Verify the regions have equal area, count the total regions, and name each region as 1/b of the whole.
Answer: 1/8
05A shape is partitioned into 2 regions of equal area. What fraction of the whole is one region?
Hint: Verify the regions have equal area, count the total regions, and name each region as 1/b of the whole.
Answer: 1/2
06A shape is partitioned into 3 regions of equal area. What fraction of the whole is one region?
Hint: Verify the regions have equal area, count the total regions, and name each region as 1/b of the whole.
Answer: 1/3
Practice
Independent practice
01A shape is partitioned into 3 regions of equal area. What fraction of the whole is one region?
Answer: 1/3
02A shape is partitioned into 4 regions of equal area. What fraction of the whole is one region?
Answer: 1/4
03A shape is partitioned into 6 regions of equal area. What fraction of the whole is one region?
Answer: 1/6
04A shape is partitioned into 8 regions of equal area. What fraction of the whole is one region?
Answer: 1/8
05A shape is partitioned into 2 regions of equal area. What fraction of the whole is one region?
Answer: 1/2
06A shape is partitioned into 3 regions of equal area. What fraction of the whole is one region?
Answer: 1/3
07A shape is partitioned into 4 regions of equal area. What fraction of the whole is one region?
Answer: 1/4
08A shape is partitioned into 6 regions of equal area. What fraction of the whole is one region?
Answer: 1/6
Common mistakes
Learn to catch the error, not just the answer.
Compare area, not appearance, and confirm the regions together exactly make the whole.
Reconnect the answer to partition shapes into equal-area fractions and verify that the model, calculation, and label describe the same quantity.
Applications & challenge
Use the idea beyond a single exercise.
Applications
- Divide maps, designs, food, or land into equal shares.
- Use partition shapes into equal-area fractions to interpret or solve a Grade 3 situation with quantities, diagrams, measurements, or data.
Challenge problems
A shape is partitioned into 3 regions of equal area. What fraction of the whole is one region?
1/3
A shape is partitioned into 4 regions of equal area. What fraction of the whole is one region?
1/4
A shape is partitioned into 6 regions of equal area. What fraction of the whole is one region?
1/6
A shape is partitioned into 8 regions of equal area. What fraction of the whole is one region?
1/8
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 4
Game mode
Partition Shapes into Equal-Area Fractions Challenge
Solve and explain Grade 3 problems involving partition shapes into equal-area fractions without relying on answer guessing.
Practice
Mastery check
01A shape is partitioned into 3 regions of equal area. What fraction of the whole is one region?
Answer: 1/3
02A shape is partitioned into 4 regions of equal area. What fraction of the whole is one region?
Answer: 1/4
03A shape is partitioned into 6 regions of equal area. What fraction of the whole is one region?
Answer: 1/6
04A shape is partitioned into 8 regions of equal area. What fraction of the whole is one region?
Answer: 1/8
05A shape is partitioned into 2 regions of equal area. What fraction of the whole is one region?
Answer: 1/2
06A shape is partitioned into 3 regions of equal area. What fraction of the whole is one region?
Answer: 1/3
07A shape is partitioned into 4 regions of equal area. What fraction of the whole is one region?
Answer: 1/4
08A shape is partitioned into 6 regions of equal area. What fraction of the whole is one region?
Answer: 1/6
Terminology
Words to know
- partition
- Divide a whole into non-overlapping parts.
- equal area
- Regions that cover the same amount of surface.
Continue learning
Connected concepts
Curriculum references
Standards and instructional references
California Common Core State Standards for Mathematics — Grade 3, 3.G.2
Primary standards alignment for Partition Shapes into Equal-Area Fractions.2023 Mathematics Framework for California Public Schools
Instructional emphasis on reasoning, representations, problem solving, and equitable access.