Solved Exercises on Understanding Thirds in Grade 2

Master thirds: fraction concepts, shape partitioning, and third identification through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Circle Thirds
Exercise 1
Draw a circle and divide it into 3 equal parts. Color 1 part. What fraction of the circle is colored?
○ → ○○○ (one third colored)
Definition:

Third: One of three equal parts of a whole

Thirds: Three equal parts that make up a whole

Equal Parts: Parts that are exactly the same size and shape

Creating Thirds Steps:
  1. Draw: Create the whole shape (circle, rectangle, etc.)
  2. Divide: Split the shape into 3 equal parts
  3. Check: Ensure all 3 parts are the same size and shape
  4. Identify: Each part is one third (1/3) of the whole
Total Parts
3 equal parts
Shaded Parts
1 part
Fraction
1/3
Step 1: Draw the whole circle

Start with one complete circle

Step 2: Divide into 3 equal parts

Draw 2 lines through the center to create 3 equal parts

Step 3: Color 1 part

Shade one of the three equal parts

Step 4: Write the fraction

1 part shaded out of 3 total parts = 1/3

1/3 of the circle is colored
Final answer:

One-third (1/3) of the circle is colored.

Applied rules:

• Thirds Rule: Exactly 3 equal parts of a whole

• Fraction Notation: 1/3 represents one third

• Equal Division: All 3 parts must be identical

2 Rectangle Thirds
Exercise 2
Draw a rectangle and divide it into 3 equal parts. Color 2 parts. What fraction of the rectangle is colored?
▭ → ▭▭▭ (2 parts colored)
Definition:

Rectangle: A four-sided shape with four right angles

Thirds: Three equal parts of any shape or object

Total Parts
3 equal parts
Shaded Parts
2 parts
Fraction
2/3
Step 1: Draw the rectangle

Create one complete rectangle

Step 2: Divide into 3 equal parts

Draw 2 vertical lines to create 3 equal sections

Step 3: Color 2 parts

Shade two of the three equal parts

Step 4: Write the fraction

2 parts shaded out of 3 total parts = 2/3

2/3 of the rectangle is colored
Final answer:

Two-thirds (2/3) of the rectangle is colored.

Applied rules:

• Equal Sizing: All 3 parts must be the same size

• Thirds Concept: Any shape can be divided into thirds

• Fraction Representation: 2/3 means two thirds

3 Third Identification
Exercise 3
Which of these shapes shows thirds? Explain why the others do not show thirds.
✅ Circle with 3 equal parts | ❌ 4 parts | ❌ 3 unequal parts
Definition:

Thirds: Exactly 3 equal parts that form a whole

Equal Parts: Parts that match in size and shape

Correct
Circle - 3 equal parts
Incorrect
Wrong number or size
Reason
Must be 3 equal parts
Step 1: Examine each shape

Look at the number and size of parts

Step 2: Check for 3 parts

Thirds require exactly 3 parts

Step 3: Check for equal size

All 3 parts must be the same size and shape

Step 4: Identify thirds

Only the circle has 3 equal parts

Only the circle shows thirds
Final answer:

The circle shows thirds because it has exactly 3 equal parts. The other shapes either have the wrong number of parts or parts of different sizes.

Applied rules:

• Exact Count: Must have exactly 3 parts

• Equality Requirement: All 3 parts must be identical

• Visual Inspection: Use eyes to compare parts

Third Concepts & Rules
\( \frac{1}{3} = \text{one third} \)
Third Notation
Thirds Rule
3 Equal Parts
Exactly 3 identical parts
Fraction Parts
1/3
One out of three parts
Whole Concept
1/3 + 1/3 + 1/3 = 1
Three thirds make one whole
Key Definitions:

Third: One of three equal parts of a whole (written as 1/3)

Thirds: Three equal parts that together make a whole

Equal Parts: Parts that are exactly the same size and shape

Whole: The complete shape or object before dividing

Third Identification:
  1. Count Parts: Ensure there are exactly 3 parts
  2. Compare Sizes: Check that all 3 parts are the same size
  3. Compare Shapes: Verify all 3 parts are the same shape
  4. Verify Total: Confirm the parts make up the whole shape
Tip 1: Thirds always involve exactly 3 equal parts.
Tip 2: The fraction 1/3 always means one third.
Tip 3: Three thirds always equal one whole (1/3 + 1/3 + 1/3 = 1).
Tip 4: Use the phrase "one out of three" to understand 1/3.
Common Mistakes: Thinking any 3 parts are thirds, not checking equality, confusing with other fractions.
Success Strategies: Practice with manipulatives, check equality visually, use physical models.
Important Rules to Remember:

• Exact Number: Thirds require exactly 3 parts

• Equality Requirement: All 3 parts must be identical

• Fraction Notation: 1/3 represents one third

• Whole Relationship: Three thirds make one whole

Solution: Exercises 4 to 5
4 Real-World Thirds
Exercise 4
Dad cuts a pie into 3 equal pieces. He gives 2 pieces to his children. What fraction of the pie did the children get? What fraction is left?
🥧 → 🥧🥧🥧 (2 pieces given to children)
Definition:

Real-World Application: Using math concepts in everyday situations

Remaining: What is left after some is taken away

Total Pieces
3 equal pieces
Children's Pieces
2 pieces
Children's Fraction
2/3
Step 1: Identify total parts

Dad cut the pie into 3 equal pieces (thirds)

Step 2: Identify children's part

Children received 2 pieces out of 3

Step 3: Calculate children's fraction

2 pieces out of 3 total pieces = 2/3

Step 4: Calculate remaining fraction

3 total - 2 given = 1 remaining

1 out of 3 pieces remaining = 1/3

Children: 2/3, Remaining: 1/3
Final answer:

The children got 2/3 of the pie. 1/3 of the pie is left.

Applied rules:

• Real-Life Context: Connect thirds to everyday situations

• Thirds Principle: 3 equal parts make a whole

• Part-Whole Relationship: Fraction represents part compared to total

5 Thirds Comparison
Exercise 5
Compare these shapes: A) Rectangle divided into 3 equal parts, B) Circle divided into 3 equal parts, C) Square divided into 2 parts. Which show thirds?
A: ▮▮▮ | B: ○○○ | C: ▣▣
Definition:

Comparison: Determining which shapes meet the thirds criteria

Criteria: Conditions that must be met for thirds

Shape A
3 equal parts ✓
Shape B
3 equal parts ✓
Shape C
2 parts ✗
Step 1: Analyze Shape A

Rectangle divided into 3 equal parts

This meets thirds criteria ✓

Step 2: Analyze Shape B

Circle divided into 3 equal parts

This meets thirds criteria ✓

Step 3: Analyze Shape C

Square divided into 2 parts

This does NOT meet thirds criteria (needs exactly 3) ✗

Step 4: Summarize results

Shapes A and B show thirds, Shape C does not

Shapes A and B show thirds
Final answer:

Shapes A (rectangle) and B (circle) show thirds because they each have 3 equal parts. Shape C (square) does not show thirds because it has 2 parts instead of 3.

Applied rules:

• Thirds Criteria: Must have exactly 3 equal parts

• Shape Independence: Any shape can be divided into thirds

• Visual Verification: Check number and equality of parts

Thirds Applications & Strategies
\( \frac{1}{3} + \frac{1}{3} + \frac{1}{3} = 1 \)
Thirds Relationship
Key definitions:

Unit Fraction: A fraction with numerator 1 (like 1/3)

Proper Fraction: A fraction where numerator is less than denominator

Visual Model: A picture or diagram representing a fraction

Thirds Creation:
  1. For Circles: Draw 2 lines through the center, creating 3 equal sectors
  2. For Rectangles: Draw 2 lines dividing length or width into 3 equal sections
  3. For Squares: Same as rectangles but all sides equal
  4. For Other Shapes: Find lines that create 3 equal parts
Tip 1: Thirds always divide something into 3 equal parts.
Tip 2: The fraction 1/3 means the same as "one third".
Tip 3: Three thirds always equal one whole thing.
Tip 4: Practice with real objects like cutting food into thirds.

Common Errors: Thinking any 3 parts are thirds, not checking equality, confusing with other fractions.
Success Strategies: Use manipulatives, practice with real objects, verify parts are equal.
Essential Thirds Rules:

• Exact Count: Must have exactly 3 parts

• Equality Requirement: All 3 parts must be identical

• Fraction Notation: 1/3 represents one third

• Whole Formation: Three thirds combine to make one whole

Understanding Thirds

🔢
What are Thirds?

Thirds are 3 equal parts of a whole:

• Exactly 3 parts

• Same size

• Same shape

3 equal parts = 1 whole
Third Notation

Thirds are written as:

Fraction: 1/3

Words: one third

Relationship: 1/3 + 1/3 + 1/3 = 1

Creating Thirds
1
Draw Shape
2
Divide in 3 Parts
3
Check Equality
4
Label Fraction
Thirds Examples

• Circle: 3 equal slices

• Rectangle: 3 equal sections

• Any shape: 3 equal parts

Practice identifying and creating thirds in different shapes!

Questions & Answers

Question: My second-grade students think any 3 parts of a shape are thirds. How can I help them understand that thirds must be equal?

Answer: Emphasize the "equal" part of "equal parts" with hands-on activities:

  • Use paper shapes that students can fold to see if parts match perfectly
  • Have them cut shapes and physically place one part on top of another to compare
  • Create examples showing unequal parts vs. equal parts side by side
  • Use manipulatives like fraction circles where pieces are pre-made to be equal

Stress that "third" means "fair share" - all 3 parts must be exactly the same size for it to be fair.

Create a chant: "Thirds, thirds, equal parts, that's how it starts!"

Question: My child is confused about the fraction 1/3. How can I explain it in a simple way?

Answer: Use simple language and real examples:

  • Explain: "1/3 means one out of three equal parts"
  • Demonstrate: Cut a pizza, cake, or sandwich into 3 equal pieces
  • Count: Show that 1 piece out of 3 total pieces is 1/3
  • Relate: "One third" and "1/3" mean the same thing

Practice with the phrase: "I took one piece out of three pieces, so I have one third."

Use visual fraction models consistently so they connect the picture to the numbers.

Question: Do thirds work with all shapes? Can I cut a triangle into thirds?

Answer: Yes, thirds work with ALL shapes! Here's how:

  • Circles: Draw 2 lines through the center creating 3 equal slices
  • Rectangles/Squares: Draw 2 parallel lines dividing into 3 equal sections
  • Triangles: Draw lines from vertices to opposite sides to create 3 equal parts
  • Any Shape: Find a way to make 3 equal parts

The key is that all 3 parts must be the same size and shape, no matter what the original shape is.

Try folding different shaped paper to see how you can make equal parts!