Solved Exercises on Area as Square Units in Grade 3

Master area as square units: counting unit squares, comparing areas, and understanding area measurement through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Counting unit squares
Exercise 1
Count the unit squares in a shape made up of 6 squares arranged in a 2×3 rectangle.
Definition:

Unit square: A square with sides of length 1 unit used to measure area

Unit square counting method:
  1. Identify each unit square in the shape
  2. Count systematically (row by row or column by column)
  3. Keep track of the count
  4. State the area in square units
Rows
2 rows
Columns
3 columns
Total
2 × 3 = 6
Step 1: Identify the unit squares

Look at each small square in the shape

Step 2: Count systematically

Row 1: 1, 2, 3 squares

Row 2: 4, 5, 6 squares

Step 3: Verify by multiplication

2 rows × 3 columns = 6 squares

Step 4: Express the area

Area = 6 square units

Area = 6 square units
Final answer:

The area of the shape is 6 square units

Applied rules:

• Unit counting: Each square counts as 1 square unit

• Systematic counting: Count in order to avoid missing any

• Area units: Always express area in square units

2 Partial square units
Exercise 2
A shape has 4 full unit squares and 2 half unit squares. What is the total area?
Definition:

Partial square units: When a shape includes portions of unit squares, these must be combined to form whole units

Full Squares
4 squares
Half Squares
2 × 1/2 = 1
Total Area
4 + 1 = 5
Step 1: Count full unit squares

There are 4 complete unit squares

Step 2: Count partial squares

There are 2 half unit squares

Step 3: Convert partial squares to whole units

2 half squares = 1 full square

Step 4: Add the totals

4 + 1 = 5 square units

Area = 5 square units
Final answer:

The area of the shape is 5 square units

Applied rules:

• Partial squares: Combine partial squares to form wholes

• Half squares: 2 half squares = 1 full square

• Area addition: Add full and converted squares

3 Area comparison
Exercise 3
Shape A has 8 unit squares. Shape B has 5 unit squares and 4 half squares. Which shape has the greater area?
Definition:

Area comparison: Determining which shape has more space inside by comparing their areas in square units

Shape A
8 sq units
Shape B
5 + 2 = 7
Comparison
8 > 7
Step 1: Calculate Shape A's area

Shape A = 8 square units

Step 2: Calculate Shape B's area

Shape B = 5 full squares + 4 half squares = 5 + 2 = 7 square units

Step 3: Compare the areas

8 > 7, so Shape A has the greater area

Step 4: State the conclusion

Shape A has the greater area

Shape A: 8 sq units | Shape B: 7 sq units
Final answer:

Shape A has the greater area (8 square units compared to 7 square units)

Applied rules:

• Partial squares: Convert to whole units before comparison

• Comparison: Compare numbers directly

• Area comparison: Higher number means larger area

Area as Square Units Fundamentals
\text{Area} = \text{Number of Unit Squares}
Area Formula
Unit Square
1 × 1 = 1
Basic area unit
Half Square
1/2 = 0.5
Partial unit
Partial Squares
Combine to Whole
2 halves = 1 whole
Key definitions:

Area: The amount of space inside a 2D shape, measured in square units

Unit square: A square with sides of length 1 unit, used to measure area

Square unit: The standard unit used to measure area

Partial square: A portion of a unit square that contributes to the total area

5-step area counting method:
  1. Identify: Recognize unit squares and partial squares
  2. Count: Count all full unit squares
  3. Convert: Combine partial squares to form whole units
  4. Calculate: Add full and converted squares
  5. Verify: Check if the answer makes sense
Tip 1: Count systematically to avoid missing any squares.
Tip 2: Group partial squares to form whole units.
Tip 3: Always include "square units" in your answer.
Tip 4: Draw a grid to help visualize unit squares.
Common errors: Forgetting to count partial squares, not including square units in answer.
Memory aid: "Count every square, combine the halves, area is always in square units!"
Key area facts:

• Area measures the inside space of a shape

• Area is measured in square units (sq units)

• 2 half squares = 1 full square

• You can count unit squares to find area

Solution: Exercises 4 to 5
4 Irregular shape area
Exercise 4
Find the area of an L-shaped figure made up of unit squares. The figure has 6 full squares and 4 quarter squares.
Definition:

Irregular shape area: Finding area of shapes that are not simple rectangles by counting unit squares and partial squares

Full Squares
6 squares
Quarter Squares
4 × 1/4 = 1
Total Area
6 + 1 = 7
Step 1: Count full squares

There are 6 complete unit squares

Step 2: Count quarter squares

There are 4 quarter squares

Step 3: Convert quarter squares to whole units

4 quarter squares = 1 full square (since 4 × 1/4 = 1)

Step 4: Add the totals

Total area = 6 + 1 = 7 square units

Area = 7 square units
Final answer:

The area of the L-shaped figure is 7 square units

Applied rules:

• Quarter squares: 4 quarter squares = 1 full square

• Partial conversion: Convert to whole units before adding

• Area addition: Add full and converted squares

5 Area comparison word problem
Exercise 5
A rectangular garden has 8 full squares and 2 half squares. A square flower bed has 9 full squares. Which has the larger area?
Definition:

Area word problem: A real-world problem that requires calculating and comparing areas using square units

Garden Area
8 + 1 = 9
Flower Bed Area
9 sq units
Comparison
9 = 9
Step 1: Calculate garden area

Garden = 8 full squares + 2 half squares = 8 + 1 = 9 square units

Step 2: Calculate flower bed area

Flower bed = 9 full squares = 9 square units

Step 3: Compare the areas

9 = 9, so both areas are equal

Step 4: State the answer

Both the garden and flower bed have the same area

Garden: 9 sq units | Flower Bed: 9 sq units
Final answer:

Both the garden and the flower bed have the same area (9 square units)

Applied rules:

• Partial squares: Convert to whole units before comparison

• Comparison: Compare calculated areas

• Word problems: Extract dimensions and partials from text

Complete Area as Square Units Guide
\text{Area} = \text{Number of Full Squares} + \text{Converted Partial Squares}
Complete Area Formula
Key definitions:

Area: The amount of space inside a 2D shape, measured in square units

Unit square: A square with sides of length 1 unit, used to measure area

Partial square: A portion of a unit square that contributes to the total area

Square unit: The standard unit for measuring area

Advanced area techniques:
  1. Grid method: Count unit squares to find area
  2. Partial conversion: Combine partial squares to form whole units
  3. Systematic counting: Count in order to avoid missing any
  4. Verification: Check if the answer makes logical sense
Tip 1: Practice with physical manipulatives to visualize area.
Tip 2: Draw grids to help count unit squares accurately.
Tip 3: Always include "square units" in your final answer.
Tip 4: Combine partial squares to make whole units easier to count.
Common errors: Forgetting to convert partial squares, not using proper units, missing squares.
Success strategies: Regular practice, visual aids, systematic counting.
Essential area facts:

• Area measures the inside space of a shape

• Area is always expressed in square units

• 2 half squares = 1 full square

• 4 quarter squares = 1 full square

Square Unit Conversion Guide
Partial Square Conversions
Understanding how partial squares combine to form whole units:
Half squares, quarter squares, and other fractions

Partial Square Conversions:

  • Half squares: 2 half squares = 1 full square
  • Quarter squares: 4 quarter squares = 1 full square
  • Third squares: 3 third squares = 1 full square
  • Combination: Add all converted squares together

Questions & Answers

Question: What if I have different types of partial squares, like 3 half squares and 2 quarter squares? How do I add them?

Answer: Convert each type of partial square separately:

  • Half squares: 3 half squares = 1.5 full squares
  • Quarter squares: 2 quarter squares = 0.5 full squares
  • Total partials: 1.5 + 0.5 = 2 full squares

Then add this to your full squares. For example, if you had 4 full squares: 4 + 2 = 6 square units.

Always convert each type separately before adding!

Question: How do I know if a shape has 3/4 of a square or just 2 half squares?

Answer: Look carefully at the shape:

  • Three-quarter square: A square with one-fourth missing (looks like 75% of a square)
  • Two half squares: Two separate shapes, each half of a square
  • Visual clue: Three-quarters is one connected shape, two halves are two separate shapes

A three-quarter square equals 0.75 square units, while two half squares equal 1 square unit.

Pay attention to how the partials are arranged!

Question: Why do we need to convert partial squares to whole units? Can't we just leave them as fractions?

Answer: Converting partial squares to whole units makes it easier to:

  • Compare areas: It's easier to compare 3 square units vs 2.5 square units
  • Understand the total: Whole numbers are simpler to comprehend
  • Communicate: It's clearer to say "the area is 5 square units"

However, you could express the area as a mixed number if needed (like 4.5 square units).

Converting helps us work with standard measurements!