Solved Exercises on Mass and Kilograms in Grade 3

Master mass and kilograms: measuring weight, comparing masses, converting units, and practical applications through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Comparing masses
Exercise 1
Which is heavier: a bag of apples weighing 2 kg or a bag of oranges weighing 1500 g?
Definition:

Mass: The amount of matter in an object, measured in grams (g) or kilograms (kg)

Kilogram: The base unit of mass, where 1 kg = 1000 g

Comparison method:
  1. Convert both measurements to the same unit
  2. Compare the numerical values
  3. State which is heavier/lighter
Apples
2 kg
Oranges
1500 g
Conversion
2000 g
Step 1: Convert to same unit

Convert 2 kg to grams: 2 kg × 1000 = 2000 g

Step 2: Compare values

2000 g (apples) vs 1500 g (oranges)

Step 3: Determine heavier

Since 2000 > 1500, the bag of apples is heavier

2 kg = 2000 g > 1500 g, so apples are heavier
Final answer:

The bag of apples weighing 2 kg is heavier than the bag of oranges weighing 1500 g.

Applied rules:

• Unit conversion: 1 kg = 1000 g

• Comparison: Only compare values with same units

• Measurement: Always specify the unit when comparing

2 Adding masses
Exercise 2
Sarah bought 3 kg of potatoes, 500 g of tomatoes, and 1.5 kg of carrots. What is the total mass of her groceries?
Definition:

Total mass: Sum of all individual masses, requiring same units for addition

Potatoes
3 kg
Tomatoes
500 g
Carrots
1.5 kg
Total
4.5 kg + 500 g
Step 1: Group same units

Potatoes + Carrots = 3 kg + 1.5 kg = 4.5 kg

Tomatoes = 500 g

Step 2: Convert to same unit

Convert 4.5 kg to grams: 4.5 kg × 1000 = 4500 g

Step 3: Add masses

4500 g + 500 g = 5000 g

Step 4: Convert back to convenient unit

5000 g ÷ 1000 = 5 kg

Total mass = 5 kg
Final answer:

The total mass of Sarah's groceries is 5 kg.

Applied rules:

• Unit conversion: Convert to same unit before adding

• Addition: Add numerical values after unit conversion

• Final unit: Express final answer in appropriate unit

3 Unit conversion
Exercise 3
Convert 4.2 kg to grams and 7500 g to kilograms.
Definition:

Unit conversion: Changing from one unit to another while preserving the same quantity

Conversion factor: 1 kg = 1000 g

From kg to g
4.2 × 1000
From g to kg
7500 ÷ 1000
Results
4200 g & 7.5 kg
Step 1: Convert 4.2 kg to grams

To convert kg to g, multiply by 1000

4.2 kg × 1000 = 4200 g

Step 2: Convert 7500 g to kilograms

To convert g to kg, divide by 1000

7500 g ÷ 1000 = 7.5 kg

Step 3: Verify conversions

Check: 4200 g ÷ 1000 = 4.2 kg ✓

Check: 7.5 kg × 1000 = 7500 g ✓

4.2 kg = 4200 g and 7500 g = 7.5 kg
Final answer:

4.2 kg = 4200 g and 7500 g = 7.5 kg

Applied rules:

• Conversion rule: To convert kg to g, multiply by 1000

• Reverse rule: To convert g to kg, divide by 1000

• Verification: Always check conversions in reverse

Rules and methods, laws,...
1 kg = 1000 g
Kilogram to Gram Conversion
Mass Units
kg → g
Multiply by 1000
Mass Units
g → kg
Divide by 1000
Comparison
Same Units
Required for comparison
Key definitions:

Mass: The amount of matter in an object (measured in kg/g)

Weight: The force of gravity on an object (often confused with mass)

Kilogram (kg): Standard unit of mass in the metric system

Complete methodology:
  1. Identify units: Check what units are given and required
  2. Plan conversion: Determine if multiplication or division is needed
  3. Apply conversion: Use the factor 1000
  4. Verify result: Check if the answer makes sense
Tip 1: Remember: kilo means thousand, so 1 kg = 1000 g.
Tip 2: When converting larger to smaller units, multiply.
Tip 3: When converting smaller to larger units, divide.
Tip 4: Always check if your answer is reasonable.
Common errors: Forgetting to convert units, misplacing decimal points, confusing kg with g.
Memory aid: Think "kilo" as in "kilometer" = 1000 meters.
Formulas to know by heart:

• Conversion: 1 kg = 1000 g

• kg to g: multiply by 1000

• g to kg: divide by 1000

• Always use same units when comparing or adding masses

Solution: Exercises 4 to 5
4 Balance scale problem
Exercise 4
On a balance scale, 3 identical boxes balance with 2 kg. What is the mass of each box?
Definition:

Balance scale: Device showing equality of masses on both sides

Total mass
2 kg
Number of boxes
3
Each box
2÷3 kg
Step 1: Set up the equation

3 boxes = 2 kg

Step 2: Divide total mass by number of boxes

Mass per box = 2 kg ÷ 3 = 2/3 kg

Step 3: Convert to grams if needed

2/3 kg × 1000 = 2000/3 ≈ 666.67 g

Step 4: Verify the result

3 × (2/3 kg) = 2 kg ✓

Each box weighs 2/3 kg or approximately 666.67 g
Final answer:

Each box has a mass of 2/3 kg (approximately 666.67 g).

Applied rules:

• Division principle: Equal parts mean dividing total by number of parts

• Balance concept: Both sides of scale have equal mass

• Verification: Multiply back to check original condition

5 Real-world application
Exercise 5
A farmer harvested 15 kg of apples on Monday, 8.5 kg on Tuesday, and 12 kg on Wednesday. He sold 20 kg on Thursday. How much does he have left?
Definition:

Net mass: Remaining mass after additions and subtractions

Harvested
35.5 kg
Sold
20 kg
Remaining
15.5 kg
Step 1: Calculate total harvest

Monday + Tuesday + Wednesday = 15 + 8.5 + 12 = 35.5 kg

Step 2: Subtract sold amount

Remaining = 35.5 kg - 20 kg = 15.5 kg

Step 3: Verify calculation

Sold + Remaining = 20 + 15.5 = 35.5 kg ✓

Step 4: Express in smaller units if needed

15.5 kg × 1000 = 15,500 g

Farmer has 15.5 kg (or 15,500 g) of apples remaining
Final answer:

The farmer has 15.5 kg of apples remaining.

Applied rules:

• Addition: Combine all harvested amounts

• Subtraction: Subtract sold from total

• Verification: Check that parts add up to whole

Key Concepts for Mass and Kilograms
1 kg = 1000 g
Unit Relationship
Key definitions:

Mass: Amount of matter in an object, measured in kilograms (kg) or grams (g)

Kilogram (kg): Base unit of mass in the metric system

Gram (g): Smaller unit of mass, 1000 g = 1 kg

Complete methodology:
  1. Identify the problem: Determine what operation is needed (compare, convert, add, subtract)
  2. Check units: Ensure all measurements are in the same unit
  3. Perform calculations: Apply appropriate arithmetic operations
  4. Express answer: Provide result in the requested unit
Tip 1: Use a balance scale visualization to understand equality of masses.
Tip 2: Draw pictures of objects to visualize mass comparisons.
Tip 3: Practice with real objects like fruits or books to build intuition.
Tip 4: Remember that 1 kg feels heavy (about 2.2 pounds).
Real-world context: Mass is used in cooking, shopping, shipping, and science.
Common benchmarks: Paperclip ≈ 1 g, Liter of water = 1 kg, Small apple ≈ 100 g.
Formulas to know by heart:

• Conversion: 1 kg = 1000 g

• kg to g: multiply by 1000

• g to kg: divide by 1000

• Comparison: convert to same units first

• Addition/Subtraction: use same units

Questions & Answers

Question: I don't understand why we need to convert units when comparing masses. Why can't I just compare the numbers directly?

Answer: Great question! It's like comparing lengths in different units. If I say I'm 5 feet tall and my friend is 60 inches tall, we might think one is taller just by looking at the numbers (5 vs 60). But actually, 5 feet equals 60 inches, so we're the same height!

Similarly, with mass: 1 kg and 1000 g represent the same amount of matter. If we compared them just by numbers (1 vs 1000), we'd incorrectly think 1000 g is much bigger. Converting to the same unit ensures accurate comparison.

Example: 2 kg vs 1500 g → Convert 2 kg to 2000 g → Now we can correctly see 2000 g > 1500 g

Question: How do I remember whether to multiply or divide when converting between kg and g?

Answer: Use this simple rule: "Go big, go divide. Go small, go multiply!"

  • Going from big unit (kg) to small unit (g): MULTIPLY by 1000
  • Going from small unit (g) to big unit (kg): DIVIDE by 1000

Think of it this way: 1 kg is huge compared to 1 g. So 1 kg needs 1000 g to equal it. That's why 1 kg = 1000 g.

Examples:
• 3 kg to g: 3 × 1000 = 3000 g (multiply because going smaller)
• 4000 g to kg: 4000 ÷ 1000 = 4 kg (divide because going bigger)

Question: My child struggles with word problems involving mass. How can I help them break these problems down?

Answer: Try the "Read, Draw, Solve" method:

  1. Read: Have your child read the problem twice to understand what's happening
  2. Draw: Sketch the situation - draw objects, boxes, or scales to visualize
  3. Solve: Identify what's given and what's needed, then apply math operations

Also teach them to identify key words:
• "Total" or "altogether" often means addition
• "Left" or "remaining" often means subtraction
• "Each" or "per" often means division

Encourage your child to always check if their answer makes sense in the real world!