Mass (Term 3) Chapter Notes | Mathematics for Grade 6 PDF Download

Mass

Understanding Mass

What is Mass?

• Mass is a measure of how heavy an object is, not its size or length.
  Example: A 1 kg packet of sugar and a 1 kg packet of flour have the same mass (heaviness) but may differ in size due to density.
• Mass is measured in kilograms (kg), the SI unit, or grams (g) for smaller quantities.
  1 kg = 1000 g.
  Example: 1 litre of pure water has a mass of about 1 kg (1000 g).

Units of Mass

• Kilograms (kg): Used for heavier objects like people, schoolbags, or bags of dog food.
  Example: A schoolbag has a mass of about 3 kg.
• Grams (g): Used for lighter objects like a box of matches or an apple.
  Example: A box of matches has a mass of about 3 g.

Conversions:

• 500 g = 1/2 kg = 0.5 kg.
• 250 g = 1/4 kg = 0.25 kg.
• 100 g = 1/10 kg = 0.1 kg.
• 50 g = 1/20 kg = 0.05 kg.

• 2.5 kg = 2 and 1/2 kg = 2 kg + 500 g.

Measuring Mass

• Bathroom scales: Used for larger masses, like a person’s mass (up to 120 kg).
• Kitchen scales: Used for smaller masses, like food items (up to 5 kg).
• Balance scales: Compare masses directly.
• Estimates: Approximate masses are described as “about” a certain value.

Example: A cupful of water (250 ml) has a mass of about 250 g.

Comparing Mass Measurements

Comparing Masses

• Objects with the same mass can differ in size due to differences in density.
  Example: A 1 kg packet of sugar and a 1 kg packet of flour have the same mass but different sizes because sugar is denser.
• Comparing masses involves ordering from heaviest to lightest or finding relationships.
  Example: If Packet A is 1 kg and Packet B is 500 g, two Packet Bs equal one Packet A in mass.
  Packet B is 1/2 the mass of Packet A.
  A packet with 500 g is 1/2 the mass of Packet A.
  A packet with 2.5 kg is 2 and 1/2 times the mass of Packet A.

Fractions and Decimals
Masses can be expressed as fractions or decimals of a kilogram:

• 1/4 kg = 0.25 kg = 250 g.
• 1/2 kg = 0.5 kg = 500 g.
• 3/4 kg = 0.75 kg = 750 g.
• 2 and 1/2 kg = 2.5 kg = 2500 g.
• 1 and 1/2 kg = 1.5 kg = 1500 g.

This helps compare masses of items like sugar, rice, or textbooks.

Reading Mass in Grams and Kilograms

Reading Scales
Scales show mass in kilograms or grams, with marked intervals (e.g., 0.1 kg or 10 g).
To read a scale:
Identify the major and minor intervals.
Estimate if the pointer is between marks.
Example: A scale showing 2.8 kg means 2 kg + 0.8 kg (800 g).

Converting readings:

• 2.8 kg = 2.8 × 1000 = 2800 g.
• 1.5 kg = 1.5 × 1000 = 1500 g.

Rounding Masses
Round to the nearest kilogram for estimates:
Example: 2.8 kg ≈ 3 kg; 1.5 kg ≈ 2 kg.

Common fraction notation:

• 0.25 kg = 1/4 kg.
• 0.5 kg = 1/2 kg.
• 0.75 kg = 3/4 kg.

Converting to grams:

• 0.25 kg = 250 g.
• 0.5 kg = 500 g.
• 0.75 kg = 750 g.

Conversions
Kilograms to grams:

• 2.8 kg = 2800 g.
• 0.5 kg = 500 g.
• 1.5 kg = 1500 g.
• 20 kg = 20,000 g.
• 60 kg = 60,000 g.

Grams to kilograms:

• 2000 g = 2000 ÷ 1000 = 2 kg.
• 250 g = 0.25 kg.
• 100 g = 0.1 kg.
• 750 g = 0.75 kg.
• 5500 g = 5.5 kg.
• 3250 g = 3.25 kg.

Solving Problems About Mass and Quantity

This section applies mass concepts to practical scenarios.

Calculating Masses

Proportional masses:
Example: If 500 paper clips have a mass of 1 kg, then:
50 paper clips = 1 kg ÷ 10 = 0.1 kg = 100 g.
10 paper clips = 100 g ÷ 5 = 20 g.
1 paper clip = 1000 g ÷ 500 = 2 g.

Example: If 30 oranges weigh 5 kg, then:
15 oranges = 5 kg ÷ 2 = 2.5 kg.
5 oranges = 5 kg ÷ 6 = 5/6 kg ≈ 0.833 kg.

1 orange = 5 kg ÷ 30 = 1/6 kg ≈ 0.167 kg.

Variations exist (e.g., not all paper clips or oranges have identical masses).

Cost Calculations
Mass-based pricing:
Example: Onions cost R12 per kg. If 1 onion is 150 g (0.15 kg):
2000 g (2 kg) = 2 × R12 = R24.
300 g (0.3 kg) = 0.3 × R12 = R3.60.
1 onion (0.15 kg) = 0.15 × R12 = R1.80.

Animal and Food Masses
Comparing animal masses:

• Duck (2.8 kg) - Pigeon (0.5 kg) = 2.3 kg heavier.
• Duck (2.8 kg) - Chicken (1.9 kg) = 0.9 kg heavier.

Food consumption:

• Pigeon eats 500 g (equal to its 500 g mass).
• Duck eats 280 g (1/10 of 2.8 kg = 2800 g).
• Pig eats 4000 g (1/50 of 200 kg = 200,000 g ÷ 50 = 4000 g).

Feeding Calculations
Example: 27 puppies need food from 2 to 6 months:
2 months: 355 g per day.
3 months: 475 g.
4–6 months: 525 g, then 530 g.
Total food and costs:
Food is bought in 25 kg bags costing R189.90 each.
150 kg costs 150 ÷ 25 = 6 bags × R189.90 = R1139.40.

Points to Remember

• Mass measures heaviness: It tells how heavy an object is, not its size or length (e.g., 1 kg sugar = 1 kg flour in mass, but sizes differ).
• Units: Use kg for heavier items (e.g., schoolbag ≈ 3 kg), g for lighter items (e.g., matches ≈ 3 g). 1 kg = 1000 g.
• Scales: Bathroom scales for people (up to 120 kg), kitchen scales for food (up to 5 kg).
• Conversions: 500 g = 1/2 kg = 0.5 kg; 250 g = 1/4 kg = 0.25 kg. Example: 2.8 kg = 2800 g.
• Fractions and decimals: Masses can be fractions (e.g., 1/4 kg) or decimals (e.g., 0.25 kg).
• Estimates: Use “about” for approximate masses (e.g., 250 ml water ≈ 250 g).
• Proportions: If 30 oranges = 5 kg, 1 orange ≈ 0.167 kg.
• Applications: Calculate costs (e.g., 2 kg onions at R12/kg = R24) or food needs (e.g., 27 puppies need 150 kg food).

Difficult Words

• Mass: How heavy an object is, measured in kg or g (e.g., a schoolbag’s mass is about 3 kg).
• Kilogram (kg): The SI unit for mass; 1 kg = 1000 g (e.g., 1 litre of water ≈ 1 kg).
• Gram (g): A smaller unit for mass; 1000 g = 1 kg (e.g., a matchbox ≈ 3 g).
• Density: How tightly packed a material is, affecting size for the same mass (e.g., sugar is denser than flour).
• Bathroom scale: A device for measuring larger masses, like a person’s (up to 120 kg).
• Kitchen scale: A device for measuring smaller masses, like food (up to 5 kg).
• Estimate: An approximate measurement, described as “about” (e.g., a cupful of sugar ≈ 250 g).
• Fraction: A part of a whole, used for mass (e.g., 500 g = 1/2 kg).

Summary