Study guide: Grade 8 Measurement and Geometry

📋 Course Outline

1. Measurement Units and Examples
2. Unit Conversion Rules
3. Perimeter of Shapes
4. Area of Two-Dimensional Shapes
5. Similar Shapes
6. Congruent Shapes

📖 1. Measurement Units and Examples

🔑 Key Concepts & Definitions

• Length: measures distance and uses millimetres (mm), centimetres (cm), metres (m), and kilometres (km).
• Mass: uses milligrams (mg), grams (g), and kilograms (kg).
• Capacity: measures how much a container can hold and uses millilitres (mL) and litres (L).

📝 Essential Points

• Time is measured in seconds, minutes, and hours.

• Examples of measurements are:

  • 3 m for length
  • 2,5 kg for mass
  • 750 mL for capacity
  • 45 minutes for time

💡 Memory Hook

L-M-C-T: length, mass, capacity, time

📖 2. Unit Conversion Rules

★ Must-know

📌 When converting from a big unit to a small unit, multiply; when converting from a small unit to a big unit, divide.

• The length conversion relationships are:
  • 1 km = 1 000 m
  • 1 m = 100 cm
  • 1 cm = 10 mm

Further detail

• The mass conversion relationships are 1 kg = 1 000 g and 1 g = 1 000 mg.

• The capacity conversion relationship is 1 L = 1 000 mL.

• The time conversion relationships are:

  • 1 hour = 60 minutes
  • 1 minute = 60 seconds
  • 1 day = 24 hours

• Examples of conversions are:

  • 2,5 km = 2 500 m
  • 450 cm = 4,5 m
  • 3,2 L = 3 200 mL

💡 Memory Hook

Big → small means multiply; small → big means divide

📖 3. Perimeter of Shapes

🔑 Key Concepts & Definitions

• Perimeter: the distance around the outside of a shape.

★ Must-know

📐 Formula — The perimeter of a rectangle is $P = 2(l + w)$, where l is the length and w is the width.

📐 Formula — The perimeter of a square is $P = 4 \times \text{side}$.

Further detail

📐 Formula — The perimeter of a triangle is $P = a + b + c$.

• A rectangle with l = 8 cm and w = 5 cm has perimeter $P = 2(8 + 5) = 26\text{ cm}$.

💡 Memory Hook

Walk around the outside edge of the shape

📖 4. Area of Two-Dimensional Shapes

🔑 Key Concepts & Definitions

• Area: the amount of space inside a two-dimensional shape.

★ Must-know

📐 Formula — The area of a rectangle is $A = \text{length} \times \text{width}$, and the area of a square is $A = \text{side} \times \text{side}$.

📐 Formula — The area of a triangle is $A = \frac{1}{2} \times \text{base} \times \text{perpendicular height}$.

Further detail

• Examples of squared area units are:

  • cm²
  • m²
  • km²

• A triangle with base 10 cm and height 6 cm has area $A = \frac{1}{2} \times 10 \times 6 = 30\text{ cm}^2$.

💡 Memory Hook

Fill the inside of the shape with square tiles

📖 5. Similar Shapes

🔑 Key Concepts & Definitions

• Similar Shapes: Similar shapes have the same shape, equal corresponding angles, and corresponding sides in the same ratio, but they do not have to be the same size.

📝 Essential Points

• For similar shapes, corresponding angles are equal and corresponding side lengths are in the same ratio.

💡 Memory Hook

Similar shapes have the same shape, not necessarily the same size

📖 6. Congruent Shapes

📝 Essential Points

• Congruent shapes remain congruent when they are:
  • rotated
  • flipped
  • moved

📌 Similar means the same shape, while congruent means exactly the same size and shape.

💡 Memory Hook

Similar means same shape; congruent means same shape and same size

📊 Synthesis Tables

Similar and Congruent Shapes

Property	Similar shapes	Congruent shapes
Shape	Same shape	Same shape
Size	Not necessarily the same size	Same size
Corresponding sides	In the same ratio	Equal
Corresponding angles	Equal	Equal