Measurement, Money, Percentage & Data
1. Measurement — Length, Weight, Capacity
Length
- 1 km = 1,000 m. 1 m = 100 cm. 1 cm = 10 mm.
Weight (Mass)
- 1 kg = 1,000 g. Light things in grams. Heavy things in kilograms.
Capacity (Volume)
- 1 L = 1,000 mL. Liquids: water, milk, oil, juice.
Practice
- Convert: 5 m = ___ cm (500 cm)
- How many grams in 3 kg? (3,000 g)
- A water bottle holds 750 mL. How many bottles fill a 3 L jug? (4 bottles)
2. Time
Reading Clocks
- Analog: Hour hand (short). Minute hand (long). Second hand (thin, fastest).
- 12-hour (AM/PM). 24-hour (military time: 14:00 = 2:00 PM).
Time Duration
- 'A movie starts at 2:30 PM and ends at 5:00 PM. Duration = 2 hours 30 minutes.'
Conversions
- 1 hour = 60 min. 1 min = 60 s. 1 day = 24 hours. 1 year = 365 days (leap: 366).
3. Money — Rupees and Paise
- ₹1 = 100 paise.
- Notes: ₹10, ₹20, ₹50, ₹100, ₹200, ₹500.
Bills and Shopping
- Add items. Calculate change. 'How much will you pay? How much change will you get?'
Profit and Loss
- Profit = SP — CP (when sold for MORE than bought). Loss = CP — SP (when sold for LESS).
4. Percentage
Percent = 'Per hundred.' Written as %. To find % of a number: (% / 100) × Number. Example: 25% of 200 = (25/100) × 200 = 50.
Conversions
- Fraction → %: Multiply by 100. 3/5 = 60%.
- % → Fraction: Write over 100. Simplify. 75% = 75/100 = 3/4.
5. Averages
Average = Sum of all values / Number of values. 'The average of 12, 18, and 24 = (12+18+24)/3 = 18.'
6. Data Handling — Reading Graphs
Bar Graph
Bars of different HEIGHTS. TALLER = MORE. Read the scale carefully. 'Each unit on the y-axis represents how many?'
Pictograph
Uses symbols/pictures. Example: 😊 = 10 students. 'Half a face = 5 students.'
Tally Marks: |||| = 4. |||| = 5.
7. Number Patterns and Symmetry
Number Patterns
- Triangular numbers: 1, 3, 6, 10, 15... (Add 2, then 3, then 4, then 5...)
- Square numbers: 1, 4, 9, 16, 25... (1², 2², 3², 4², 5²...)
Symmetry
A shape has LINE SYMMETRY if one half is a MIRROR IMAGE of the other. The fold line = line of symmetry. Square: 4 lines. Rectangle: 2. Equilateral triangle: 3. Circle: INFINITE.
