77
How units of area are related
Textbook: Part 3, lesson 77, pp. 28–30
GoalHow all units of area are related: each neighbouring unit differs by a factor of 100; calculating with mixed areas.
New words
relationship · bog‘lanishpatch, piece · parchacovering · qoplashpatchwork quilt · quroq ko‘rpa
Explanation
The chain of units of area: mm² → cm² → dm² → m² → are → hectare. Each step changes the number by a factor of 100. So 1 m² = 100 dm² = 10 000 cm² = 1 000 000 mm², and 1 a = 100 m² = 10 000 dm². From big to small multiply by 100; from small to big divide by 100. For several steps multiply 100 by itself: 2 steps – 10 000, 3 steps – 1 000 000.
Worked examples
2 m² = 200 dm² = 20 000 cm²; 50 000 cm² = 500 dm² = 5 m².
A carpet 150 cm × 200 cm: 150 × 200 = 30 000 cm² = 3 m².
Class activity
“Patchwork quilt”: children cut 10 cm × 10 cm paper squares and find how many pieces make 1 dm² and how many make 1 m².
Practice
1
3 m² = ? cm²
30000
2
600 000 mm² = ? dm²
60
3
4 a = ? dm²
40000
4
A quilt is 160 cm × 200 cm. How many square patches with side 10 cm are needed to make it?
320
5
A sheet measures 3 m × 2 m. What is its area in dm²?
600