112
Problem solving
Textbook: Part 4, lesson 112, pp. 13–15
GoalProblems about symmetry: area of symmetric shapes, sectors, patterns.
New words
pattern · naqshhalf · yarmicopying · nusxa ko‘chirishsector · sektor
Explanation
If half of a symmetric shape is known, the whole area is twice that. When a circle is split into equal sectors, the sectors have equal area. A common way to make a pattern is to draw one part and copy it into the others. In a problem we decide what to find and draw a diagram.
Worked examples
Half of a symmetric shape is 18 squares: the whole shape is 18 × 2 = 36 squares, that is 36 cm².
A circle is split into 8 equal sectors and one has area 30 cm². Five sectors have area 30 × 5 = 150 cm².
Class activity
“Pattern maker”: children draw an 8 × 8 square on squared paper and split it into 4 quarters with two axes. They draw a pattern in one quarter and reflect it across the axes into the other quarters. Then they count the coloured squares and write what fraction of the square they are.
Practice
1
Half of a symmetric shape is 18 squares (1 square = 1 cm²). What is the area of the whole shape in cm²?
36
2
A symmetric pattern covers 16 squares of an 8 × 8 square. What fraction of the square is that?
16/64
3
A circle is split into 8 equal sectors and one sector has area 30 cm². What is the area of 5 sectors in cm²?
150
4
One square is cut from each of the four corners of a square with side 6 squares. How many squares are left in the shape?
32
5
A symmetric butterfly picture has 7 dots on its left wing and 3 dots on its body. How many dots are there in the whole picture?
17