34
Problem solving
Textbook: Part 1, lesson 34, pp. 105–107
GoalConvenient calculation and solving “times” and “more/less” problems with a diagram.
New words
convenient calculation · qulay hisoblashdiagram · sxematimes · martadifference · farq
Explanation
To multiply by 4 we multiply by 2 twice: 470 × 4 = 470 × 2 × 2 = 940 × 2 = 1 880. To multiply by 8 we multiply by 2 three times. Products such as 25 × 4 = 100 and 8 × 125 = 1 000 make work easy. For a diagram problem we draw the small part as one segment and the large part as several such segments, and see how many segments the difference equals.
Worked examples
25 × 247 × 4 = (25 × 4) × 247 = 100 × 247 = 24 700.
There are 18 fewer boys than girls, and 3 times fewer. The difference is 2 segments = 18, so 1 segment = 9 (boys) and the girls are 27. Altogether 36 children.
Class activity
“Segments”: children draw diagrams with segments for “times as many” and “how many more” problems and solve each other's problems.
Practice
1
Calculate 382 × 4 conveniently (multiply by 2 twice).
1528
2
Calculate 25 × 247 × 4 conveniently.
24700
3
Work out 375 × 8.
3000
4
In a dance club there are 18 fewer boys than girls and 3 times fewer. How many children are there in total?
36