A SELECTION OF PROBLEMS AND "CATCH"

QUESTIONS IN ARITHMETIC,

ARRANGED UNDER THE VARIOUS STANDARDS.

It is impossible to give such a selection of questions as will include every way in which an ingenious examiner can twist about even the four simple rules. The following problems are selected from inspectors' questions, and various test cards and arithmetics, and will at any rate be suggestive. Many different ways of stating the same problem may easily be made by a ready teacher, and if every new method of reasoning be fully explained, and the class be led, step by step, to see into it, the working of problems will become far more common than it is. This species of question is practical, and the correct working of such sums proves to an inspector that the work has been thorough, that children know the why and the wherefore of what they are doing. Hence most inspectors pass children who work a problem correctly, but who, having done the mechanical sums by a correct method, have made some slight "slip,' and so failed to get a correct answer. Children should be made to write, after each step of the working what it means, and not simply leave the figures without any word of explanation, as is too often the case, causing the inspector both annoyance and waste of time in trying to find out which is the answer. For instance, take the third sum in Standard II. It should be arranged thus on the paper :— 143 girls and infants 143 boys, same number

63 infants

80 girls

143 total girls and infants.

286 total in school.

To work a sum as above is sure to atone, in an inspector's eyes, for slight imperfections, such as bad figures, or an unfortunate blot on the paper, and is besides a proof of careful teaching.

Standard II.

If I am 10 years old, and my brother is 4 years older, find the sum of our ages. 24 years.

A boy had 50 marbles. He won 7 and afterwards bought 12 more. How many had he then? 69 marbles.

In a school there were 63 infants and 80 girls. The number of boys was just equal to the infants and girls put together. Find the total number of scholars in the school. 286 scholars.

If John was born in 1860, and William in 1874, how much older is John than William? 14 years.

A maid took 3 score eggs to market and sold 22. How many were left? 38 eggs.

A boy had 12 sums right. How many were wrong if he had done 15 sums? 3 wrong.

How many less than 53 is 39? 14.

How many must be added to 12 to make 100? 88.

If I were born in 1868, how old am I this year, 1877? 9 years. It is now 1878. Tell me in what year I was born if I am now 13 years old.

1865.

A farmer had thirty cows, half as many calves, and as many sheep as the cows and calves put together. How many had he in all? 90 animals.

I wanted to plant 67 dozen of potatoes, but found I only had 549. How many more did I require? 255 potatoes.

In walking 2,146 yards how often would a little girl step if each step measured half a yard.? 4,292 times. William had 100 marbles. how many had he left? 75

After giving a quarter of them away marbles.

Divide the product of the sum and difference of 98 and 57 by 5. 1,271.

My father is 50 years old, and my mother 5 years younger than my father. Find the sum of their ages. 95 years.

If you can buy 15 large nails for a halfpenny how many would you get for a shilling? 360 nails.

John has 60 marbles. If Henry had 24 more than John how many had they both together? 144 marbles.

If a shoemaker uses 47 nails in making 1 boot how many would he use in making 12 pairs? 1,128 nails.

How many legs have 40 dozen pigs? 1,920 legs.

How much greater is 6 times 9 than 5 times 5? 29.

Two numbers added together make 1,000. If one of the numbers is 90 what is the other? 910.

Divide 100 apples equally among 7 boys and 3 girls and tell me how many each will have. 10 each.

Tom has 89 marbles, Sam has nine times as many as Tom, and Joe has six times as many as both. How many has Joe? 4,806. How many times does a clock strike in 12 hours? 78 times. In a school there were 500 children. If 280 were boys and 120 were girls, find the number of infants. 100 Infants.

Divide ten thousand pounds among eight boys and girls, giving the girls twice as much as any of the boys. 625.

How often will a wheel 23 feet in circumference turn in a distance of 47,518 feet? 2,066 times.

What is the eighth part of 67,904? 8,488.

Find the eighth part of one-fourth of ten thousand. 312+4.

In what year will my father be 60 years of age if he were born in 1840? 1900.

How many dozen eggs are there in a hamper holding 18,504 ? 1,542 dozen.

If a boy walks 4,000 yards in 2 hours how many yards does he walk in half an hour? 1,000 yards.

If a man is able to

count 100 sovereigns per minute how many

should he count in 3 minutes? 350.

Standard III.

What sum must be added to £46 16s. 01d. to make a total of £3,004 16s.? £2,957 19s. 11ąd.

Subtract 1,209 farthings from the same number of pence, and give the answer in £. 8. d. £3 15s. 6d.

What amount must be taken from £505 1s. 10d. so as to leave £219 18s. 5d.? £285 3s. 5d.

Divide £2 3s. 9d. between Tom and Sam, and give Sam twice as much as Tom. What will be the share of each? Tom, 14s. 7d.; Sam, £1 9s. 2d.

Find the price of 98 dozen eggs @ 3 for 2d. £3 5s. 4d.

Divide the product of the sum and difference of 98 and 57 by 5. 1,271.

A family of father, mother, and two sons earn together £3 10s. Od. in a week. The mother earns 5s. 4d., and each of the sons 16s. 8d. What does the father earn in the week? £1 11s. 4d.

Add together 24 guineas, 38 threepences, 31 sixpences, and 7 florins.

£27 3s.

From a total of 337,380,104 shillings how many bags could be filled, the number required for each bag being 3,064? 110,111 bags. For how many days could 499 pounds per day be paid out of 7,504,960 pounds? 15,040 days.

If 39 towns contain a population of 196,053, what is the average number of people in each? 5027 each.

How many nineteens are there in 817? 43.

Add together one of each of the coins of the realm-gold, silver, and copper. £2 1s. 8 d.

If I put into a clothing club 64d. a week for a year, and receive at the end 30s., how much did I get as a bonus? 1s. 10d.

A man bought 100 eggs for 1s. 14d. per score and sold them @ 1d. each. How much did he gain? 2s. 6d.

A boy sold walnuts @ 8 a 1d., and received for them in a week £1 19s. 11d. How many did he sell? 3,832 walnuts.