the 345 hundreds, leaving a remainder of 42 hundreds. Bring down the 7 tens. Proceed in this manner until the units' figure is obtained. ل 1. In a record flight an aviator traveled in an aeroplane a total distance of about 1320 miles in 24 hours. Find the average speed in miles per hour for this trip. 2. The fastest steamships now cross the Atlantic Ocean, a distance of about 3000 miles, in 5 days. Find the average number of miles per hour traveled by these fast ocean steamships. 3. The yearly rent of a house is $420. What is the rent per month? 4. A class of 25 children together had a sleighing party which cost $5.00. How much did each one have to pay, the expenses being shared equally? 5. There are 324 children in a 12-room school. This is an average of how many in each room? 6. In a 21-room school there are 945 children. This is how many in a room? Compare the quotient in each example with the dividend. We find from the above examples that dividing a number ending in zero by 10 merely cancels off the last zero. Show a short method of dividing a number ending in two zeros by 100; of a number ending in three zeros by 1000. 1. Divide 160 by 40. Divide (160÷10) by (40÷10). How do the two quotients compare? 2. Divide 2800 by 400. Divide (2800÷100) by (400÷100). Compare the two quotients. These examples show that both dividend and divisor can be divided by the same number without changing the quotient. 3. Divide 720 by 90, using the short form. 8 9Q)720 Dividing both the dividend and divisor by 10 merely cancels off a zero from each, leaving 72 ÷ 9, a short division problem. 4. Divide 8400 by 700. 12 700)8400 Dividing both dividend and divisor by 100 merely cancels off two zeros from each. The problem then becomes 847, a short division problem. 5. Divide 144000 by 9000 in a similar way. Perform the following by short division: Exercise 37 Divide each number in each of the following lists by its corresponding divisor in the first column: Addition, Subtraction, Multiplication, Division To the Teacher: These exercises are prepared for use as rapid drill exercises, one of which should be given at the opening of each arithmetic recitation. The following time limits should be used for each exercise: 3888 Grade Fifth 2 min. Sixth 2 min. 2 min. 3 min. 3 min. 3 min. The use of the three time limits allows for the individual differences which exist in every class and provides an incentive for the rapid workers as well as the slow ones. Each exercise should be accurately timed with a watch, the teacher announcing the three time limits in succession as 2 min. ....3 min.....34 min. Have each pupil indicate by E, G or F the time in which he finishes the exercise. Some of the exercises can be conveniently done by placing a strip of paper under the problems in the book and writing the answers on it. The exercises which contain several rows of problems can be more conveniently done by folding a piece of paper into as many strips as there are rows of problems and unfolding as the successive rows of answers are written. Some exercises such as those in long division should be copied or mimeographed in order to give plenty of room for working the examples. A record should be kept for each pupil, showing in what time limit he finished each exercise and how many errors were made. In exercises not completed, the number of problems correctly worked should be indicated. Work for the E time limit and 100% accuracy. Pupils who are especially slow should be given special help after their difficulties have been diagnosed. For example-if a pupil is slow in column addition, the teacher should attempt to diagnose the difficulty. First see if he knows the 45 combinations so that he can give the results rapidly. If not, he should be drilled on them. A pupil may know the 45 combinations, but not know how to add by endings. Have him add a long column and see if he fails in that important step in addition. If that is his difficulty, the special help should be given on adding by endings rather than more drill on the combination. |