1) The weight of a glass bowl and the marbles it contains is 50 ounces. If the number of marbles in the bowl is doubled, the total weight of the bowl and marbles is 92 ounces. What is the weight of the bowl? (Assume that each of the marbles has the same weight).
2) Square ABCD and rectangle AEFG each have an area of 36 square meters. E is the midpoint of AB. What is the perimeter of rectangle AEFG?
3) A slow clock loses 3 minutes every hour. Suppose the slow clock and a correct clock both show the correct time at 9 A.M. What time will the slow clock show when the correct clock shows 10 o'clock the evening of the same day?
1) Method 1: Since the weight of one bowl and the marbles it contains is 50 ounces, the weight of two bowls and twice as many marbles is 100 ounces. It is given that the weight of one bowl and twice as many marbles is 92 ounces. Then the difference of weights between 100 ounces and 92 ounces is the weight of the bowl, or 8 ounces.
Method 2: The increase in weight from 50 ounces to 92 ounces occurs because the weight of the marbles is doubled. That increase therefore is the weight of the original set of marbles, 42 ounces. If follows that the bowl weighs 8 ounces.
2) The length of a side of the square is 6m. The dimensions of rectangle AEFG are 3m and 12m. The perimeter of the rectangle is 2 x (3m + 12m) which is equivalent to 30 m.
3) There are 13 hours between 9 AM and 10 PM. Thus the slow clock will lose 13 x 3 or 39 minutes and show 9:21 or 21:21 on a 24-hour clock.
1) Suppose the time is now 2 o'clock on a twelve-hour which runs continuously. What time will it show 1,000 hours from now?
2) When a natural number is multiplied by itself, the result is a perfect square. For example, 1, 4, and 9 are perfect squares because 1 x 1 = 1, 2 x 2 = 4 and 3 x 3 = 9. How many perfect squares are less than 10,000?
3) A work team of four people completes half of a job in 15 days. How many days will it take a team of ten people to complete the remaining half of the job? (Assume that each person of both teams works at the same rate as each of the other people).
1) The time 2 o'clock is repeated every twelve hours. There are 83 twelves in 1,000 plus a remainder of 4. Therefore the clock will show a time of 6 o'clock 1,000 hours from now.
2) Since 10,000 = 100 x 100, each of the perfect squares 1 x 1, 2 x 2, 3 x 3, . . . , 99 x 99 is less than 100 x 100. There are 99 numbers in the above sequence.
3) Four people working 15 days is equivalent to one person working 60 days. To complete the other half of the job, ten people would have to work 6 days which is also equivalent to one person working 60 days.
The app, "MADS 24" is a great app for practicing the intermediate version of 24.
1) A chime clock strikes 1 chime at one o'clock, 2 chimes at two o'clock, 3 chimes at three o'clock, and so forth. What is the total number of chimes the clock will strike in a twelve-hour period?
2) A boy has the following seven coins in his pocket: 2 pennies, 2 nickels, 2 dimes, and 1 quarter. He takes out two coins, records the sum of their values, and then puts them back with the other coins. He continues to take out two coins, record the sum of their values, and put them back. How many different sums can he record at most?
3) The product of two numbers is 144 and their difference is 10. What is the sum of the two numbers?
1) Method 1: T, the total number of chimes, equals 1 + 2 + 3 + 4 + ... + 10 + 11 + 12. The sum of this series is 78.
Method 2: T = 1 + 2 + 3 + 4 + ... + 10 + 11 + 12
T = 12 + 11 + 10 + 9 + ... + 3 + 2 + 1
2T = 13 + 13 +13 +13 + ... + 13 + 13 + 13
Notice that the series on the second line is the reverse of the series on the first line. Each time we add a term and the corresponding term above, the sum is 13. then 2T is equal to 12 x 13 or 156. But 2T is twice the sum of the first series. Therefore, T = 78.
2) The following pairs of numbers represent the values of the two coins the boy could take from his pocket:
(1,1) (1,5) (1,10) (1,25)
(5,5) (5,10) (5,25)
Each of the above pairs has a sum that is different from the sum of each of the other pairs. Therefore there are 9 different sums.
3) Examine the pairs of whole number whose product if 144. The only pair that has a difference of 10 is 18 and 8. Their sum is 26.
Kindergarten: Different ways to represent numbers
1st Grade: Modeling 2 digit numbers with base ten blocks
2nd Grade: Doubles Plus 2 for Addition
3rd Grade: Compensation Strategy for Subtraction
4th Grade: Building Down when Multiplying by 9
5th Grade: Mental Math Division Strategies
Next week will be the first week I draw a winner for the Weekly 24 Challenge. I am excited and hope a lot of kids will participate!
Wish List: We use skinny dry erase markers in the lab constantly and are running low.