1) Suppose the time is now 2 o'clock on a twelvehour 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). Solutions 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 twelvehour 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? Solutions: 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) (10,10) (10,25) 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. For Primary Cards: Choose the side that you can use the numbers to equal the number in the middle.
For Intermediate Cards: Make 24 using all 4 numbers once and only once. Turn in your answers for a chance to win a weekly prize 1) A motorist made a 60mile trip averaging 20 miles per hour. On the return trip, he averaged 30 miles per hour. What was the motorist's average speed for the entire trip?
2) 100 pounds of chocolate is packaged into boxes each containing 1 1/4 pounds of chocolate. Each box is then sold for $1.75. What is the total selling price for all of the boxes of chocolate? 3) In the multiplication problem below, A and B stand for different digits. Find A and B. A B x B A 1 1 4 3 0 4 3 1 5 4 Solutions: 1) The average speed for any trip is the total distance divided by the total time spent in traveling. The total distance was 120 miles and the total time was 5 hours. The average speed equals (120 miles)/(5 hours) or 24 miles/hour or 24 mph. 2) We need to know the number of boxes that were packaged in order to find the total selling price. The number of boxes is obtained by dividing 100 by 1 1/4: 100 divided by 5/4 = 100 x 4/5 = 80. 3) The first partial product 114 is equal to the product of AB and A. The second partial product 304 is equal to the product of AB and B. Then A must be less than B. Method 1: Since the product of AB and A is 114, A is a divisor of 114. Therefore A may be 2, 3, or 6. Since AB x A = 114, A cannot be 2 because AB x A would then be less 60. Similarly, A cannot be 6 since AB x A would then be greater than 360. Therefore A must be 3 and AB must be 114/3 or 38. Thus A = 3 and B = 8. Method 2: From the first partial product, observe that B x A must end in 4. Since A is less than B, A = 2 and B = 7, or A = 3 and B = 8, or A = 4 and B = 6. But 27 x 2 = 54, 46 x 4 = 184, and 38 x 3 = 114. Only the third equation satisfies the given conditions. So A = 3 and B = 8. Method 3: From the second partial product 304, we see that B x B ends in 4. Then B = 2 or 8. If B =2, then A must be 1 because A is less than B. But 12 x 21 = 252. If B = 8 and AB x B = 304, then AB = 304/8 or 38 and 38 x 83 = 3154. Therefore A = 3 and B = 8. it. Primary:
1 Dot: Can you make 4 using 7 and 11 or 6 and 11? How? 2 Dots: Can you make 3 using 8/11/7 or 2/12/7? How? 3 Dots: Can you make 24 using 8/9/21 or 17/14/7? How? Intermediate: 1 Dot: How can you make 24 using 2, 4, 8, and 4? 2 Dots: How can you make 24 using 1, 9, 4, and 7? 3 Dots: How can you make 24 using 2, 3, 5, and 3? 1) Five brothers, each born in a different year, share a gift of $100 according to the following arrangement: each boy, except the youngest, gets $5 more than his next younger brother. How much does the youngest boy get?
2) When I open my math book, two pages face me and the sum of the two page numbers is 317. What is the number of the very next page? 3) 6, 14, and 15 are factors of the natural numbers N. What is the smallest value that N can have? Solutions: 1) Method 1: The average amount received by the 5 boys is $20. In order of age, the third boy receives the average amount of $20. The youngest receives $10 less than the third boy. Therefore, the youngest receives $10. Method 2: Let Y represent the amount received by the youngest boy. Then the amounts received are Y, Y + 5, Y + 10, Y + 15, and Y + 20. These amounts can be regrouped and totaled as Y + Y + Y +Y + Y + 5 + 10 + 15 + 20, or more simply as 5Y + 50. Then, 5Y + 50 = 100, 5Y = 50, and Y = 10. The youngest receives $10. 2) The average of the two consecutive page numbers is 317/2 = 158.5. Then the page numbers are 158 and 159, with 159 being the number of the righthand page. The next page number is 160. 3) Method 1: The LCM of a set of numbers is the smallest number N which each number of the set will divide exactly. LMC(6,14,15) = 210. Method 2: List the prime factors of each of the given factors of N: 6 = 2 x 3; 14 = 2 x 7, 15 = 3 x 5. N must have 2, 3, 5, and 7 as factors. Then N = 2 x 3 x 5 x 7 = 210. 
AuthorMrs. Lovett Archives
January 2019
Categories
All
