1) The numbers 2, 4, 6, and 8 are a set of four consecutive even numbers. Suppose the sum of five consecutive even numbers is 320. What is the smallest of the five numbers?
2) Twelve people purchased supplies for a tenday camping trip with the understanding that each of the twelve will get equal daily shares. They are then joined by three more people, but make no further purchases. How long will the supplies then last if the original daily share for each person is not changed? 3) Amy can mow 600 square yards of grass in 1 1/2 hours. At this rate, how many minutes would it take her to mow 600 square feet? Solutions 1) Method 1: The middle number of an odd number of consecutive numbers is always the average of the set. Then the average of the numbers is 320/5 or 64 which also is the third or middle number. Count back by twos. The required number is 60. Method 2: Represent the middle number by n. Then the five consecutive even numbers are n  4, n  2, n, n + 2, and n + 4. The sum of the five numbers is 5n. Since 5n = 320, n = 64. Thus n  4, the first number, is 60. 2) Since each person of the original group had 10 daily shares, the total supplies are equivalent to 120 daily shares. When 3 people join the group, the total number of people becomes 15. Then each person in the new group will have 120/15 or 8 daily shares. The supplies will last 8 days. 3) Method 1: 1 square yard = 9 square feet. Then 600 square yard = 600 x 9 square feet. Since 600 square feet is 1/9 of 600 x 9 square feet, the time needed to mow 600 square feet is 1/9 of the time required to mow 600 square yard. Therefore, 1/9 of 1 1/2 hours is 1/9 x 3/2 = 1/6 hour or 10 minutes. Method 2: Since 9 square feet = 1 square yard, 1 square foot = 1/9 square yard. Then the time needed to mow 1 square foot is 1/9 of the time needed to mow 1 square yard. Therefore, 600 square feet will require 1/9 of 1 1/2 hour or 1/6 hour or 10 minutes.
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Primary Cards:
1 Dot: Which of these make 6: 3 and 3 or 4 and 11? How? 2 Dots: Which of these make 6: 8, 11, and 1 or 10, 3, and 7? How? 3 Dots: Which of these make 24: 11, 17, and 14 or 20, 5, and 9? How? Intermediate Cards: How can you make 24 using all 4 numbers once? 1 Dot: 7, 8, 5, and 1 2 Dots: 6, 1, 3, and 6 3 Dots: 8, 5, 8, and 2 1) A bicyclist wants to make a 600mile trip on his twowheel bicycle. He has a spare wheel which is used to replace either of the other two wheels. Suppose each of the three wheels is to have the same mileage for the trip. How many miles should each wheel travel?
2) How many even numbers between 1 and 101 are multiples of 3? 3) In the subtraction problem below, all five of the digits 3, 5, 6, 7, and 9 are to be placed, one in each box. What is the smallest difference that can be the result? Solutions 1) No matter which two wheels are actually used at any time during the 600mile trip, the total miles traveled by those wheels together is 1200 miles. Since three wheels are to share that total equally, each will travel 400 miles. 2) The even multiples of 3 are 6, 12, 18, . . . The largest multiple of 6 less than 101 is 16 x 6 = 96. Multiples of 6 less than 101 are: 1 x 6, 2 x 6, 3 x 6, 4 x 6, . . . , 16 x 6. There are 16 even multiples of 3 between 1 and 101. 3) Make the 3digit number as small as possible and the 2digit number as large as possible, as shown at the right. The smallest possible difference is 259. 3 5 6  9 7 2 5 9 Primary:
1 Dot: Could you make 4 using 4 and 8 or 1 and 4? How? 2 Dots: Could you make 10 using 5, 3, and 1 or 6, 7, and 11? How? 3 Dots: Could you make 24 using 16, 6, and 4 or 13, 7, and 4? How Intermediate: 1 Dot: How can you make 24 using 1, 7, 2, and 6? 2 Dots: How can you make 24 using 8, 2, 4, and 9? 3 Dots: How can you make 24 using 7, 5, 4, and 5? Primary:
1 Dot: Which will make 9: 6 and 5 or 10 and 1? How? 2 Dots: Which will make 3: 10, 12, and 1 or 10, 9, and 5? How? 3 Dots: Which will make 24: 16, 6, and 4 or 13, 7, and 4? How? Intermediate: 1 Dot: How can you make 24 using 4, 7, 8, and 5? 2 Dots: How can you make 24 using 6, 8, 7, and 5? 3 Dots: How can you make 24 using 6, 4, 4, and 2? We were able to accomplish a lot in October including our first 24 Math tournament for 2nd5th graders. The Math Lab received 13 iPads at the end of last week and they are now set up and ready to be used to enhance the lessons we are doing in the lab. Thank you to all the parents for their generosity and to the foundation for their hard work in making this happen for our Pirates!
Here is what we are working on in the lab in November in addition to problem solving and writing constructed responses to go with our problem solvers. Kindergarten: Decomposing(breaking numbers apart) 1st Grade: We will continue to look at 10 more, 10 less, 1 more, and 1 less on a hundreds chart 2nd Grade: Adding double facts and near double facts 3rd Grade: Subtracting double facts and near double facts 4th Grade: Double, double again when multiplying by 4 and Double, double, double a third time when multiplying by 8 5th Grade: Finish up dividing by 8 by Half, half again, half a third time and start working on adjusting both the dividend and divisor to make an easier division problem. 1) I have exactly ten coins whose total value is $1. If three of the coins are quarters, what are the remaining coins?
2) A group of 21 people went to the county fair with 9 people on a stagecoach and 3 people in a buggy. On the return trip, 4 people rode in each buggy. How many people returned on the stagecoach? 3) In the addition problem below, each letter stands for a digit and different letters stand for different digits. What digits do the letters H, E, and A each represent? H E H E H E + H E A H Solutions 1) We have to find 7 coins whose value is $0.25. If the coins were nickels, their total value would be too large. There must be at least 5 pennies. Then we need two coins whose value is $0.20. The coins are dimes. Therefore the remaining coins are 5 pennies and 2 dimes. 2) Going to the fair, 12 people rode in the buggies. Since 3 people rode in each buggy, there were 4 buggies. On the return trip, 4 people rode in each buggy. Then 16 people rode in the buggies. Since the total number of people was 21, 5 rode in the coach. 3) In the tens column, H is less than 3. Otherwise the sum would be a threedigit number. H = 1 or 2. In the units column, the sum of 4 Es is an even number. Then H in the sum must be 2. It follows that E must be either 3 or 8. If E = 8, the sum will be a threedigit number. Thus E = 3, H = 2, and A = 9. 
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June 2019
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