1) The product of 7 x 7 may be written as 72, 6 x 6 x 6 as 63, and 5 x 5 x 5 x 5 as 54. Let A = 25, B = 34, C = 43, and D = 52. Write A, B, C, and D in order of their values beginning with the smallest
value at the left. 2) The cost of mailing a letter firstclass is $0.29 for the first ounce and $0.23 for each additional ounce. A letter weighs exactly N ounces where N is a natural number, and the total mailing cost is $1.90. What is the value of N? 3) A group of 30 bikers went on a trip. Some rode bicycles and the others rode "tandems." (A tandem is a bicycle that is ridden by 2 people at the same time). If the total number of bicycles and tandems was 23, how many tandems were used? Solutions 1) A = 2 x 2 x 2 x 2 x 2 = 32; B = 3 x 3 x 3 x 3 = 81; C = 4 x 4 x 4 = 64; D = 5 x 5 = 25. Answer: D, A, C, B; or 52, 25, 43, 34; or 25, 32, 64, 81. 2) Since the cost of the first ounce was $0.29, the total cost of the remaining ounces was $1.61. Since the cost of each of the remaining ounces was $0.23 per ounce, the number of remaining ounces was $1.61/$0.23 = 7. The total number of ounces in the letter was 8. 3) If there were no tandems on the trip, only 23 people could have gone on the trip. Then 7 people of the 30 would have been left out. There must have been 7 tandems for the 7 extra people.
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Kindergarten: Students went around the room and counted various items and recorded the numeral to match. Students also solved a story problem and did a move it activity where they counted pennies. We also had a Number Talk based on the number 9.
1st Grade: Students did a move it activity where the practiced identifying even and odd numbers. They aslo practiced solving basic addition and subtraction facts using a color by number sheet. 2nd5th Grades: Practiced the basic facts that are on their level by completeing a color by number sheet. Some classes were able to do problem solving using the Thinking Blocks app on IPads. 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. Kindergarten: Students played a partner game like tictactoe where they practiced subitizing. 1st Grade: They completed a scavenger hunt around the room where they wrote the numeral to go with the base ten representation. 2nd5th Grades: They had a 24 tournament. Each class has a winner. The class winners will compete on Friday to find grade level winners. 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 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 at the right, 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. Kindergarten: The students practiced subitizing by counting the dots on dominoes and feeding them to the hungry trolls. We did a number talk using 9 and some problem solving on the Promethean Board. Students exercised while counting by 2s. Students also watched a video about pennies.
1st Grade: Students worked on place value by filling in a place value chart based on base ten blocks and writing a numeral to match. The students solved an addition story problem using Singapore Model Drawing. First graders also practiced counting by 2s while exercising and did a number talk based on ten frames. 2nd/3rd Grades: Students practiced the near double fact by doing a troll scavenger hunt. The students worked on their own level by choosing the troll character that challenged them a little but was attainable. They identified the double fact that could solve the given fact and solved the equation. Students used model drawing to solve story problems. 4th/5th Grades: Students practiced using the Double Double strategy for the 4 facts. Students challenged themselves by picking the troll character that would challenge them but was attainable. Students solved a multistep story problem using model drawing. 
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October 2017
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