1) A tractor wheel is 88 inches in circumference. How many complete turns will the wheel make in rolling one mile on the ground? (1 mile = 5,280 feet)
2) In the addition problem below, each letter represents a digit and different letters represent different digits. What four-digit number does D E E R represent?
+ R I D
D E E R
3) Alice and Betty run a 50-meter race and Alice wins by 10 meters. They then run a 60-meter race, and each girl runs at the same speed she ran in the first race. By how many meters will Alice win?
1) When the wheel makes one complete turn, it has rolled a distance of 88 inches. The number of turns equals 1 mile divided by 88 inches
(1 mile = 5280 feet = 5280 x 12 inches).
Dividing yields 5280 x 12 inches = 720
2) D in the sum DEER must be 1. The R in the second addend must be 9. It follows that E must be 0 and DEER represents 1009.
3) Method 1
Alice runs 50m in the same time that Betty runs 40m. Thus Alice runs 5m for every 4m that Betty runs. Therefore in the 60m race, Alice will run 12 x 5m or 60m, and Betty will run 12 x 4 = 48m. So Alice wins by 12m.
Since Alice wins the 50m race by 10m, Alice must gain 2m over Betty for every 10m that Alice runs. Therefore, in a 60m races, Alice will gain 6 x 2m or 12m.
I am amazed at how much growth I have seen in our Pirates this year and know that they are going to do a great job on the upcoming Milestones! To help students be as prepared and confident as possible I will be doing some test prep lesson in Math Lab with 3rd-5th graders. We will work on some test taking strategies, practice another type of constructed response, and look at some words that they might encounter on the test and what they mean(see picture below for the 12 Powerful Words).
I am going to start working with 1st and 2nd graders on writing constructed responses using a graphic organizer this month. 1st and 2nd graders will also be working on addition strategies.
Kindergarten will continue to work on addition and number sense using manipulatives. PTA bought us a class set of Rekenreks recently and the students are getting a lot of number sense and addition practice on them. They are great for working with the benchmark numbers of 5 and 10!
I hope to have information about the 2019-2020 Math Olympiad team some time this month. I am looking for feedback on next year's shirt, the survey can be found here. The team will be open to 4th and 5th graders.
1) When certain numbers are placed in the empty boxes, the sum of the three numbers in each of the three rows, three columns, and two diagonals is the same. What number should be placed in the center box?
2) I am less than 6 feet tall but more than 2 feet tall. My height in inches is a multiple of 7 and is also 2 inches more than a multiple of 6. What is my height in inches?
3) The square below is divided into four congruent rectangles. The perimeter of each of the four congruent rectangles is 25 units. How many units are there in the perimeter of the square?
1) Since the sum of the three numbers in each diagonal is the same, and since they have the same middle number, the sum of each pair of numbers in opposite corners must be the same: 9 + 13 = 5 + ?. Clearly ? = 17. The bottom row now has a sum of 33. The middle number must be 11.
2) List multiples of 7 greater than 24 and less than 72. Also list the multiples of 6 which are less than and closest to each of the corresponding multiples of 7.
3) Each of the four congruent rectangles has a perimeter equivalent to 2 1/2 sides of the square. Since the length of 2 1/2 sides = 25 units, then, by doubling, we get the length of 5 sides = 50 units. Clearly, the length of one side is 10 units. Therefore the perimeter of the square is 40 units.
I would love some input for next year's Math Team T-Shirt, especially from current 3rd and 4th graders. Here is a link to a quick survey.
1) Suppose the counting numbers from 1 through 100 are written on paper. What is the total numbers of 3s and 8s that will appear on the paper?
2) In the "magic-square" below, five more numbers can be placed in the boxes so that the sum of the three numbers in each row, in each column, and in each diagonal is always the same. What value should X have?
3) The U-shaped figure at the right contains 11 squares of the same size. The area of the U-shaped figure is 176 square inches. How many inches are in the perimeter of the U-shaped figure?
1) (a) 3 occurs in the units place once in each group of ten consecutive numbers. Therefore 3 will appear 10 times in the units place.
(b) 3 occurs in the tens place ten times in 100 consecutive numbers: 30, 31, 32, 33, . . . , 38, 39.
(c) Statements (a) and (b) are also true for occurrences of 8. Therefore there will be a total of 40 occurrences of 3s and 8s in the numbers from 1 through 100.
2) Method 1
From the first column, we see that the sum for each row, column, and diagonal should be 90. Then the missing number in the 3rd row is 40, and the missing number in the lead diagonal is 30. The sum for the second column is 40 + 30 + X or 70 + X. Then X must be 20.
Since the numbers in the two diagonals have equal sums and the same middle number, then the two numbers in the corners of each diagonal have equal sums; 25 + 35 = 15 + ? It follows that ?, the number in the lower right corner, is 45. Since the sums of the numbers in any row, column, or diagonal is 90, the bottom row sum 25 + X + 45 = 90. Thus X = 20.
3) The area of each square is 176/11 or 16 inches. Then the length of each side of a square is 4 inches. The perimeter of the U-shaped figure is equivalent to the total length of 24 sides or 96 inches.