T. H. Rogers Math Tournament 2/24/16 Calling all Mathletes! Hear Ye! Hear Ye!
Register! Register by 2/19/16. Think! Solve! Win!
There are NO multiple choice answers in the sample exam for grades 3-5 (45 minutes available to complete the entire paper). Mathletes do not have to write units for any answer.
3rd, 4th grade and 5th grade Problems for Mathletes. Solve and write the answer in the space provided.
Program for the afternoon on Jan. 27th 2016: 45 minutes for the written paper, then break time for correction, then the countdown round for the top 4 or 6 individuals. Vote of Thanks and Awards Ceremony at the end.
1.
Knights and a dragon. 3 knights came to their king and told him that they had killed a dragon.
Knight A: “Knight B killed the dragon!”
Knight B: “Knight C killed the dragon!”
Knight C: “I killed the dragon!”
1. If two knights told the truth and one lied, then who killed the dragon? ______knight
2. One mini pie has 4 slices. 1224 kids ate 3 slices of mini pie each. How many mini pies did they eat in all? ______pies
3 The picture shows the number 930. If it showed 806, how many more cells have turned color?
______
4. 2,500 years ago, in ancient Mesopotamia, ones were written as, tens as, and 60 as. How would they write 134 in Mesopotamia those days?
______
5. What is the ratio of the area of the circle to its radius, with a diameter of 14 cm?
______: ______
6. Which cannot be a pattern in a keleidescope?
Bicycles and trucks could not
Trucks and letter K could not
Butterflies and trucks could not
Butterflies and bicycles
The letter K and butterflies
7. How many numbers from 1 to 100 have the digit ‘6’ in them? ______
8. If you roll two six sided dice, what are the chances that your total will be 4? Express your answer as a ratio, and simplify.
______:_____
9. A math contest began at noon one day and ended 990 minutes later. At what time did the contest end? Include a.m. or p.m. in the answer. ______
10. What is the perimeter of the shown polygon? 15 inches ______
12 inches
11. An advertisement read: “Buy three tires at the regular price and get the fourth tire for $3.” Jack paid $240 for the set of four tires at the sale. What was the regular price of one tire? $______
12. Nicole saw a dress in store for $36.00. However, she had a 25% discount coupon. Her mom offered to pay for half the dress. How much did Nicole pay? $______
13. A restaurant charges 15% as a tip for the waiters. There are 6 waiters who share the tips equally. The restaurant makes $3000 a day. How much tip does each waiter get at the end of the day? $______
14. What is the sum of the two smallest prime factors of 250? ______
15. In trapezoid, is perpendicular to,, = 4, = 4, and =8. In addition, E is on, and is parallel to. Find the area of. ______
A 4 B
4
D 8 C
16. There are 460 families who contributed to charity. Each family gave 30 cans of food. How many cans of food were collected in all? ______cans
17. Mount Everest is about 29,030 feet high. Mount Kilimanjaro is about 19, 330 feet high. How much shorter is Kilimanjaro than Everest? ______feet
18. Your mom bought a 2-year swimming pass for $390.00. How much will she be paying each month if she pays the same amount each month for 2 years? $______
19. A spinner is divided into 12 sections. 3 sections are red, 6 are blue, 2 are orange, 1 is brown. If you spin the spinner once, what is the probability that you will land on blue?
______
20. Solve:
______
21. The area of polygon, in square units =______
22. The bar graph shows the grades in a mathematics class for the last grading period. If A, B, C, and D are satisfactory grades, what fraction of the grades shown in the graph is satisfactory?
______
23. How many positive factors of 36 are also whole multiples of 4? ______
24. The 64 whole numbers from 1 through 64 are written, one per square, on a checkerboard (an 8 by 8 array of 64 squares). The first 8 numbers are written in order across the first row, the next 8 across the second row, and so on. After all 64 numbers are written, the sum of the numbers in the four corners will be ______
These are a few problems in the sample paper. The question paper will have many more types of problems and will have higher skill level problems. Paper is for 3-5 grades.
Register for the T.H. Rogers Math Tournament by 1/20/16.
Countdown Round Examples. All mental math only. Scratch paper will be provided the first correct response wins each round. We will have the top 4 or 6 contestants matched up with each other and one person wins it at the end. This person gets to be the “T.H. Rogers Elementary Mathlete of the year!” until next year’s tournament. Every year only one student from our elementary school will get this Honor.
1. 10X 9 X 25 = 2250
2. What is the formula for the area of the rectangle? = length X width
3. What is the difference between the numbers 99 and 63? = 36
4. 8 X 125 = 1000
5. 17 X 9 = 153
6. 17 X 19 = 323
7. And many more such questions.
Programs for the afternoon on Early Dismissal Day:
Explain rules, written round, explain rules for countdown round, countdown round, giving certificates by the Principal Ms. Winn and Vote of Thanks.
Volunteers: Current 8th, 7th grade students.
Solutions for 3rd, 4th and 5th grade problems
1. knight C
2. 1224 X 3 slices = 3672 / 4 = 918 pies
3. 2 more cells have turned color for 806. 37 cells for 806 and 35 cells for 930
4. ▼▼∆∆∆∆ = 120 + 10 + 4 = 134
▼ stands for 60 ▼ + ▼ = 60+ 60 = 120
∆ = 1 ∆∆∆∆ = 1+1+1+1 = 4 ▼▼∆∆∆∆ = 120 +4 =___124___
5. 7 pi: 1
6. Butterflies and trucks could not
7 6, 16, 26, 36, 46, 56, 66, 76, 86, 96, 60, 61, 62, 63, 64, 65, 67, 68, 69 Total = ___19__
8. The combinations for the dice to get a 4 will be (1, 3) or (2, 2), (3, 1). There are only 3 possible combinations out of the total 36 combinations of the two dice.
So the ratio for the combination to get a 4 is 3: 36 ___1:12__
9. 990/60 = 16.5 hours. 12.00 noon to 12.00 midnight is 12 hours and then 4.5 hours is _4.30 a.m._ the next day.
10. (15 + 12) X 2 = 27 X 2 = __54__
11. $ 240 –- $ 3 = $ 237 $ 237 / 3 tires = $___79___
12. The dress costed = ___$ 36.00___
Dress after 25% discount = 36 X (25/100) = 36/4 = 9 36-9 = 27
Nicole and Mom pay for half the dress each 27/2 = $___13.5___
13. Tips the hotel makes per day = 3000 X (15/100) = $__450___
Each waiter’s tip at the end of the day is = 450/ 6 = $___75___
14. Solution: 2 + 5 = ___7___
15. AB = AD = DE = BE = 4
So, BC = 1/2 .4 X 4 = _8_
16. 46 X 3 X 100 = ___13,800__ cans.
17. 29,030 – 19,330 = ___9,700___ feet
18. $390 divided by 24 months 390/24 = $_16.25__
19. A spinner is divided into 12 sections. 3 sections are red, 6 are blue, and 2 are orange, 1is brown. Therefore, 6/12 = 1/2__
20. = _1____
21. Continue to draw segment until it reaches the right side at to create two rectangles – the top is bigger than the bottom.
The area of is Length X Width =.
, and,
So
The area of the bottom rectangle is then
Finally, add the areas of both the rectangles:.
22.
22. Fraction = Number of people who got grades that are “satisfactory”
Total number of people
The number of people who got acceptable grades is: 5 people got A’s, 4 people got B’s, 3 people got C’s and 3 people got D’s. 5+ 4+ 3 + 3 = 15.
So we know the top of the fraction is 15. Only 5 people got “unacceptable” scores, so there are 15 + 5 = 20 scores.
15/20 = ¾ is the fraction.
23. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18 and36.
The multiples of 4 upto36: 4, 8, 12, 16, 20, 24, 28, 32 and36.
Only 4, 12 and36 are factors and multiples, so the answer is ___3__
24. Obviously 1 is in the top left corner, 8 is in the top right corner, and 64 is in the bottom right corner. To find the bottom left corner, subtract 7 from 64 which is57.
1+8+57+64 = 130__