2017-2018 - miami-dade county public schoolsmath.dadeschools.net/documents/1718/01/secme-math...

2017-2018 MIAMI-DADE COUNTY PUBLIC SCHOOLS

DISTRICT SECME OLYMPIAD

“SECME: The Gold Standard in STEM”

ELEMENTARY MATHEMATICS PRACTICE PACKET

Name: ___________________________________

SECME Olympiad Elementary Mathematics Practice Questions

Please have SECME students complete the problems over the next two months in preparation for the SECME Math Challenge. Students should fully understand the critical thinking involved in solving these types of problems.

1. Annie, Silvia, and Raquel are on a basketball team. Each needs to choose a number for their basketball jersey. The available numbers are 34, 25, 18, and 37. Use the clues to find each player’s number:

Clues: • Annie and Raquel want an even number on their jersey,

but Silvia wants an odd number. • Silvia loves “lucky number 7.” She wants the sum of the

digits on her jersey to be 7. • Raquel likes Silvia’s idea and also wants the sum of the

digits on her jersey to be 7.

Answer: Annie’s number is ______ Silvia’s number is ______ Raquel’s number is ______

34 25 18 37



2. Look at the pencil below: What is the length of the pencil to the nearest quarter inch? Use the ruler provided. Answer: __________



3. Earlier this year, Sue and Michael are reading the novel The Lighthouse by The Shore. Each night, they held a competition on who could read the most pages. One evening, Sue read from the top of page 35 to the bottom of page 45. Michael read 10 pages of the novel. Who read more pages? Show your work. Answer: __________ read more pages than __________ .



4. Kenneth’s parents are going to celebrate his birthday at a park. He can invite 10 friends. Some parents with mini vans volunteered to drive the kids to the park so that all the kids can arrive at the same time and enjoy every minute together. If each of the mini vans could comfortably seat 4 kids, what is the least number of mini vans needed to take the kids to the park? All other parents, who want to attend, will drive themselves to the park. Show your work.

Answers: ___________



5. There are 4 bookshelves in the classroom. Each bookshelf has room for 20 books. If Mrs. White has 90 books, how many books will not be able to fit on the shelves?

Answer: ______ books



6. On the grid below, plot and label each ordered pair. Connect the points in order, connecting the last point to the first to make a closed figure.

1st 2nd 3rd 4th 5th

B(1,2) H (2,3) W (4,3) X (4,1) K (2,1)

Name the figure. Answer: The figure is a _______________ .

4

3

2

1

0 1 2 3 4



7.

It’s About Time! a) Name two hours when the hands of the clock form a right angle: ___________________________________________________ b) Name four hours when the hands of the clock form an acute

angle: ___________________________________________________ c) Name four hours when the hands of the clock form an obtuse

angle: ___________________________________________________



8. How many rectangles are in the figure?

Answer: _________rectangles



9.

Write in the boxes the numbers to show the arrows’ position on the number line: Answers: Write numbers in the indicated boxes.

100 700



10. The cafeteria staff at Village Green Elementary took a poll of fourth grade students to find out how many students liked pizza, chicken nuggets, or hamburgers. The results are shown in the Venn Diagram: Answers: Write responses on the lines provided. 1) Sixty-eight students liked pizza. How many students liked hamburger? __________________ 2) How many students liked both chicken nuggets and hamburger, but not pizza? ____________

3) How many students liked all three types of food? ____________________________________

Hamburger

13

29 7 8

11 21 25



11. Mrs. Raines brought home 1

2 dozen eggs. She accidentally

dropped the carton on the floor and 13 of the eggs broke.

How many eggs does she have left? Answer: _______ eggs



12. Place > or < in the box:

12 + 3

4

23 + 1

2

Answer: Write symbol in the box.



13. Maria’s bike odometer read 63 miles. She rode her bike to school and back 4 days last week. On Saturday, she rode to the park and back, a total distance of 3 miles. At the end of the five trips, her odometer showed 74 miles. Find the distance d from her house to school and back. Use a strategy of your choice to find d. Answer: d = ______ miles



14. Say you are a fifth grader: Assume it takes about 735 turns of an average 5th grader’s bicycle tire to go 1 mile. How many times, to the nearest thousand, would your tire turn around if you biked beside the runners in a 26-mile marathon? Show your work. Answer: __________ miles



15. Write each number from 1 through 10 in a box; numbers do not repeat! Each box must contain a number that is the difference of two boxes above it, if there are two boxes above it. You may use the numbered paper tiles to help you find the answer; don’t forget to write your final answer (numbers in the boxes)! Answers: Write the numbers in the boxes…



16. The first 500 people to visit Disney were given a choice of an

autograph book, T-shirt, a pin, or a canvas bag, each with the Disney theme park logo.

It turns out that 1

4 of the people chose the autograph book, 1

2

chose a T-shirt, and 110

chose a pin. How many of each gift was given away?

Answers: _________ autograph book _________ T-shirt __________ pin _________ canvas bag



17. Four classmates are to stand in order from tallest to shortest. Tom is taller than Sally. Sally is taller than Bob. Maria is taller than Bob but shorter than Sally. Using the clues, place the four friends in order from tallest to shortest.

Answers: Tallest ________ ________ ________ ________ Shortest



18. You have been asked to paint the outside surface of this figure made of cubes glued together. It will take approximately one pint of paint per square face. You do not have to paint the bottom.

A. How many pints of paint will you need? B. If the paint costs $4.99 per pint, estimate the cost of the

paint to the nearest dollar.

Answers:

A.

B.



19. Dogs, cats, and donkeys had a tug-of-war. Four cats tied with three dogs. Two donkeys tied with six dogs. Which side won when one donkey tugged with five cats?

Answers: __________

=

=

?



20. Peter found a magic square that would grant him a wish if he solved it. First, he must make sure the digits 1-9 are in each square and they do not repeat. Second, the sum of the digits across each row and down each column, must be the same as the sum along each diagonal. Solve the magic square.

5 6 2 3 7

Answers: place your answers in the boxes



21. Mike needs to buy 4 packages of pencils at 89¢ each, 2 packages of paper at $1.19 each, and an eraser package for 95¢. He has $10. Estimate, to the nearest dollar, how much money he will have left. Answer: about $ _________



22. The owner of “Pets on the Go” pet store currently has the following animals in his store: 5 dogs, 4 cats, 12 birds, 2 turtles, 3 snakes, 2 giant lizards, 1 pot-bellied pig, and 4 spiders.

How many legs were on the 33 animals? No, there are no animals with missing legs…

Answer: _______ legs



23. A worm is at the bottom of a 10-foot hill. He crawls up the hill

214 feet a day. At night when he rests, he

slides down 212 feet. How long does it take the

worm to crawl up the hill?

Answer: _______ days



24. What fraction of the square is shaded?

Answer: _________ is shaded



25. A number n is divided by 3 and the result is multiplied by 7. The 6 is subtracted from the result to give 36. What is the original number n?

6]7)3([ −×÷n gives 36. What is n? Answer: n = _______

2017-2018 MIAMI-DADE COUNTY PUBLIC SCHOOLS

DISTRICT SECME OLYMPIAD

“SECME: The Gold Standard in STEM”

ELEMENTARY MATHEMATICS PRACTICE PACKET

ANSWER KEY



18 25 34

1. Annie, Silvia, and Raquel are on a basketball team. Each needs to choose a number for their basketball jersey. The available numbers are 34, 25, 18, and 37. Use the clues to find each player’s number:

Clues: • Annie and Raquel want an even number on their jersey,

but Silvia wants an odd number. • Silvia loves “lucky number 7.” She wants the sum of the

digits on her jersey to be 7. • Raquel likes Silvia’s idea and also wants the sum of the

digits on her jersey to be 7.

Answer: Annie’s number is ______ Silvia’s number is ______ Raquel’s number is ______

34 25 18 37



4 12

inches

2. Look at the pencil below: What is the length of the pencil to the nearest quarter inch? Use the ruler provided. Answer: __________



3. Earlier this year, Sue and Michael are reading the novel The Lighthouse by The Shore. Each night, they held a competition on who could read the most pages. One evening, Sue read from the top of page 35 to the bottom of page 45. Michael read 10 pages of the novel. Who read more pages? Show your work. Answer: Sue read more pages than Michael. .



3 mini vans

4. Kenneth’s parents are going to celebrate his birthday at a park. He can invite 10 friends. Some parents with mini vans volunteered to drive the kids to the park so that all the kids can arrive at the same time and enjoy every minute together. If each of the mini vans could comfortably seat 4 kids, what is the least number of mini vans needed to take the kids to the park? All other parents, who want to attend, will drive themselves to the park. Show your work.

Answers: ___________



10

5. There are 4 bookshelves in the classroom. Each bookshelf has room for 20 books. If Mrs. White has 90 books, how many books will not be able to fit on the shelves?

Answer: ______ books



H W

X K

B

pentagon

6. On the grid below, plot and label each ordered pair. Connect the points in order, connecting the last point to the first to make a closed figure.

1st 2nd 3rd 4th 5th

B(1,2) H (2,3) W (4,3) X (4,1) K (2,1)

Name the figure. Answer: The figure is a _______________ .

4

3

2

1

0 1 2 3 4



3:00 and 9:00

1:00, 2:00, 10:00 and 11:00

4:00, 5:00, 7:00 and 8:00

7.

It’s About Time! a) Name two hours when the hands of the clock form a right angle: ___________________________________________________ b) Name four hours when the hands of the clock form an acute

angle: ___________________________________________________ c) Name four hours when the hands of the clock form an obtuse

angle: ___________________________________________________



15

8. How many rectangles are in the figure?

Answer: _________rectangles



9.

Write in the boxes the numbers to show the arrows’ position on the number line: Answers: Write numbers in the indicated boxes.

100 700 250 400



57

8

29

10. The cafeteria staff at Village Green Elementary took a poll of fourth grade students to find out how many students liked pizza, chicken nuggets, or hamburgers. The results are shown in the Venn Diagram: Answers: Write responses on the lines provided. 1) Sixty-eight students liked pizza. How many students liked hamburger? __________________ 2) How many students liked both chicken nuggets and hamburger, but not pizza? ____________

3) How many students liked all three types of food? ____________________________________

Hamburger

13

29 7 8

11 21 25



4

11. Mrs. Raines brought home 1

2 dozen eggs. She accidentally

dropped the carton on the floor and 13 of the eggs broke.

How many eggs does she have left? Answer: _______ eggs



12. Place > or < in the box:

12 + 3

4

23 + 1

2

Answer: Write symbol in the box.

>



2

13. Maria’s bike odometer read 63 miles. She rode her bike to school and back 4 days last week. On Saturday, she rode to the park and back, a total distance of 3 miles. At the end of the five trips, her odometer showed 74 miles. Find the distance d from her house to school and back. Use a strategy of your choice to find d. Answer: d = ______ miles



19,110

14. Say you are a fifth grader: Assume it takes about 735 turns of an average 5th grader’s bicycle tire to go 1 mile. How many times, to the nearest thousand, would your tire turn around if you biked beside the runners in a 26-mile marathon? Show your work. Answer: __________ turns



15. Write each number from 1 through 10 in a box; numbers do not repeat! Each box must contain a number that is the difference of two boxes above it, if there are two boxes above it. You may use the numbered paper tiles to help you find the answer; don’t forget to write your final answer (numbers in the boxes)! Answers: Sample Answer – answers may vary.

8 10 3 9

2 7 6

5 1

4



250 125

50 75

16. The first 500 people to visit Disney were given a choice of an

autograph book, T-shirt, a pin, or a canvas bag, each with the Disney theme park logo.

It turns out that 1

4 of the people chose the autograph book, 1

2

chose a T-shirt, and 110

chose a pin. How many of each gift was given away?

Answers: _________ autograph book _________ T-shirt __________ pin _________ canvas bag



Tom Sally Maria Bob

17. Four classmates are to stand in order from tallest to shortest. Tom is taller than Sally. Sally is taller than Bob. Maria is taller than Bob but shorter than Sally. Using the clues, place the four friends in order from tallest to shortest.

Answers: Tallest ________ ________ ________ ________ Shortest



32

$160

18. You have been asked to paint the outside surface of this figure made of cubes glued together. It will take approximately one pint of paint per square face. You do not have to paint the bottom.

A. How many pints of paint will you need? B. If the paint costs $4.99 per pint, estimate the cost of the

paint to the nearest dollar.

Answers:

A.

B.



Cats

19. Dogs, cats, and donkeys had a tug-of-war. Four cats tied with three dogs. Two donkeys tied with six dogs. Which side won when one donkey tugged with five cats?

Answers: __________

=

=

?



20. Peter found a magic square that would grant him a wish if he solved it. First, he must make sure the digits 1-9 are in each square and they do not repeat. Second, the sum of the digits across each row and down each column, must be the same as the sum along each diagonal. Solve the magic square.

5 6 2 3 7

Answers: Provided in the boxes

4 9

10

8



3.00

21. Mike needs to buy 4 packages of pencils at 89¢ each, 2 packages of paper at $1.19 each, and an eraser package for 95¢. He has $10. Estimate, to the nearest dollar, how much money he will have left. Answer: about $ _________



112

22. The owner of “Pets on the Go” pet store currently has the following animals in his store: 5 dogs, 4 cats, 12 birds, 2 turtles, 3 snakes, 2 giant lizards, 1 pot-bellied pig, and 4 spiders.

How many legs were on the 33 animals? No, there are no animals with missing legs…

Answer: _______ legs



4

23. A worm is at the bottom of a 10-foot hill. He crawls up the hill

214 feet a day. At night when he rests, he

slides down 212 feet. How long does it take the

worm to crawl up the hill?

Answer: _______ days



38

24. What fraction of the square is shaded?

Answer: _________ is shaded



18

25. A number n is divided by 3 and the result is multiplied by 7. The 6 is subtracted from the result to give 36. What is the original number n?

6]7)3([ −×÷n gives 36. What is n? Answer: n = _______

2017-2018 - miami-dade county public schoolsmath.dadeschools.net/documents/1718/01/secme-math...

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