Orange County Math Council Math Field Day Selected Sample Problems Number Sense Consists of two tests added together: Estimation (counts for 40% of score) and Mental Math (counts for 60% of score). Estimation Team Test — Six stations are located around the perimeter of the room. Problems usually involve estimating some sort of measurement: length, area, volume, weight, liquid volume, metric or standard measurements. Teams must work together. SAMPLE QUESTIONS: Estimation Stations Students will participate in the Estimation competition immediately following the Mental Math activity. Each team will need one answer sheet. No calculators are allowed. The stations need to be set up according to the following information: Station 1: Estimate the number of Popsicle sticks it would take to equal one pound in weight. Materials: Baggie of 10 Popsicle sticks, sign Station 2: Estimate the total length in inches of all these straws laid end to end. Materials: Baggie of straws, sign Station 3: Estimate the cubic inches inside this box of pasta. Materials: Pasta box, sign Station 4: Estimate, in square centimeters, how much paper it would take to make a label for the can (assume there is no seam overlap) Materials: Soup can, sign. Mental Math Individual Test – Students will be shown 40 different mental math questions via a PowerPoint presentation. They will have five seconds to study the problem, and five seconds to write the answer. No work is allowed; all answers must be done mentally. Answers are written on a given answer sheet. It is important to note that correct answers written on the wrong line will be counted as incorrect. Students are encouraged to draw a line or an X in the answer space when a problem has been skipped. Individual scores are added together to form one team score. SAMPLE QUESTIONS: See PowerPoint for sample Mental Math test. Answers to Mental Math test below: 1. 3lbs 14 oz + 2lbs 6 ox = 6lbs 4 oz 11. 4 at $1.24 = $4.96 12. ½ ÷ ¼ = 4/2 = 2 2. 7/8 – 1/4 = 5/8 13. 82 – 52 = 39 3. 864 ÷ 8 = 108 14. 5lbs 1oz – 15oz = 4 lbs 2oz 4. 14 dozen = 168 15. Double 12 dozen = 288 5. (37-25) x 3 + 4 = 40 6. 2/5 of $55 = $22 7. -43 + 13 = -30 8. 3/7 x 2/5 = 6/35 9. 9:45 + 1:30 = 11:15 10. 55 x 2 x 15 x 0 + 3 = 3 16. 300% of 60 = 180 17. 5.05 + 0.5 + 0.03 = 5.58 18. 1m - 35 cm = 65cm 19 $77 + $23 - $60 = $40 20. 2 – 0.491 = 1.509 Algebra & Functions Team Test – Each team will answer 9-10 Algebra and Functions questions…most problems are word problems or logic puzzles. Teams must work together on one page at a time. Ties are broken by comparing the quality and accuracy of work shown in the spaces provided. SAMPLE QUESTIONS: At the school store, 3 pens cost the same as 2 notebooks. Eight pencils cost the same as 1 pen. If a pencil costs $0.10, how much does a notebook cost? Answer _____________________ Place six different non-‐zero numbers in the rectangle below so that no number is greater than 18, and the sum of any two adjacent numbers is a different multiple of 7. Answer ____________________ The diagram below represents black and white floor tiles at a size of five by five. If you were asked to add to this pattern to make it nine by nine, how many black tiles would you add to the existing pattern? Answer ____________________ A bird collector wants to buy 100 budgies and wants to spend exactly $100. Blue budgies cost $10 each, green budgies cost $3 each, and yellow budgies cost 50 cents. The collector wants to purchase at least one budgie of each color. How many blue, green, and yellow budgies could he buy? Answer: Blue budgies ___________________ Green budgies ____________________ Yellow budgies ____________________ On the planet Mars, they have coins that are called pays, quays, rays, says and tays. A quay is worth less than a ray. A say is worth less than a quay. There is more than one coin worth less than a quay. A pay has the second largest value. A say is not worth the least. Write the coins in order starting with the one having the greatest value. Answer ________________________ What is the least number of dancers that are needed if a choreographer wants to arrange them in groups of 6, 8 or 9 with none left over? Answer _______________________ Math Reasoning Team Test — 25 word problems Students must show as much work as possible in the spaces provided. No scratch paper will be given. Diagrams, charts, etc. help with scoring points. Teams must work together on one page at a time. Ties are broken by comparing the quality and accuracy of work shown in the spaces provided. SAMPLE QUESTIONS: The figure is made up of five congruent squares. The perimeter of the figure is 72 cm. Find the area of the figure. Include the correct units. Answer:__________________________ One morning Sandy took out half of the coins from her coin bank, and in the evening she put in 20 coins. The next morning she took out one third of the coins in the bank, and that evening she put in 4 coins. The next morning, she took out half the coins in the bank, leaving 15 coins. How many coins were in the bank to begin with? Answer:__________________________ Exactly one of the numbers 2, 3, 5 and 7 is placed in each of the other 4 regions formed by circles A, B, and C so that the sum of the numbers in each circle is the same. Each number is used. What is the sum of the numbers in each circle? A B 6 4 1 C Answer: _________________________ Statistics, Data Analysis, and Probability Team Test — Each team will answer about 10-15 multiple-step questions relating to statistics and probability, then conduct an experiment, predict results, gather data, and analyze the experiment based on their outcomes. Teams must work together on one page at a time. Ties are broken by comparing the quality and accuracy of work shown in the spaces provided. SAMPLE QUESTIONS: Show as much work as possible on this test. Make sure all answers are written on the answer line. Work as a team, but work quietly. You may use a calculator. TEST MAY NOT BE TAKEN APART!! Good Luck. 1. All students in a fifth grade class measured their heights. The table shows their heights. 4’10” 4’6” 5’2” 4’7” 5’1” 4’3” 4’8” 4’7” 4’9” 5’ 5’3” 4’11” 4’4” 4’5” 5’9” 4’” 4’8” 5’ 4’10” 4’7” a. What is the mode? __________________ b. What is the median? __________________ c. What is the minimum? __________________ d. What is the range? __________________ e. What is the outlier? __________________ 2. The table gives the record for Joan Dyer’s last 100 times at bat during the softball season. She is now coming up to bat. Use the data to answer the following questions: Home runs 9 Triples 2 Doubles 16 Singles 24 Walks 11 Out 38 Total 100 What is the probability that Joan will get a home run? __________________________________________ What is the probability that she will get a hit? __________________________________________ Is she more likely to get a hit or an out? __________________________________________ Explain your thinking. ___________________________ ___________________________________________ Geometry & Measurement Team Test — Each team will be asked to build an object using materials provided. Students must sketch their construction prior to building, then test it with multiple trials. Object is judged using a rubric. Team Directions: Your task is to build a boat that will hold the most pennies. 1. Write your district, school name, and grade on your score sheet. 2. Each team will receive a 3” x 3” piece of cardstock and a paper label. 3. Draw a design for your boat first. You will receive 10 points for your drawing. 4. You may use only the cardstock and the label. You may not ask for or use any other materials. 5. Take your boat to Tub Lake to be measured. 6. Your boat will be measured by length, width, and height in centimeters. 7. Put your boat into the water. If it floats, you will receive five points. 8. Place pennies into you boat, one by one, until the boat sinks. 9. The judges will count all pennies except the last penny that sinks the boat. 10. All boats and pennies must be turned in at the end of the session. Have a swimmingly good time! Please do not discuss the activity with anyone. Let them be surprised! Draw your boat design here: