Every week the students will be challenged with a Problem of the Week (POTW). The purpose of the POTW is for the students to practice math problems seen in every day life. It is also important to recognize there is a different language in mathematics. Students are asked to plan, analyze, and explain how they got their answer. It will be given to them in class on Mondays and will be due on the Friday of that week. It will also be posted on the website. Make sure you follow the "Guidelines to Success" for a superb answer.
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POTW September 27 - October 1 You are in charge of setting up the table tennis tournament for the After School Club. There are 6 club members competing. Each member should play every other member once. Create a schedule for the tournament. POTW October 4 - October 8
Ms. Domelle and Ms. Clancy went on a business trip together. They decided to share all their expenses equally. Ms. Domelle spent $125.00. Ms. Clancy spent $85.00. Ms. Domelle's thinking: $125.00 - $85.00 = $40.00 Ms. Clancy owes $40.00. There is something wrong with Ms. Domelle's thinking. Show how you would find the answer to the problem. POTW October 12 - October 15 Thanksgiving Trip to Frannie's Granny Once a year, The family of Fannie, Drives to visit their dear old Granny. After their journey Is 3/5 over They stop for lunch In a town called Dover. If the entire trip Is 100 km - no more - How far is Dover from Granny's front door? POTW October 18 - October 22 Tyler collects pokemon cards. He read in a collector's magazine that one of his rare cards should double in price every seven years. How many times should its present value be worth in 21 years?
POTW October 25 - October 29 The Good Food Restaurant party room has 24 square tables that can be arranged in different ways. Since only one person can sit at a side of a table, most guests ask to have the tables put together to form a rectangle. How many different rectangular arrangements can the restaurant make using all 24 tables? Which rectangle arrangement will seat the greatest number of people? How many people will that arrangement seat? Which rectangular arrangement will seat the fewest number of people? How many people will that arrangement seat? POTW November 1 - November 5 There are two taxi companies in Small Town and they have different rates for determining how much to charge for a ride. Speedy Cab Service $3.00 for the first kilometre $0. 50 for each additional kilometre
Whirlwind Cab Company $1.00 per kilometre With which taxi company would you pay less for a 3km ride? Which taxi company would be less expensive for a 10km ride? For what distance ride will the two companies charge exactly the same amount? Explain how you find your answers. POTW November 8 - November 12 Of the 15 books that Jeremy donated to the book exchange, there were half as many adventure books as mystery books. The number of biographies was the same as the number of mystery books. How many of each type of book did Jeremy give to the book exchange? POTW November 15 - November 18 Your neighbour, Ms. Steadman, wants you to take care of her pets for 3 days. She will pay a total of $25.00. Ms. Steadman has two cats and one dog. There are a number of conditions. a) The pets must be fed twice a day and given fresh water every day. b) You must pay for the pet food yourself. c) Each cat eats one small can of cat food each day. d) The dog eats one large can of dog food each day. e) A small can of cat food costs $0.89 and a large can of dog food costs $1.09. Would you take the job? Explain how you made your choice. POTW due Friday, November 26 Emily bought 30 roses to place on the tables in her cafe. Her bud vases can hold either 1 or 2 flowers. If she fills the same number of vases with 1 flower as she does with 2 flowers, how many vases will be required? POTW due Friday, December 3 Fiona saw a sweater that she liked at Winners, but it cost $90, which was more than she wanted to spend. Fiona decided that if the store put the sweater on sale and the price dropped to $30 or less, she would buy it. Last week, Fiona checked and found the sweater had been marked down 1/3. This week and ad in the paper said that all sweaters at the store were being reduced another 1/3 of their sale price. Fiona reasoned that 1/3 + 1/3 = 2/3 off. Since 2/3 of 90 is 60, there would be $60 off of the price of the sweater, making the sweater $30 ($90-$60=$30). She decided she would buy it. Will Fiona be able to buy the sweater for $30? If not, how much will the sweater cost?
POTW due Friday, December 10 The Toronto District School Board has ruled that starting next year, all students will be required to wear school uniforms. Pants and skirts will have to be navy blue. Shirts can be light blue, white, or blue and white striped. Button down or pullover sweaters can be worn over a shirt. The sweaters can be light blue, navy blue, or plum. Emily K.'s Mom bought Emily a skirt, a pair of pants, 3 shirts (one of each colour), a button down sweater in each colour, and a plum-coloured pullover. How many different outfits can Emily create with these clothes? POTW due Friday, December 17 When Ms. Clancy took a travel survey of her class, 60% of the students said they had been to Florida, and 40% of the students said they had been to New York. Jamie concluded that everyone in the class had been to one of those states. Samantha thought there must be something wrong with the survey because she had not been to either of those states. There was nothing wrong with the survey. Can you explain the error in Jamie's thinking? POTW due Friday, January 7 Last year Hillcrest School's basketball team won 80% of its games. So far this year, the team has played 5 games and won 3. It is scheduled to play a total of 20 games this season. How many more games must the team win in order to equal last year's record? POTW due Friday, January 14 A lizard was attempting to climb a slippery three-foot tree. He started on the ground and at first climbed to 12 inches from the top of the tree. He slipped back 6 inches. He then climbed back up 9 inches and slipped back 2 inches. Not a lizard to give up easily, he then climbed up 3 inches and slipped back 5 inches. Jamila figures that the lizard is 11 inches from the ground. Jamila's thinking is 12 + 9 + 3 = 24 6 + 2 + 5 = 13 and 24 - 13 = 11 There is something wrong with Jamila's thinking. Show how to get the correct solution. Explain the error in Jamila's thinking. POTW due Thursday, January 20 Noah is a carpenter. He can cut a plank into six pieces in ten minutes. Noah figures that working at the same rate, it would take him 20 minutes to cut the plank into 12 pieces. Noah's thinking - 6 cuts take 10 minutes. There are twice as many pieces, so it will take twice as long to cut 12 cuts will take 20 minutes. There is something wrong with Noah's thinking. Show how to get the correct solution. Explain the error in Noah's thinking. POTW due Friday, January 28 Ms. Lerner wants to buy pencils to sell in the school store. She can buy them for $0.15 each. He can also buy them in packages of twenty for $2.50, or in boxes of one hundred for $10.00. Write two questions you can answer about the pencils. Find the answer to one of your questions. Show your work. NO POTW due this week, Friday, February 4th POTW due Friday, February 11th You and two friends are planning on attending a University of Toronto football game. You will each need a ticket, and you would like to have some money left to buy snacks. Altogether, you have $50.00 to spend. The ticket and snack prices are listed below: SEATING box seats..........................................................$15.00 Lower reserved section.............................$12.00 Upper reserved section.............................$10.00 Bleacher seats................................................$ 7.50 SNACKS Hot dog..............................................................$ 1.50 Soda....................................................................$ 1.00 Ice Cream........................................................$ 1.25 Peanuts..............................................................$ 0.75 Which tickets would you buys? Explain your choice. Show the total amount you would spend for tickets and food. Also, include the amount of money you would have left over. POTW due Thursday, February 17 Ms. Wilson needed 3,800 brochures printed for her classroom. The clerk at the print shop asked Ms. Wilson if she would like to order 4,000 brochures in order to take advantage of the price break. Ms. Wilson decided not to change the order because she thought getting so many extra brochures would wind up costing her more money. There is something wrong with Ms. Wilson's thinking. BROCHURES 1 to 3,999...................................... $0.14 each 4,000 to 5,999.......................... 10.4 cents each 6,000 or more............................$0.08 cents each Show how you would solve the problem. Explain the error in Ms. Wilson's thinking.
POTW due Friday, February 25 Alexander already owed Ms. Clancy $2.20 when they agreed to buy a Scholastic book together for $10.00 and split the cost equally. Ms. Clancy paid for the book. Alexander figures he now owes Ms. Clancy $6.10. Alexander's thinking: $10.00 + $2.20 = $12.20 $12.20 divided by two is $6.10 There is something wrong with Alexander's thinking (could this be true????? :). 1. Show how you would solve the problem. 2. Explain the error in Alexander's thinking. POTW due Friday, March 11 Hayley spent $37.38 on 42L of gasoline. At that rate could she get another 40L for less than $35?
POTW due Friday, March 25 Leni used eight rolls of flim to take pictures of her family on her trip to England. Some of the rolls of film contained 24 pictures and others contained 36 pictures. How many pictures did she take on her trip? 1. What is the question? 2. What information do you know from the problem? 3. What else do you need to know to solve the problem? 4. Pick numbers that will tell how many pictures were on each roll of film. 5. Now find out how many pictures Leni took on her trip.
POTW due Friday, April 1st Jake and his family ordered a large pizza for dinner. The pizza was cut into eight equal slices. Jake ate three slices of the pizza, and this sister, Lauren, ate two slices. Mr. Vamos asked Jake if he knew what fraction of the pizza he and his sister had eaten. Jake's thinking - I ate 3 of the 8 pieces. That's 3/8. Lauren ate 2 of the 8 pieces. That's 2/8. 3/8 + 2/8 = 5/16. Together, we ate 5/16 of the pizza. There is something wrong with Jake's thinking. Using ALL the steps in the POTW show how you would solve the problem and explain the error made in Jake's thinking. DON'T FORGET TO PROVE YOUR WORK!!!
POTW due Friday, April 8 For Spirit Day, Ms. Lerner ordered 256 hats for four classes. When the hats arrived, she asked a student from each class to come to her office and take 1/4 of the hats. Odysseus arrived first and took 1/4 of the hats. Next, Nat arrived and took 1/4 of the hats that were there. Then, Nick came and took 1/4 of the hats that were left. Finally, Sophia came and took 1/4 of the hats that were there. The next morning Ms. Lerner arrived and was suprised to find 81 hats in her office. Explain what happened. Think of these questions: How many hats should each class receive? How many hats did Ody take? How many are now left? How many did Nat take? How many are now left? and so on... Why did each class rep take a different number of hats? How could Ms. Lerner have made the directions more clear? Explain your strategy. REMEMBER TO USE ALL THE STEPS IN THE POTW. IF YOU MISS ANY STEPS YOU WILL NOT RECEIVE THREE STICKERS!!!
POTW due Friday, April 15 The following are resting heart rates for animals: Lion – 40 beats in 60 seconds, Giraffe – 5 beats in 12 seconds, Hummingbird – 41 beats in 10 seconds. Which animal has the slowest heart rate? Remember ALL of the steps of the POTW for full stickers!!
POTW due Thursday, April 21
One store charges $4.20 for a package of 4 items. Another store charges $2.97 for a package of 3 of the same items. Which is a better buy?
Remember all the steps in the POTW. You are doing really well with proving your answer (PROOF). Think of how you can show your work a different way. For example, if you use multiplication as your strategy then you could use division as your proof (the opposite order of operation). Estimating is also a good way to see if your answer is close. For example, if your estimation is way off then perhaps your answer is wrong. With fractions and decimals you can always use a picture. Good luck!
POTW due Friday, April 29th Ian has some markers. When he put them in groups of 3, there were 2 left over. If he had fewer than 15 markers, how many could he have? Remember to use the new process for the POTW with only three steps! Look at the top of this page for the details. Good Luck! POTW was cancelled for this week; however, it will resume next week. POTW due Friday, May 13th You have some boards that total 20m in length. You want to use them to enclose a rectangular sandbox. What size can you make the sandbox? Remember to use the new process for the POTW with only three steps! Look at the top of this page for the details. Good Luck!
POTW Due Thursday, May 19th After 4 pickup stops, every passenger seat in a school bus was taken. Half as many students got on at the second stop as the first stop, and half as many got on at the third stop as the second stop. At the fourth stop, 5 students got on, the same number at the third stop. How many passenger seats were there in the bus? POTW Due Thursday, May 19th After 4 pickup stops, every passenger seat in a school bus was taken. Half as many students got on at the second stop as the first stop, and half as many got on at the third stop as the second stop. At the fourth stop, 5 students got on, the same number at the third stop. How many passenger seats were there in the bus? Remember to use the new process for the POTW with only three steps! Look at the top of this page for the details. Good Luck! POTW Due Friday, March 27
POTW Due Friday June 3rd One morning grasshopper fell down a hole 2 metres deep. He would climb 1/4 of a metre every day but at night he slid down 1/8 pf a metre. At this rate, how many days until the grasshopper gets out? POTW Due Friday June 10 In 1989 the price of a soccer ball was $8.00. A financial analyst predicted that the price would rise $0.25/year for the next 10 years. In what year will the price be $9.75? POTW Due Friday June 17
Melanie and Kevin are going shopping for their mom at the Celtic Bakery. They were told to buy 15 onion rolls, 10 hamburger buns and 2 loaves of rye bread. How much will it cost them? Final POTW For our last problem I'd like you to create your own POTW question and provide a solution, as well. I will be choosing the submitted POTWs to be used in class. Have fun! |
"NEW" GUIDELINES FOR THE POTW As before, the students are still required to work on their POTW througout the week. We have decided to change the format of the POTW to a three-step process, rather than a five-step process. The new process will consist of the following steps: 1. What information do I know? 2. Show my work. 3. Justify (or prove) my answer by showing it another way. The POTW will now be marked out of four levels (1-4). We will be looking at their "thinking" and "communication" process. GOOD LUCK!
GUIDELINES FOR THE POTW Students are encouraged to work on their POTW throughout the week. They may start with the first 3 steps on their first try, and then re-visit the steps while continuing to solve the problem. Students may seek teacher assistance for feedback, before handing in their POTW at the end of the week.The information below outlines the steps to follow for every POTW.
1. Retell
Write down the important parts of the question in your own words.
2. Choose a Strategy (or Strategies)
a) Break the problem into parts then solve each part individually
b) Make a model or draw a diagram
c) Choose the appropriate operations (e.g. addition, subtraction, multiplication, division)
d) Work backwards
e) Look for a pattern
f) Use logical thinking
g) Guess and check
h) Make a table
3. Show Your Work
4. Proof
Why is your answer reasonable? At this step, explain in as much detail as possible why you think your answer is right. Did you double check your answer?
** Remember one way to "prove" your answer is right is to make an estimate then compare your final answer to the estimate - usually if your answer is close then your final answer should be correct**
5. Final Complete Answer
Conclude your soulution with a final complete sentence. Use words from the question in your answer.
GOOD LUCK!!
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