YouCubed My Heart ProblemWe borrowed this idea from Jo Boaler and the group at www.youcubed.org . This problem was launched to the entire school--Kindergarten to Grade 9! Each grade entered the problem at their skill or readiness level. Lots of great conversations ensued! What do you notice about this heart? What is the area of this shape? What is the perimeter of this shape? Can you build a different shape, using the same blocks, that has the same perimeter and is a tessellation? How many hexagons can you find? How many rhombuses can you find? How many triangles can you find? How many chevrons can you find? How would you colour this heart? Can you colour it using 4 different colours and not have the same colour touch? Can you do it with 3 colours? Can you recreate this exact figure using different pattern blocks? How many cubes do you see? What is the volume of this heart made of cubes?
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Harry Potter Inspired Problems.This month, all our problems are inspired by Harry Potter. There are several problems for each group. You can solve them all, or choose the one you want to try. Good luck! Remember to submit your solutions to Matt MoTishun in the office. K-6 Problems are adapted from Teaching Children Mathematics, 2017, National Council of Teachers of Mathematics. Volume 24 Number 1, pp 18-19. 7-9 Problems adapted from www.openmiddle.com Kindergarten to Grade 3Each Hogwarts Quidditch team has 3 chasers, 2 beaters, 1 seeker, and 1 keeper. There are 3 extra players on each team. Hogwarts has 4 quidditch teams altogether, one for each house. How many students get to play quidditch for one house? How many quidditch players are there at Hogwarts? Professor McGonagall thinks students make too much noise when they line up for lessons. To cut down on the chatter, she lines up students by their houses in this order: Griffindor, Hufflepuff, Ravenclaw and Slytherin. From which house will the 6th student in line be? The 10th student? The 15th student? The 20th student? If there are 29 students in line, from which house will the last student be? Can you figure out to which house the 50th student belongs? Each year, new students are sorted in their houses (Griffindor, Hufflepuff, Ravenclaw and Slytherin) by the magical Sorting Hat. Each house gets exactly the same number of students. Between 4 and 100, which numbers of new students will divide exactly into the 4 houses? Find more than one way to solve this problem. (numbers may need to be adjusted for each grade level) Grade 4 to 6The Weasley family includes 7 siblings separated by a total of 11 years. In order of their ages, 6 boys (Bill, Charlie, Percy, Fred, George and Ron) are followed by 1 girl (Ginny). Fred and George are twins. All the boys are at least 2 years apart (except, of course, the twins). If the ages of all the boys add up to 32 in the year Ginny was born, how old were each of the children? How old is each when Ron graduates from Hogwarts at age 18? Mrs. Weasley was 25 when Charlie was born. How old will she be when Ginny graduates from Hogwarts? What will the ages of all the Weasley children add up to when Ginny is 22? After hours of reading about potions, you have worked out how to make a potion that will help you get a perfect score on your next potions exam. The recipe, which makes enough for 3 students, requires 8 fairy wings and 12 drops of dragon’s blood. If you have 48 fairy wings how may drops of dragon blood do you need? How many does of potion could you make with this amount of potion? What would you need to make enough for 24 doses? 75 doses? 135 doses? The Hogwarts Express leaves Platform 9 ¾ at exactly 11:00 a.m. on the first day of September each year. If the locomotive travels 140 kilometres per hour, and the length of the trip is 970 kilometres, at what time is the train expected to arrive at Hogwarts? New students at Hogwarts are sorted into the 4 houses by the magical Sorting Hat. Each student has an equal chance of being chosen for Gryffindor, Hufflepuff, Ravenclaw or Slytherin. Also, each house gets exactly the same number of new witches and new wizards. This year, 56 new students started at Hogwarts. How many new witches entered each house? Grade 7 to 9Harry and Ron need to access a secret room at Hogwarts. The code for the room is a balanced equation. So far, they have discovered the following:
Hermione has found a magic rubrics cube made up of 27 identical cubes. But, in order for the magic to be released to its full potential, she has to create a surface area of 78 square units by removing some cubes. How many cubes does she need to remove? What patterns might she notice? George and Fred Weasley have invented 2 equations that, when true, create a new kind of magical toy that uses slope as part of its magic. Ron is desperate to figure them out, so he can patent it and get all the money it will potentially make. He has seen the blank equations, but doesn’t know which numbers go where to make it true. Knowing his brothers, they have not repeated a numeral in the formula. He also need to figure out how the 2 equations are related. He needs your help! Percy Weasley works for the Ministry of Magic. Part of his job is to crunch numbers. He has been given the task of finding all the combinations of 5 whole numbers from 1 to 20 that have the same mean, median and mode. Here is what he has so far:
{2, 3, 4, 5, 7}, {3, 4, 6, 8, 9}, {6, 8, 11, 16, 20}, {7, 8, 13, 17, 20} Is he correct? Make a case to support that Percy’s work is correct or incorrect. Can you find more combinations where the median, mean and mode are equal? Wheels, Wheels and More Wheels!K-3 Problem Mr. Smith owns a bicycle shop where he builds and repairs bikes, trikes and unicycles. One day, he received an order from a customer for some wheeled vehicles. However, the customer did not tell him how many of each type of vehicle to build. The order only said 24 wheels were needed. Mr. Smith tried to contact the customer, but has not been able to reach him. In an attempt to be proactive, Mr. Smith wants to present as many options to this customer as possible. He needs to figure out how many different ways he can fill this order. Help Mr. Smith by making as many plans as you can that use all 24 wheels.
7-9 Problem
Your family has just bought a new car with an EPA highway rating of 15 kpl (kilometers per litre). The gas tank holds 60 litres of gasoline. You are planning a trip to St. John's, Newfoundland, which is approximately 6 125 km from Calgary. Assume your are driving mostly on a highway and a constant rate of speed--100 km per hour. How much gasoline will you need for the entire trip (there and back)? Gasoline cost, on average, $1.20 per litre. How much will you need to budget for fuel? How many hours will it take to make the trip, assuming you average 8 hours of traveling time each day? How often will you need to stop for gas? Each stop takes about 30 minutes to complete (snacks/bathroom breaks, etc.). You could take a different car that has an EPA highway rating of 12 kpl (kilometers per litre), but it only has a 50L tank. How would taking this car change the cost and the amount of time required to get to Newfoundland? |
AuthorThis page is authored by the staff at East Lake School. Archives
March 2020
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