This problem can be done by students at any age. While it deals with area and perimeter concepts investigated in grade 3 and up, younger students might enjoy playing with these ideas. You have 25 square post-it notes. Create a picture using your post-its. 1. Brainstorm some ideas of what you want to create 2. Sketch your ideas to explore various designs and organize your thoughts. Do not overlap your post-it notes. 3. Decide which design you will use; use your design to help you complete the final product 4. Create your picture(s). Here's some math you can do: Calculate the perimeter of your artwork (the edge of the post-it note = 1 unit of length). Remember, perimeter is the distance around a figure. Calculate the area of your artwork (each post-it note is 1 square unit). Remember, area is the surface covered by a figure. What is the greatest perimeter you can create with your post-it notes? What is the greatest area you can create with your post-it notes? What do you notice about the relationship between area and perimeter? What regular polygons can you find in your design? (Regular polygons are squares, rectangles, triangles, pentagons, hexagons, octagons, rhombuses, quadrilaterals, etc)
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Party Time! All problems have been adapted from Teaching Children Mathematics Vol.24, No. 3, Nov/Dec 2017
K-2 Problems : BEAN BAG TOSS : Lukas invited 3 friends to his birthday party. One of the games they played was Bean Bag Toss. Lukas’s mom had a prize for each round of the game. Unfortunately, some of her data was missing. Help Lukas’ mom figure out who gets the prize for each round of the game. NAME Toss 1 Toss 2 Toss 3 TOTAL Lukas 12 -- 5 20 Almass __ 10 __ 25 Amaya __ __ __ 32 Bella 5 9 4 __ Challenge: Find as many different ways this chart can be filled in. ACTIVITY SCHEDULE: Mya decided her party would be a “choose your own adventure” party. She gave each guest an activity chart and asked them to schedule 1-hour of activities. There are 5 people at her party. Use the activity chart to create 5 different activity schedules for Mya’s guests. Activity Time in minutes Making slime 25 Friendship bracelets 30 Bouncy Castle 15 Bean Bag Toss 20 Face Painting 10 Piñata 5 Make your own pizza 35 Jumping rope 5 What is the fewest number of activities a guest can do in one hour? What is the most activities a guest can do in one hour? If Mya did all the activities, how much time would it take? 3-4 Problems: Location, Location, Location Carter wants to invite 20 people to his party. His parents have $200.00 to spend on the party location. Carter has done some research about possible locations and the cost of each. Which locations might he be able to book? What adjustments might he need to make to be able to access all the locations as possibilities for his party? Location One-time rental fee Cost per guest Zoo $59.00 $8.00 Telus Spark $100.00 $5.00 Shakers $145.00 $2.00 Timing Carter’s party begins at 11:45 am. If the party is three and one-half hours long, at what time will it end? If the magician needs to leave at 2:00 pm and his performance is 50 minutes in length, what is the latest he should start performing? Carter has planned out his party based on how much time he thinks each activity will take. He created a table for the activities. Does he have enough time to complete everything before the party ends? What adjustments might he need to make to fit everything in? Activity Amount of time needed in minutes Magician 50 Cutting cake 10 Opening presents 30 Games 105 Eating cake 20 Goodie bags 15 Water fight 30 Let’s eat! Carter hired a caterer for his party. The caterer has many different options available for each guest. Guests can choose one item from each category. Category Options Food Veggie, Pepperoni, Cheese pizza Drink Water, cola, milk Snack Chips, cookies, fruit Olive can’t decide what she wants. What are the possibilities? If lemonade is added as a drink option, how many more possible combinations are there? Is there a relationship between the number of choices in each category and the total number of different lunch possibilities? Sharing the cake Carter’s birthday cake was cut into equal-size pieces. Carter ate 2/8 of the cake. Susan ate 3/12 of the cake. Susan thinks she ate more cate than Carter. Is she correct? Draw a picture that explains your thinking. Grade 5-6 problems Grandparents Michael’s grandparents are attending is birthday party. His grandfather is 6 times as old as Michael, and he is twice as old as Michael’s mom. Together their ages equal 110 years. How old is Ben? How old is his grandfather? His mother? Party Supplies Amir has $20 to spend on party supplies. He has 28 guest coming to his party and knows he needs napkins, plates and cups. His mom told him he needs to get enough of each for his guests plus his mom and himself. Help Amir find 5 different combinations of supplies that meet his mom’s requirements. Which combination gives him the most amount of change? The least? Which combination do you think he should choose? Explain your thinking. Napkins Plates Cups $1.75 for a 10-pack $1.99 for an 8-pack $2.99 for a 12-pack $2.99 for a 25-pack $3.95 for a 15-pack 2 for $6; 15 in each pack $4.95 for a 40-pack $6.75 for a 30-pack $5.75 for a 35-pack This month's problems have been adapted from Teaching Children Mathematics (Jan/Feb 2018), Mathematics in the Middle School (Jan/Feb 2018), and Take Action: Implementing Effective Mathematics Teaching Practices (M. Smith, D. Huinker and V. Bill, 2017, NTCM, Reston, VA) Which Rainforest Animal is Best? Find out a bit about the following animals: Harlequin frog, salamander, banded tree anole and a turnip-tailed gecko. Next, take a class poll to find out which animal is the most intriguing. Or, which animal you would want as a class pet. Or, which animal is the favourite of the class. Use the data you collect to make a graph or pictogramme. Write 3 comparison statements about your information. How Much Food is Needed? Amazon spider monkeys eat fruit, leaves, nuts and spiders. The leader of the troop is usually in charge of gathering the food. Each spider monkey likes to eat 2 fruit, 5 leaves, 10 nuts and 3 spiders each day. How much food does the leader need to gather for his troop of 7 monkeys? Can you find more than one way to represent your answer? If the leader brought back 16 pieces of fruit, would he have enough food to feed all the other monkeys? Justify your answer. The leader finds a log with 75 spiders on it. How many days will this log feed the monkeys? (imagine the spiders do not move very far from the log!) Band Concert Problem The spring band concert is fast approaching, and your class has been asked to ensure there are enough chairs in the gym for all the parents. The gym has a capacity for 450 chairs. The band will take up 1/3 of the gym. How many chairs do you need to ask Mr. Jonathan to find? For safety reasons, Mme Waite insists there is an isle between each group of chairs. How would you place the chairs in the gym so people can move in and out easily, and still be able to count the chairs quickly? Make a drawing of at least 2 different ways the chairs can be placed for easy access and safety. Maya thinks you will only be able to place 300 chairs in the gym. Kyle thinks the number of chairs is 330. Which student is correct? How do you know? The Brownie Problem Your mom made some brownies for the concert. She left 7 brownies at home for you to share with your 3 friends who are staying with you. Everyone needs to get exactly the same amount, or it won't be fair. How much of the brownies will everyone get? Draw and explain how you know this is true. How many brownies would there need to be for everyone to get 2 1/2 brownies? How do you know? The Seven Billion People Problem
In November 2011, the seven billionth person was born. Is it true that if you laid out all the people on earth end to end, they would encircle the earth 266 times? (The circumference of the earth is approximately 24, 901 miles) Is it true that if all seven billion people stood shoulder to shoulder, we would fit into Los Angeles? (LA is approximately 500 square miles) List some of the question you are asking yourself as you solve this problem? Is there information you need, but do not have? How might you find this information? Document how you solved this problem. How would your answers change with today's population numbers? (7.6 billion as of March 6, 2018) |
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