# Winter Math Word Problems

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3 NAME q1 A snowman is made up of three spheres stacked on top of each other. A large sphere is used for the base, a medium sized sphere for the body and a small sphere for the head. The medium sized sphere is 2/3 of the height of the large sphere, and only 15cm higher than the small sphere. The small sphere is 30cm high. a) What is the height of the large sphere? b) What is the total height of the snowman in metres? q2 If 3 boys can build 4 snowmen in 24 minutes, how many snowman will 9 boys finish building in an hour? q3 A 85cm tall snowman begins to melt when the sun is shining directly on him. If the snowman loses 3cm in height for every hour the sun shines on him, and the sun only shines on him for 6.5 hours a day. How many days will it take for the snowman to melt completely? q4 Two children are making a snowman. If they have four different hats, two different sets of eyes, two different sets of arms and two different coloured scarfs, how many different combinations could they dress the snowman up with?

4 NAME q1 If you could throw a snowball so that it travels at 75 centimetres a second, how long will it take to hit the target that is 15 metres away? q2 You are participating in a massive snowball fight. On average 5 people use 12 snowballs every minute and 2 people can make 4 snowballs every 15 seconds. If you have 60 people on your team what is the minimum amount of people you need to have making snowballs so that your team will never run out of ammunition? q3 When throwing snowballs at each other Albert had an accuracy of 8/15, Ben s was 5/8 and Charlie s was 6/10. Out of the three boys who had the best accuracy? q4 A child threw 6 snowballs and measured the distance that they travelled. The first travelled 12.34m, the seconds travelled 11.56m, the third 13.03m, the fourth 12.75, the fifth 10.87m and the sixth travelled 11.87m. What was the average distance thrown by the child? q5 If you cut a snowball in half the diameter of the cross section is 72mm. If the area of a circle is equal to πr2 and π = 3.14, what is the area of the cross section of the snowball?

5 NAME Monthly Climate Information from Edmonton, Alberta in Canada q1 a) Which month recorded the lowest daily minimum in the 2012/2013 season? b) What is the difference in temperature between the daily maximum and minimum in March? c) Which month out of December and February has the biggest difference between their extreme maximum and minimum temperature? d) Which month recorded the highest extreme maximum temperature and if the year is 2014, how many years ago did this occur? e) What is the average snowfall per month over the 6 months that have been recorded? q2 If on average 15mm of snow fell every 5 days, how much snow would have fallen during the months of October to February? (Assuming it is not a leap year.) q3if 2.48 metres of snow fell in the month of January, on average how much snow fell per day?

6 NAME q1 Working in the snow requires a person to have winter clothing to stay warm. At a store a snow jacket costs \$103.75, the snow pants cost \$75.99, the hat cost \$23.45, the gloves cost \$65.20 and the snow boots cost \$ a) How much do you need to spend to buy all the equipment? b) If the council wanted to outfit 4 workers with all the correct gear and had \$1,500 to spend on clothing, how much money is left over after they have bought the gear needed by the 4 workers? q2 When ice forms on roads it makes it dangerous for cars because their tires have no traction on the road. One way to clear the road is to use salt which melts the ice and stops it from forming on the road. If one bag of salt can cover 600 metres of road, how many bags are needed to cover 30km of road? q3 A snowplough truck can clear 1.5km of a single lane in 15 minutes. How long will it take the truck to clear 9km of a four lane road? q4a single man can remove 5m 3 of snow in 30 minutes. If the driveway was 4 metres wides, 17 metres long and the snow depth was 1.5 metres deep, how many hours would it take a man to completely remove all the snow from the driveway? (Round to the nearest hour.)

7 NAME q1 A giant slalom skier uses skies that are one-sixth longer than her height. If she is 174cm tall, how long are her skies? q2 Ski jumping is an event where skiers try to travel as far as they can in the air before they land. In 1951 Tauno Lurio from Finland held the world record at 139 metres. In 2011 Johan Evensen from Norway now holds the world record for the longest successful jump at metres. What is the difference in distance between Tauno s and Johan s jumps? q3 When a snowboarder performs a trick where he spins completely around in a circle it is known as a 360 (There is 360 o in a circle). If he only spins half way around it is a 180. If on a single run down the half pipe a snowboarder performs a 1080, 360, 900, 720 and 180, how many full rotations did the snowboarder perform in total? q4 Speed Skiing is a sport where skiers race downhill in a straight line as fast as they can. The current world record for speed skiing is kilometres per hour (156 miles per hour) held by Simone Origone. The highest set speed limit for cars in the world is 140 kilometres per hour (156 miles per hour). How much faster was Simone going than the highest speed limit in the world in kilometres per hour? q5 You are in a downhill ski race. There are 10 people altogether in the race. Just before you cross the finish line you pass the person who is coming 2nd. What position are you in as you go over the finish line?

8 NAME ANSWERS q1 A snowman is made up of three spheres stacked on top of each other. A large sphere is used for the base, a medium sized sphere for the body and a small sphere for the head. The medium sized sphere is 2/3 of the height of the large sphere, and only 15cm higher than the small sphere. The small sphere is 30cm high. a) What is the height of the large sphere? = 45cm (Medium Sphere) 45 2 = = 67.5cm Answer = Large Sphere is 67.5cm high. b) What is the total height of the snowman in metres? = 142.5cm Answer = The snow man is 142.5cm high. q2 If 3 boys can build 4 snowmen in 24 minutes, how many snowman will 9 boys finish building in an hour? 24 4 = 6 3 boys build I snowman in 6 mintues 3 x 3 = 9 1 x 3 = 3 9 boys build 3 snowmen in 6 mintues 1 hour = 60 mintues 60 6 = 10 3 x 10 = 30 Answer = 9 boys can build 30 snowman in an hour. q3 A 85cm tall snowman begins to melt when the sun is shining directly on him. If the snowman loses 3cm in height for every hour the sun shines on him, and the sun only shines on him for 6.5 hours a day. How many days will it take for the snowman to melt completely? 3 x 6.5 = 19.5cm lost in height every day 19.5 x 4 = x 5 = 97.5 Answer = It will take 5 days for the snowman to melt completely. q4 Two children are making a snowman. If they have 4 different hats, two different sets of eyes, two different sets of arms and 2 different coloured scarfs, how many different combinations could they dress the snowman up with? 4 x 2 x 2 x 2 = 32 Answer = There are 32 different combinations.

9 NAME ANSWERS q1 If you could throw a snowball so that it travels at 75 centimetres in a quarter of a second, how long will it take to hit the target that is 15 metres away? 75 x 4 = 300cm = 3m 1 seconds to travel 3m 15 3 = 5 5 x 1 = 5 seconds Answer = It will take 5 seconds to reach the target. q2 You are participating in a massive snowball fight. On average 5 people use 10 snowballs every minute and 2 people can make 2 snowballs every 15 seconds. If you have 60 people on your team what is the minimum amount of people you need to have making snowballs so that your team will never run out of ammunition? 10 5 = use 2 snowballs per mintue per person 2 x 4 = = 4 snomwballs made per mintue per person 40 x 2 = x 4 = 80 Answer = You need 40 people throwing snowballs and 20 people making snowballs q3 When throwing snowballs at each other Albert had an accuracy of 8/15, Ben s was 5/8 and Charlie s was 6/10. Out of the three boys who had the best accuracy? A = 8/15 x 8/8 = 64/120 B = 5/8 x 15/15 = 75/120 C = 6/10 x 12/12 = 72/120 Answer = Ben has the best accuracy. q4 A child threw 6 snowballs and measured the distance that they travelled. The first travelled 12.34m, the seconds travelled 11.56m, the third 13.03m, the fourth 12.75, the fifth 10.87m and the sixth travelled 11.87m. What was the average distance thrown by the child? = = 12.07cm Anwer = The average throw was 12.07cm. q5 If you cut a snowball in half the diameter of the cross section is 72mm. If the area of a circle is equal to πr2 and π = 3.14, what is the area of the cross section of the snowball? 72 2 = 36mm 3.14 x 36 x 36 = mm 2 Answer = The cross section of the snowball is mm 2

10 NAME ANSWERS Monthly Climate Information from Edmonton, Alberta in Canada q1 a) Which month recorded the lowest daily minimum in the 2012/2013 season? Answer = January b) What is the difference in temperature between the daily maximum and minimum in March? = 9.4 o C Answer = 9.4 o C c) Which month out of December and February has the biggest difference between their extreme maximum and minimum temperature? Answer = December d) Which month recorded the highest extreme maximum temperature and if the year is 2014, how many years ago did this occur? = 27 Answer = It occured 27 years ago in October. e) What is the average snowfall per month over the 6 months that have been recorded? = = 17 Answer = 17mm per month of snow. q2 If on average 15mm of snow fell every 5 days, how much snow would have fallen during the months of October to February? (Assuming it is not a leap year.) 15 3 = 5mm per day = x 5 = 755cm Answer = 755cm of snow will have fallen. q3if 2.48 metres of snow fell in the month of January, on average how much snow fell per day in centimetres? 2.48m = 248cm = 8cm Answer = On average 8cm of snow fell per day.

12 NAME ANSWERS q1 A giant slalom skier uses skies that are one-sixth longer than her height. If she is 174cm tall, how long are her skies? = = 203cm Answer = The skies are 203cm long. q2 Ski jumping is an event where skiers try to travel as far as they can in the air before they land. In 1951 Tauno Lurio from Finland held the world record at 139 metres. In 2011 Johan Evensen from Norway now holds the world record for the longest successful jump at metres. What is the difference in distance between Tauno s and Johan s jumps? = 107.5m Answer = There is a difference of 107.5m q3 When a snowboarder performs a trick where he spins completely around in a circle it is known as a 360 (There is 360 o in a circle). If he only spins half way around it is a 180. If on a single run down the half pipe a snowboarder performs a 1080, 360, 900, 720 and 180, how many full rotations did the snowboarder perform in total? = = 9 Answer = The snowboarder made 9 full rotations in the run. q4 Speed Skiing is a sport where skiers race downhill in a straight line as fast as they can. The current world record for speed skiing is kilometres per hour (156 miles per hour) held by Simone Origone. The highest set speed limit for cars in the world is 140 kilometres per hour (156 miles per hour). How much faster was Simone going than the highest speed limit in the world in kilometres per hour? = q5 Answer = 111.4km faster than the highest set speed limit for cars in the world. You are in a downhill ski race. There are 10 people altogether in the race. Just before you cross the finish line you pass the person who is coming 2nd. What position are you in as you go over the finish line? To pass the person coming 2nd you need to have been coming 3rd. This means you finish the race in 2nd.

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