A Math Journey Through Extreme Sports

A Math Journey Through Extreme Sports — page 1 — SKYRUNNING Your first mission will take you up some of the world’s highest mountains to try skyrunning This extreme sport involves running races against other competitors at altitudes of more than 2000 meters You’re given a score for each race which you add up over the season MISSION 1 LEARN IT ABOUT MENTAL ADDITION There are lots of strategies to make adding lists of numbers in your head easier Have you tried these Look for numbers in the list that can be added together to make 10 or a multiple of 10 such as 7 3 36 14 88 12 and so on This strategy can be used on both sides of this equation 04 170 170 70 70 30 100 70 36 38 34 32 30 70 70 30 Another strategy is to add the Tens and Ones separately especially if the Ones digits are small To add 40 42 31 62 and 51 first add their Tens 40 40 30 60 and 50 which equals 220 Then add on the Ones leftover from each number 2 1 2 and 1 Adding these brings the total to 226 In a third strategy you can use multiplication if the numbers in the list being added are close to each other For example the numbers 44 46 44 46 and 48 all have at least 44 in them Multiply 44 by the number of numbers which is 5 Multiply by Tens first 40 5 200 4 5 20 then by Ones 220 Then add the differences between the original numbers and 44 which is 2 2 and 4 This brings the total to 228

A Math Journey Through Extreme Sports — page 2 — In a fourth strategy round the numbers in the list to the nearest 10 For example if the last digit is 5 or more round the number up to the next multiple of 10 If it’s 4 or less round it down To add 34 88 61 27 and 59 first add their rounded numbers together 30 90 60 30 and 60 270 Then write down how much larger or smaller each number is than its rounded number 34 is 4 more than 30 which we can write as 4 88 is 2 less than 90 which we can write as 2 61 is 1 more than 60 which we can write as 1 27 is 3 less than 30 which we can write as 3 59 is 1 less than 60 which we can write as 1 Next adjust the total of rounded numbers by the differences 270 4 2 1 3 1 269 GO FIGURE In each skyrunning season competitors enter at least five races Each competitor’s best four results are added up and the runner with the highest total is the champion They win points according to where they finish 1st 100 points 2nd 88 points 3rd 78 points 4th 72 points 5th 68 points After 5th points go down by twos to the 40th position which is 2 points RACE Race 1 Spain May 25 Race 2 Italy June 21 Race 3 Switzerland August 10 Race 4 Switzerland August 28 Race 5 Italy October 10 Sam 88 78 64 88 78 Jo 78 100 54 38 100 1 Figure out the total of Francis’s five scores all together Use one of the mental strategies suggested 2 Now figure out the total of Jamie’s five scores Who scored the most points in the five races all together Francis or Jamie COMPETITOR Francis 66 66 64 62 68 Al 100 42 6 74 64 Alex Jamie 05 2 88 78 100 88 20 64 4 78 82 lowest worst score 3 For each competitor write their 4 Taking only their best four scores and ignoring their worst score find the total for each competitor 5 Which of the competitors has the highest score and should be crowned champion

A Math Journey Through Extreme Sports — page 3 — MISSION 2 SKELETON Next get your courage up to participate in the skeleton In this dangerous sport you travel on a special small sled at very high speeds without brakes along an icy track Your nose is just centimeters from the ground 06 LEARN IT ABOUT DECIMALS Decimals are another way of writing fractions For example the grids below each have 100 squares The number of colored squares can be represented as a number out of 100 or as a decimal fraction decimal two hundredths one tenth 14 hundredths 113 hundredths 2 100 10 100 14 100 113 100 ones tenths hundredths 0 0 0 1 0 1 1 1 2 0 4 3 When comparing decimals remember that the place value to the right of the decimal point becomes smaller as you move column to column from left to right So you must start by comparing the left-hand columns after the decimal The column to the right of the hundredths column would be thousandths and so on When comparing numbers it helps if the numbers have the same number of digits after the decimal point To do this we can write zeros in the end positions that have no digits For example one tenth can be written as either 0 1 or 0 10 Written both ways each has 1 tenth and 0 hundredths But adding a zero makes it easier to see that 0 10 lies between 0 02 and 0 14 as in the example above

A Math Journey Through Extreme Sports — page 4 — Let’s use the extra zeros to put these numbers in order 1 3 1 25 and 1 287 This makes it easy to see that 1 300 is the largest followed by 1 287 and then 1 250 GO FIGURE There are only a few official skeleton ice tracks around the world They have varying lengths and vertical drops and have different numbers of curves Country Austria Russia Russia Canada Canada Germany Germany Germany Germany Track Igls Paramonovo Sochi Calgary Whistler Königssee Winterberg Oberhof Altenberg United States Lake Placid United States Park City Switzerland St Moritz Latvia France Japan Italy Norway Sigulda La Plagne Nagano Cortina d'Ampezzo 1 35 Lillehammer 1 365 Length km 1 22 1 6 1 814 1 475 1 45 1 306 1 33 1 069 1 413 1 455 1 34 1 722 1 2 1 507 1 36 Vertical drop m Curves 98 1 105 131 9 121 48 152 117 110 96 37 122 22 107 103 9 130 111 5 119 113 120 45 114 3 14 19 19 14 16 13 14 15 17 20 15 16 16 19 14 13 16 07 1 Look at the lengths of the first two tracks above Which is longer 2 Which of the two Canadian tracks a has the longer length b has the longer vertical drop c has more curves length starting with the longest 3 Put Germany’s four tracks in order of 4 Which of all the tracks a is the longest b has the greatest vertical drop c has the most curves

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