A Math Journey Through Extreme Sports

A Math Journey Through Extreme Sports book cover — A Math Journey Through EXTREME SPORTS Hilary Koll Steve Mills Crabtree Publishing Company www crabtreebooks com

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

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