A Math Journey Under the Ocean

A Math Journey Under the Ocean — page 1 — MISSION 1 LEARNING TO DIVE Your first mission is to make sure you are ready to dive so you can explore the underwater world safely LEARN IT ABOUT NEGATIVE NUMBERS 04 Negative numbers are numbers that are less than zero Positive numbers are numbers that are greater than zero The surface of an ocean is called sea level To measure how high a mountain is or how deep something is under the ocean we start our measurement from sea level If sea level is at zero then each meter below sea level can be described as a negative number One meter below sea level is written as 1 two meters below is 2 and so on You know that the number 20 is lower than 30 but it works the opposite way for negative numbers The number 20 is actually higher than 30 See for yourself on the number line shown to the right When diving or rising from an underwater position count up or down the number line For example if you are at 20 m and dive five meters lower count downward from 20 to 25 40 30 20 10 0 10 20 30 40 sea level

A Math Journey Under the Ocean — page 2 — To find how far two negative numbers are apart on a number line you can count the interval or the distance between the two numbers The interval will be the same as if the numbers were both positive For example this number line shows that the distance between 30 and 5 is 25 It is the same as the distance between 30 and 5 25 25 30 20 10 0 10 20 30 05 GO FIGURE It’s important to know how far below the surface you are when diving Going too deep can make you sick For your own safety answer these questions using the number lines on these pages to help count 1 Here are some depths below sea level 6 m 32 m 18 m 40 m 25 m a Which of these is the deepest b Put them in order from highest to deepest 2 You dive down to a depth of 35 m 35 meters below sea level a If you rise by 10 m what depth would you be at b From this new position what depth would you be at if you dove down a further 17 m 3 You are at 28 m If you want to get to 7 m how many meters must you rise 4 An octopus is at 31 m How many meters is the octopus below you if you are at a 3 m b 16 m c 2 m above sea level inside the boat

A Math Journey Under the Ocean — page 3 — MISSION 2 06 CORAL REEFS Your next mission takes you to the world’s coral reefs Home to many colorful plants and animals these underwater ecosystems are being threatened by human activities Measure the reefs and note any changes LEARN IT ABOUT PERCENTAGES AND PERCENTAGE CHANGE Percentages are fractions in which the denominator or bottom number is 100 For example 75 75 100 We can use percentages to describe fractions in a way that makes them easier to compare To compare fractions change them all to percentages by dividing the fraction’s numerator or number on the top by its denominator and then multiplying the answer by 100 The example below compares three fractions to find out which one is the largest as a percentage is 3 4 100 75 is 160 250 100 64 3 4 160 250 63 90 We can easily see that 75 is greater than 70 and 64 so ¾ is the largest of the three fractions is 63 90 100 70 To compare how much things have changed over time find the percentage it increased or decreased by like this For example if a piece of coral was 10 cm in length and it grew to 12 cm over a period of time the percentage increase is New amount minus the original amount Original amount 100 12 10 10 100 2 10 100 20 increase

A Math Journey Under the Ocean — page 4 — GO FIGURE You visit three of the world’s largest coral or barrier reefs the Great Barrier Reef in Australia the Mesoamerican Barrier Reef which runs through Mexico and Central America and the Andros Barrier Reef in the Bahamas You collect data on how much area in km2 each coral reef covers today in order to compare it with their measurements in 1999 Show the figures as percentage increases or decreases 1 What is the difference in area in km2 between 1999 and the present day for a Reef A b Reef B c Reef C 2 Has each reef increased or decreased in area between 1999 and the present day 3 Find the percentage decrease for each reef using the formula on the previous page A GREAT BARRIER REEF Today 200 km2 1999 250 km2 B MESOAMERICAN REEF 1999 320 km2 Today 224 km2 C ANDROS BARRIER REEF 1999 900 km2 Today 495 km2 greatest percentage change 4 Which reef’s area has had the 5 There used to be around 400,000 km2 of coral reef on Earth but there is now only about 280,000 km2 By what percentage has the total amount of coral reef decreased 07

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