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Sea Creatures Barker Sea Creatures Solving Equations and Inequalities Lori Barker

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Page 1: Sea Creatures - Academic Therapy...Sea Creatures Barker TCM 14457 ! The ocean is home to thousands of creatures, and new species are being discovered every day. Explore how fast a

Algebra and Algebraic Thinking

Sea C

reatures

Barker

TCM 14457 ●

The ocean is home to thousands of creatures, and new species are being discovered every day. Explore how fast a sailfish can leap from the water, and how often a sea horse’s dorsal fin flutters by solving equations and inequalities. Learn about some of the most unique creatures of the deep, like the newly-discovered squid worm. Using equations and inequalities, you will be making your own ocean discoveries in no time!

Sea Creatures

Sea Creatures

Solving Equations and InequalitiesSolving Equations and Inequalities

Lori Barker

Page 2: Sea Creatures - Academic Therapy...Sea Creatures Barker TCM 14457 ! The ocean is home to thousands of creatures, and new species are being discovered every day. Explore how fast a

Lori Barker

Sea Creatures

Solving Equations and Inequalities

Page 3: Sea Creatures - Academic Therapy...Sea Creatures Barker TCM 14457 ! The ocean is home to thousands of creatures, and new species are being discovered every day. Explore how fast a

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Publishing CreditsDona Herweck Rice, Editor-in-ChiefRobin Erickson, Production DirectorLee Aucoin, Creative DirectorTimothy J. Bradley, Illustration ManagerSara Johnson, M.S.Ed., Senior EditorAubrie Nielsen, M.S.Ed., Associate Education EditorJennifer Kim, M.A.Ed., Associate Education EditorNeri Garcia, Senior DesignerStephanie Reid, Photo EditorRachelle Cracchiolo, M.S.Ed., Publisher

Consultants

Pamela Dase, M.A.Ed.National Board Certified Teacher

Barbara Talley, M.S. Texas A&M University

Teacher Created Materials 5301 Oceanus Drive

Huntington Beach, CA 92649-1030 http://www.tcmpub.com

ISBN 978-1-4333-3457-3 © 2012 Teacher Created Materials, Inc.

The classroom teacher may reproduce copies of materials in this book for classroom use only. The reproduction of any part for an entire school or school system is strictly prohibited. No part of this publication may be transmitted, stored, or recorded in any form without written permission from the publisher.

Image CreditsCover Neil Balderson/Shutterstock; p.1 Neil Balderson/Shutterstock; p.4 (inset) Johan Swanepoel/Shutterstock; p.4 (back) Andrey Yurlov/Shutterstock; p.5 ANP MARCEL ANTONISSE/Newscom; p.6–7 Galushko Sergey/Shutterstock; p.7 Wong Hock Weng/Shutterstock; p.8 alohatroy/BigStock Photo; p.9 Reinhard Dirscherl/Photolibrary; p.10 Dr. Paul A. Zahl/Photo Researchers, Inc.; p.12 (left) Stubblefield Photography/Shutterstock, (right) Teguh Tirtaputra/Shutterstock, International Pty Ltd/Alamy; p.12–13 Studio 37/Dreamstime; p.14 (left) Peter David/Getty Images, (right) Getty Images/National Geographic Creative, (bottom) Peter David/Getty Images; p.15 Stubblefield Photography/Shutterstock; p.16 ifishifish/iStockphoto; p.17 (left) Jung Hsuan/Shutterstock, (right) MIXA/Getty Images; p.18 Cigdem Sean Cooper/Shutterstock; p.19 Eric Isselée/Shutterstock; p.20 Stephen Frink/Getty Images; p.21 Stephen Frink/Getty Images; p.22 Stuart Westmorland/Getty Images; p.22–23 Nastya Pirieva/Shutterstock; p.23 lavigne herve/Shutterstock; p.24 Getty Images/Flickr RM; p.25 (inset) Teguh Tirtaputra/Shutterstock; p.25 (bottom) James van den Broek/Shutterstock; p.26–27 AFP/Getty Images; p.28 Rich Carey/Shutterstock; p.29 Undersea Discoveries/Shutterstock; All other images: Shutterstock

Page 4: Sea Creatures - Academic Therapy...Sea Creatures Barker TCM 14457 ! The ocean is home to thousands of creatures, and new species are being discovered every day. Explore how fast a

In the Sea 4

Monster Crabs 5

Fastest Fish 8

Stallions of the Sea 10

Fishing Fish 14

Poisonous Pufferfish 17

Portuguese Man-of-War 20

The Octopus: An Amazing Escape Artist 22

New Discoveries 26

Problem-Solving Activity 28

Glossary 30

Index 31

Answer Key 32

Table of Contents

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Page 5: Sea Creatures - Academic Therapy...Sea Creatures Barker TCM 14457 ! The ocean is home to thousands of creatures, and new species are being discovered every day. Explore how fast a

The sea is full of amazing creatures. Some weigh more than 100 pounds (45.4 kg). Others are too tiny to be seen without a microscope. Some live their lives near the surface of the ocean. Others live so deep that they are never exposed to sunlight.

Who are these creatures of the sea?

The ocean covers approximately 71% of Earth. About half of all the known species (SPEE-seez) on Earth live in ocean waters.

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In the Sea

Page 6: Sea Creatures - Academic Therapy...Sea Creatures Barker TCM 14457 ! The ocean is home to thousands of creatures, and new species are being discovered every day. Explore how fast a

The Japanese spider crab is the largest crab in the world. It lives on the ocean floor. It is found about 650 to 1,000 feet (198–305 m) below the surface. Some have been found much deeper.

A Japanese spider crab’s body can be up to 15 inches (38 cm) wide. That is pretty big, but its body is not what makes it the largest crab. That comes from its leg span. The longest confirmed leg span is close to 13 feet (4 m)! There have been unconfirmed reports of leg spans even greater than that.

Did You Know?The Japanese spider crab has a life expectancy of about 100 years.

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Monster Crabs

Page 7: Sea Creatures - Academic Therapy...Sea Creatures Barker TCM 14457 ! The ocean is home to thousands of creatures, and new species are being discovered every day. Explore how fast a

A Japanese spider crab can weigh up to 40 pounds (18 kg), although most do not reach that weight. The average weight is about 11 pounds (5 kg).

We can write an algebraic expression to figure out how many kilograms a certain number of crabs would weigh based on their average weight. If c stands for the number of crabs, then 5c stands for the combined average weight of crabs in kilograms. The letter c is a variable. A variable is a symbol or letter that stands for a number, which can be a different value depending on the problem. In this case, c stands for the number of crabs. This variable, multiplied by the average weight of 5 kilograms, forms the algebraic expression 5c.

The table shows the total weight of different numbers of crabs with an average weight of 5 kilograms.

Number of Crabs(c)

Average Weight (in kg) Multiplied by

Number of Crabs

Total Weight (in kg)(w)

1 5 • 1 5

2 5 • 2 10

3 5 • 3 15

4 5 • 4 20

5 5 • 5 25

c 5 • c 5c

Let w stand for the total weight of any number of crabs. The equation w = 5c shows the total weight (w) of c crabs.

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Page 8: Sea Creatures - Academic Therapy...Sea Creatures Barker TCM 14457 ! The ocean is home to thousands of creatures, and new species are being discovered every day. Explore how fast a

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Independent and Dependent Variables In the equation 5c = w, there are two variables. The variable c is the independent variable. The variable w is the dependent variable. That means the value of w depends on the value of c.

The Missing Multiplication Sign In algebraic expressions, the multiplication sign is omitted. When a number is written directly before a variable, for example 5c, that means the number (5) is multiplied by the variable (c).

We can solve the equation w = 5c using substitution. If we have 2 crabs, we can substitute the number 2 for the variable c. That would be w = 5(2), or w = 10. The combined average weight of 2 crabs is 10 kilograms.

Each crab has 2 feeding arms with pincers.

a. Determine the total number of feeding arms, f, for 0–6 crabs. Write your answers in the table like the one on page 6.

b. Write an equation to represent the total number of feeding arms, f, on x crabs.

c. Look at the equation you wrote for problem b. Identify the dependent and independent variables.

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Page 9: Sea Creatures - Academic Therapy...Sea Creatures Barker TCM 14457 ! The ocean is home to thousands of creatures, and new species are being discovered every day. Explore how fast a

The sailfish is the fastest fish in the sea. It has been clocked leaping out of the water at 68 miles (109 km) per hour. The leaping speed is not a speed the fish maintains over a long period of time, though. The sailfish has been known to maintain a rather rapid speed of 20 miles (32 km) per hour. This speed is equal to about 1,760 feet (536 m) per minute. That is one-third of a mile every minute!

This table shows the total distance a sailfish travels at a rate of 1,760 feet per minute.

Time (in minutes)(t)

1,760 Feet per Minute (r) Multiplied by the

Time (in minutes)(r • t)

Total Distance (in feet)(d)

1 1,760 • 1 1,760

2 1,760 • 2 3,520

3 1,760 • 3 5,280

t 1,760 • t 1,760t

The distance (d) the fish swims equals the rate (r) multiplied by the time (t). The equation for finding a distance (d = rt) is called the distance formula. In this case, d = 1,760t. By substituting values for the independent variable (t) we can find the dependent variable (d).

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Fastest Fish

Page 10: Sea Creatures - Academic Therapy...Sea Creatures Barker TCM 14457 ! The ocean is home to thousands of creatures, and new species are being discovered every day. Explore how fast a

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Along with being fast, sailfish are also fairly large fish. They can be longer than 10 feet (3 m) and weigh up to 220 pounds (100 kg). They are found in the warm waters of the Atlantic, Pacific, and Indian Oceans, usually near the surface but far from land. Sailfish feed on squid and octopus, as well as schools of smaller fish.

A sailfish is 400 feet (122 m) from a coral reef. It swims farther away from the reef at a rate of 900 feet (274 m) per minute.

a. Make a table like the one on page 8 to show the sailfish’s distance from the reef (d) after 1, 2, 3, and t minutes.

b. Write an equation that can be used to find the total distance (d) the sailfish will be from the reef in t minutes.

c. Identify the independent and dependent variables in the equation that you wrote for problem b.

d. Write a problem situation that could be described by d = 8t + 200.

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Page 11: Sea Creatures - Academic Therapy...Sea Creatures Barker TCM 14457 ! The ocean is home to thousands of creatures, and new species are being discovered every day. Explore how fast a

Despite its unusual look, the sea horse is actually a fish. This bony fish tends to be anywhere from 0.6 to 14 inches (1.5–36 cm) in length. Sea horses live in warm, shallow waters. Their habitat typically includes tall grasses or coral reefs. They use the grasses or coral reefs to help them hide from predators.

The sea horse spends much of its time resting with its prehensile (pri-HEN-sil) tail wrapped around a nonmoving object.

Sea Horse DadsMale sea horses play an important role in caring for their young before they are born. First, a female sea horse deposits eggs into a front pouch of the male. The male then carries the eggs in his pouch for two to four weeks. The eggs hatch in the pouch. Then the male sea horse gives birth to live babies.

male sea horse giving birth

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Stallions of the Sea