Math Concept Reader MCR g5 halfpipe

Math Concept Reader

Math Concept Reader

DIGITAL FINAL PROOF

Expedition: Antarctica

by Aenea Mickelsen

by Ilse Ortabasi

Math Concept Reader

Copyright © Gareth Stevens, Inc All rights reserved.

Developed for Harcourt, Inc., by Gareth Stevens, Inc.

This edition published by Harcourt, Inc., by agreement with Gareth Stevens, Inc

No part of this publication may be reproduced or transmitted in any form or by any

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Requests for permission to make copies of any part of the work should be addressed

to Permissions Department, Gareth Stevens, Inc., 330 West Olive Street, Suite 100,

Milwaukee, Wisconsin 53212 Fax: 414-332-3567.

HARCOURT and the Harcourt Logo are trademarks of Harcourt, Inc., registered in the

United States of America and/or other jurisdictions.

Printed in the United States of America

ISBN 13: 978-0-15-360198-9

ISBN 10: 0-15-360198-1

1 2 3 4 5 6 7 8 9 10 179 16 15 14 13 12 11 10 09 08 07

DIGITAL FINAL PROOF

Chapter 1:

Halfpipe Dreams



It is early September and Mr Dunbar’s students are in science class

Outside, the weather is still warm, but the public swimming pools in Boise,

Idaho, are already closed for the season The crowds disappear shortly after the

Labor Day holiday The lifeguards return to school or to their winter jobs

Mr Dunbar stands before the class as he introduces the first science unit

He says that the class will study Newton’s Laws of Motion He asks if any of

the students have ever heard of these laws of physics When nobody answers, he

asks the class whether any of them have snowboarded before Only a few of the

students raise their hands Then, he asks how many of them have watched the

Winter Olympics snowboarding competitions

It turns out that quite a few of the students have watched snowboarding on

television The students don’t have much experience snowboarding, but they do

have some knowledge about the sport and the tricks that the athletes do

Everybody in the class wonders what snowboarding could possibly have to

do with Newton’s laws

This is a diagram of a halfpipe.



Melanie tells the class that she loves to watch snowboarders ride down the

halfpipe and up the other side Melanie makes the shape of a trough with her

hands to show the other students what the halfpipe looks like The halfpipe is

dug right into the snow and the walls can be as much as 18 meters across

Eduardo says that he likes to watch snowboarders do tricks like a rodeo flip

He explains that a rodeo flip is a 720-degree sideways somersault

Mr Dunbar explains that Newton’s Laws of Motion help the snowboarder

maneuver and do tricks He says that Newton’s first law states that an object at

rest remains at rest This law also states that an object in motion continues at

a constant speed and in a straight line unless acted on by an outside force Mr

Dunbar tells the class that this is the reason that snowboarders can soar so high

in the air Because they are in motion when they reach the top of the pipe, they

stay in motion Next, he explains that Newton’s second law of motion states that

the Earth’s force of gravity pulls the snowboarder back down to the ground!

10 to 18 meters

1.5 to 3 meters

Entry Ramp

Flat

Lip

Vertical Platform

Transition Wall

10 to 30 centimeters

50 to 100 meters

DIGITAL FINAL PROOF

When class is over, the students continue to talk about snowboarding.



Melanie and her friends continue to talk about snowboarding when class is

over They think about how great it would be if they could go snowboarding this

winter Many of them know how to ride skateboards, but Melanie and her friends

have never tried snowboarding

Cathy pictures herself on a snowboard, flying down the mountain at full

speed Eduardo has gone snowboarding before, and he tells his friends all about

it He explains that when carving, a snowboarder must turn without any skidding,

making a single, thin line in the snow It is a skill that is very difficult to learn

Eduardo pretends to carve up the halfpipe and perform a trick in the air He lands

with a thump on the grass on the playground He gets up, and declares that this

year he wants to go snowboarding again

Michael walks over and joins the group of friends He tells Eduardo and

the others that the Mogul Valley Resort nearby runs snowboarding lessons for

schools He saw an article about the resort in the sports section of the local

newspaper

This snowboarder wears the proper safety equipment as he enjoys his run through the halfpipe.



Melanie is excited about the idea of taking lessons She reminds her friends

that it will be expensive for the whole class to go Michael says the cost for one

day is $25.00 a person This cost includes the lesson as well as the use of a

snowboard and boots

“The price even includes all the safety equipment,” Michael says “Because

snowboarding is an extreme sport, we should wear wrist guards, knee pads, and

hip pads Hip pads are used to cushion your falls and keep your seat warm and

dry They are stretchy and pull on like bike shorts You have to wear a

snowboard helmet while snowboarding, too.”

“You also need a safety leash,” adds Eduardo “The leash is designed to

keep your board attached to your leg That way, if the board comes loose from

your boots, the leash will stop it from sliding away down the hill.”

Cathy wonders how the students would travel to the slopes Michael explains

that even the bus transportation and lift tickets are included in the cost of the

lesson Now, the students believe that they can raise the money so they can all

go snowboarding together this winter

DIGITAL FINAL PROOF

Mr Dunbar explains how Newton’s laws affect snowboarding.



Michael brings the newspaper article about the snowboarding lessons to

school the next day Mr Dunbar asks him up to read the article to the class The

article says, “The program is designed to teach winter sports It focuses on the

safe enjoyment of snowboarding as a lifetime sport Qualified instructors help

students develop their snowboarding skills Level 1 classes are for those students

who have never snowboarded before.”

The class cries out, “That’s us!”

Michael looks at his teacher Mr Dunbar has already decided that the

experience of snowboarding would work very well with his lesson on Newton’s

laws of motion He cannot think of a better way for his students to learn and

understand Newton’s laws than experiencing them firsthand on the slopes On the

slippery snow, his students will see for themselves what it means for objects to

stay in motion!

Mr Dunbar lets the class know that he will help them raise the funds He

will also help organize the class trip to Mogul Valley Resort The students are so

excited about the trip that they all clap and cheer

$25.00 × 27 = $675.00

,

The students decide that the first step they need to take is to calculate how much money they need for the trip The class includes a total of 27 students Michael multiplies 27 by $25.00, which is the cost for each student The product

is $675.00 Thatʼs how much money the class needs to pay for the trip

Cathy suggests they raise the funds for the trip by selling popcorn A friend

of hers in another class raised funds that way last year, and the school can

purchase cases of popcorn for students to sell Mr Dunbar talks to the schoolʼs principal She thinks the popcorn fundraiser is a good idea and agrees to help the class

Mr Dunbar orders the popcorn for the fundraiser Half of the money the students collect will pay for the popcorn, while the other half will be the profit for the trip The popcorn arrives in October Each student in Mr Dunbarʼs class agrees to sell at least one case of popcorn Some students hope to sell even more than that Students work hard to sell popcorn right away because the date of the December trip is not far away

Melanie’s mother volunteers to help with the fundraiser She comes to school

often to collect money from the popcorn sales Melanie and Michael help her add

up the money

The class meets their goal for selling popcorn They made $1,470.00! First,

the students need to pay for all of the popcorn The school paid $735.00 for the

popcorn

Mrs Petty, the principal’s assistant, subtracts this amount of money from the

amount collected by the students She uses that money to pay for the popcorn

$1,470.00 − $735.00 = $735.00

The students have $735.00 left over That amount is more than enough to pay

for the trip The trip costs $675.00

They did it! The fundraiser was successful Everyone in the class will go on

the snowboarding trip Mr Dunbar and the students celebrate their success with a

few bags of popcorn

$ 1,470.00

− $ 735.00 $ 735.00

Results: Men’s and Women’s Snowboard Halfpipe

Chapter 2:



Mr Dunbar prepares his math lesson with his students’ interest about

snowboarding in mind He always likes to make connections to the real world

in his lessons Today’s lesson is called “Fascinating Facts about Snowboarding.”

This is one lesson that the students can’t wait to start

Eduardo seems to be very knowledgeable about snowboarding Mr

Dunbar asks him to explain to the class what the halfpipe snowboarding event

is all about Eduardo describes the halfpipe as a half-cylindrical field about 145

meters long that is dug into the snow Snowboarders enter the halfpipe from a

ramp at the top

Eduardo explains how the snowboarders must cross the halfpipe from side to

side six to eight times during a competition They must use the full length of the

pipe They do this while performing acrobatics, called maneuvers or tricks

Five judges award points for the maneuvers They give points for the height

of the snowboarder’s jumps In addition, the judges score the overall technical

quality of the performance This portion of the score includes the quality of the

landings Snowboarders are supposed to have clean, smooth landings They’re

not supposed to fall, or use their hands to keep them from falling

DIGITAL FINAL PROOF

The 12 snowboarders who achieve the highest scores in the two

qualifying runs advance to the final round of competition The final round

consists of two runs, each of which includes five jumps The snowboarders get

a score for each run, but only the better of the two scores counts That allows

them to take chances If they fall on their first run, they always have another run

to impress the judges

Mr Dunbar brought the results from a men’s and women’s halfpipe

competition to share with the class He wants the class to determine the winner

of each final event, as well as how the first four competitors ranked Mr Dunbar

says ranking means putting the competitors in first, second, third, and fourth

positions, according to their scores Then he adds, “This can be done by adding

and subtracting decimals.”

Mr Dunbar projects a table on the screen of the classroom’s computer The

table shows the points the five judges gave the male snowboarders The class will

compute the scores for each snowboarder in the competition, and rank the top

four To find the score for each athlete in both runs, they need to add up the points

for all jumps

Athlete’s

Bib Number Jump 1 Jump 2 Jump 3 Jump 4 Jump 5

st Final Run

nd Final Run

Results from Final Men’s Halfpipe Competition

A snowboarder completes a maneuver on the halfpipe.

11

“You know how to add whole numbers, so you already know how to add

numbers with decimals,” Mr Dunbar says “You just need to line up the decimal

points You can give your decimals the same number of places by adding on

zeros That makes it easier to keep track of places as you do your addition.”

As an example, Mr Dunbar stands in front of the class and computes the

first final run score for the snowboarder with bib number 31 He takes the

snowboarder’s five jump scores and adds them together by lining up the

decimal points and adding zeroes so that all of the scores have the same

number of places after the decimal

Soon the whole class is busy figuring out who won the men’s halfpipe

competition Eduardo reminds the class that the run with the highest score is the

one that counts for each snowboarder He doesn’t know if that scoring rule is

the same for all Olympic winter sports, though Eduardo, Roy, and Angela work

together They finish adding the scores for the men’s halfpipe snowboarding

competition

DIGITAL FINAL PROOF

The snowboarder who was wearing bib number 8 ranked number 1 He had

the highest score on his first run! The second highest ranked snowboarder

received his best score on the second run The third and fourth highest ranked

snowboarders received their best score on their first runs

Mr Dunbar tells the class that not all of the sports in the Winter Olympics are

scored the same way as snowboarding In ski jumping, the winner is the athlete

who receives the highest total score from two jumps Unlike in snowboarding, the

worst score isn’t thrown out

Eduardo wonders whether that different method of scoring would have

changed the results of the snowboarding halfpipe competition Melanie raises

her hand and tells the class that she has already done the computations in her

notebook She added up scores from the first and second final runs for each

snowboarder, and ranked them based on total score If the Olympic judges had

computed the points according to the ski jumping rules, the final ranking of the

snowboarders would have been different!

Athlete’s 1 st Final Run 2 nd Final Run

Bib Number Total Score Total Score

Athlete’s Rank Bib Number Score

Final Rankings

Melanie tells the class that if the scores from the two runs had been added

together, first place would have gone to the snowboarder wearing bib number

31 Snowboarder number 8 would have finished in second place instead of first

place The third ranking athlete would be number 25 and the fourth ranking

athlete would be number 19

The class concludes that the scoring rules can make a big difference on

where each snowboarder finishes in the final rankings They also agree that for

snowboarding, keeping just one score is a good idea Otherwise, the athletes

might not try as many risky tricks, and it might not be as exciting to watch

As the school bell rings, Mr Dunbar passes out the data from the women’s

final event and tells the class that the computations of the results of the women’s

final event will be their homework assignment

The next day, Mr Dunbar goes over the homework with his students The

class meets in groups to review their computations Angela and the other

students in her group made a table of the results for the second final run in the

women’s halfpipe snowboarding competition

Athlete’s

Bib Number Jump 1 Jump 2 Jump 3 Jump 4 Jump 5

Results from 2nd Final Run Women’s Halfpipe Competition

Athlete’s Bib Number Score

DIGITAL FINAL PROOF