Real Numbers - PWR Transitional Math

Algebra I & Mathematics IAlgebra I & Mathematics I

Student EditionStudent Edition

Real Numbers

ISBN 978-1-940836-06-5 — Teacher Edition

ISBN 978-1-940836-05-8 — Student Edition

© 2014

For Information Contact: Center for Mathematics, Science, and Technology 210 W. Mulberry St Illinois State University Normal, IL 61790 309-438-3089 http://cemast.illinoisstate.edu

S T E M Science Technology Engineering Mathematics

Real Numbers

All rights reserved. This file is intended for use by teachers in Illinois only. Any reproduction, or use in any

form or by any means — graphic, electronic, or mechanical, including photocopying, recording, taping,

information storage and retrieval systems — by anyone other than Illinois teachers without written

permission of the publisher is prohibited.

Printed in the United States of America.

Real Numbers: Pathways to Common Core Mathematics 287

Chapter 8

Connecting Algebra and Geometry

How Much Elbow RoomDo You Need?

Illinois Pathway: Architecture and Construction; Agriculture, Food, and Natural Resources

Objectives• Find arc length.• Find the area of a sector.• Find the area of geometric shapes.

IntroductionDetermininghowmanypeoplecanfitcomfortablyatthetableisaproblemfacedbyfamiliesandrestaurantsalike.Duringthe holidays or special occasions families try to cram as many people as they can around their available tables. Restaurants needtodeterminethemaximumandminimumnumberofpeopletheycanfitatcertainsizedtablestomaximizethespacetheyhaveandaccommodatetheirguests.Wearegoingtofindouthowmuchelbowroomeachpersonshouldgetdependingonthesizeandshapeofthetableandhowmanypeoplecanfitaroundit.

Student Edition

288 How Much Elbow Room Do You Need?

Chapter 8

T�� I�

UsetheactionfiguresizedTable 1 and a ruler for the following calculations.

1 Find how much elbow room (arc length) eachactionfigurehasatTable 1.

2 Findtheareaofeachactionfigure’splacesettingzoneatTable 1.

D�� I�

1 Howdidyoudeterminehowmuchelbowroomeachactionfigurehas(arc length) at Table 1?

2 Howdidyoudeterminetheareaofeachactionfigure’splacesettingzoneatTable 1?



T�� I�

UsetheactionfiguresizedTable 2 and a ruler for the following calculations.

1 Find the area of the shared access zone for Table 2.

2 FindtheplacesettingzoneforeachactionfigureatTable 2.

D�� I�

1 HowdidyoudeterminethesharedaccesszoneforTable 2?

2 HowdidyoudeterminetheplacesettingzoneforeachactionfigureatTable 2?

3 What is the use of the shared access zone?

4 In what situations would you need to have more shared access zone at a table?



A�� I�

1 Find how much elbow room (arc length) each person has if six people are seated at a 72 inch diameter table.

2 Find the area of each place setting zone if six people are seated at a 72 inch diameter table with no shared access.

3 What is the interior angle for six people at the table?

4 Find how much elbow room each person has if eight people are seated at a 72 inch diameter table.

5 Find the area of each place setting zone if eight people are seated at a 72 inch diameter table with no shared access.

6 What is the interior angle for eight people at the table?

7 Howmanypeoplecouldfitatacirculartablewithaninteriorangle of 24º?

8 Howmuchmorespacedoeseachpersonhaveattheirplacesettingzonewithsixpeopleatthetablecomparedtoeight?Photos Copyright ©1979

Human Dimension & Interior Spaceby Julius Panero and Martin Zelnick

Photos Copyright ©1979Human Dimension & Interior Spaceby Julius Panero and Martin Zelnick



InteriorAngle

Place-SettingZone

24 in

.

Place-SettingZone

24 in.

SHARED ACCESSZONE

InteriorAngle

Place-SettingZone Place

SettingZone

SHARED ACCESSZONE





InteriorAngle

Place-SettingZone

24 in

.

Place-SettingZone

24 in.

SHARED ACCESSZONE

InteriorAngle


SettingZone

SHARED ACCESSZONE

Chapter 8


9 Giventhateachpersonneedsatleast24inchesofelbowroom,whatisthemaximumnumberofpeoplethatcanfitcomfortably around a 72 inch table?

10 Find how much elbow room each person has given any number of people seated at any size table.

11 Find the area of each place setting zone given any number of people seated at any size table with no shared access.

12 Are there any parameters or limitations to take into consideration when determining the number of people that can be seated at a table?

E�� I�

1 Find the area of each place setting zone if six people are sitting at the 72 inch diameter table shown at the right, given the shared access zone pictured.

2 Find the area of each place setting zone if eight people are sitting at the 72 inch diameter table shown on the next page, given the shared access zone pictured.





InteriorAngle

Place-SettingZone

24 in

.

Place-SettingZone

24 in.

SHARED ACCESSZONE

InteriorAngle


SettingZone

SHARED ACCESSZONE


Chapter 8

3 Howmuchlessspacedoeseachpersonhavewhenthesharedaccess zone is taken into account?

4 Why is it important to take into consideration the shared access zone?





InteriorAngle

Place-SettingZone

24 in

.

Place-SettingZone

24 in.SHARED ACCESS

ZONE

InteriorAngle


SettingZone

SHARED ACCESSZONE



Table 1 Table 2

ELBOW ROOMELBOW ROOM

SHAREDACCESSZONE

SHAREDACCESSZONE

PLACESETTING

ZONE

PLACESETTING

ZONE

Real Numbers - PWR Transitional Math

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