by for teachers and students thanks for checking us out ... · assignments are also provided as...

Sample Pages from

Created by Teachers for Teachers and Students

Thanks for checking us out. Please call us at 800-858-7339 with questions or feedback, or to order this product. You can also order this product online at www.tcmpub.com.

For correlations to State Standards, please visit www.tcmpub.com/administrators/correlations

800-858-7339 • www.tcmpub.com

Teacher’s Guide

L

evel 6

M

athematics R

eaders

Teacher’s Guide

Level 6

TCM 14444

© Teacher Created Materials #14444—Mathematics Readers, Teacher’s Guide Level 6 3

Table of ContentsIntroduction

Research on Mathematics and Literacy . . . . 5How to Use This Product . . . . . . . . . . . . . . . 12

Organization of the Books . . . . . . . . . . 12Components of the Product . . . . . . . . . 15Assessment Strategies . . . . . . . . . . . . . . 18Reading Levels Chart . . . . . . . . . . . . . . . 19Level 6 Pacing Plan . . . . . . . . . . . . . . . . . 20

Program Scope and Sequence . . . . . . . . . . . 22Mathematics Chart . . . . . . . . . . . . . . . . 22Nonfiction Literacy Chart . . . . . . . . . . 25

Book Summaries . . . . . . . . . . . . . . . . . . . . . . . 26Standards Correlations . . . . . . . . . . . . . . . . . . 30

NCTM Correlations . . . . . . . . . . . . . . . . 31McREL Language Arts Correlations . . 32TESOL Correlations . . . . . . . . . . . . . . . . 32

Using the BooksUnit 1: Ratios and Proportions . . . . . . . 33–56

On the Road BookLesson Plan . . . . . . . . . . . . . . . . . . . . . . . 36Student Reproducibles . . . . . . . . . . . . . . 39

Our New Car BookLesson Plan . . . . . . . . . . . . . . . . . . . . . . . 41Student Reproducibles . . . . . . . . . . . . . . 44

Focused Mathematics LessonPre-test . . . . . . . . . . . . . . . . . . . . . . . . . . . 46Lesson Plan . . . . . . . . . . . . . . . . . . . . . . . 47Student Reproducibles . . . . . . . . . . . . . . 50

Using the Problem-Solving TransparenciesLesson Plan . . . . . . . . . . . . . . . . . . . . . . . 52Student Reproducibles . . . . . . . . . . . . . . 54

Unit 2: Fractions, Decimals, and Percents . . . . . . . . . . . . . . . . . . . . . . . . 57–80

What Did I Eat? BookLesson Plan . . . . . . . . . . . . . . . . . . . . . . . 60Student Reproducibles . . . . . . . . . . . . . . 63

How Do They Make That? BookLesson Plan . . . . . . . . . . . . . . . . . . . . . . . 65Student Reproducibles . . . . . . . . . . . . . . 68


Using the Problem-Solving TransparenciesLesson Plan . . . . . . . . . . . . . . . . . . . . . . . 76Student Reproducibles . . . . . . . . . . . . . . 78

Unit 3: Writing, Simplifying, and Evaluating Expressions . . . . . . . . . . . . . 81–104

Watch It Grow BookLesson Plan . . . . . . . . . . . . . . . . . . . . . . . 84Student Reproducibles . . . . . . . . . . . . . . 87

Where Germs Lurk BookLesson Plan . . . . . . . . . . . . . . . . . . . . . . . 89Student Reproducibles . . . . . . . . . . . . . . 92


Using the Problem-Solving TransparenciesLesson Plan . . . . . . . . . . . . . . . . . . . . . . 100Student Reproducibles . . . . . . . . . . . . . 102

Unit 4: Solving Equations and Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .105–128

Land Animals BookLesson Plan . . . . . . . . . . . . . . . . . . . . . . 108Student Reproducibles . . . . . . . . . . . . . 111

Sea Creatures BookLesson Plan . . . . . . . . . . . . . . . . . . . . . . 113Student Reproducibles . . . . . . . . . . . . . 116

Focused Mathematics LessonPre-test . . . . . . . . . . . . . . . . . . . . . . . . . . 118Lesson Plan . . . . . . . . . . . . . . . . . . . . . . 119Student Reproducibles . . . . . . . . . . . . . 122

#14444—Mathematics Readers, Teacher’s Guide Level 6 © Teacher Created Materials4

Table of Contents (cont.)


Unit 5: Perimeter and Area . . . . . . . . . 129–152

A Sense of Art BookLesson Plan . . . . . . . . . . . . . . . . . . . . . . 132Student Reproducibles . . . . . . . . . . . . . 135

Landscape by Design BookLesson Plan . . . . . . . . . . . . . . . . . . . . . . 137Student Reproducibles . . . . . . . . . . . . . 140



Unit 6: Surface Area and Volume . . . 153–176

Package Design BookLesson Plan . . . . . . . . . . . . . . . . . . . . . . 156Student Reproducibles . . . . . . . . . . . . . 159

Pack It Up BookLesson Plan . . . . . . . . . . . . . . . . . . . . . . 161Student Reproducibles . . . . . . . . . . . . . 164



Unit 7: Measures of Central Tendency . . . . . . . . . . . . . . . . . . . . . . . . . 177–200

Hurricane Hunters BookLesson Plan . . . . . . . . . . . . . . . . . . . . . . 180Student Reproducibles . . . . . . . . . . . . . 183

Tornado Chasers BookLesson Plan . . . . . . . . . . . . . . . . . . . . . . 185Student Reproducibles . . . . . . . . . . . . . 188



Unit 8: Using Data and Graphs . . . . . 201–223

Tonight’s Concert BookLesson Plan . . . . . . . . . . . . . . . . . . . . . . 204Student Reproducibles . . . . . . . . . . . . . 207

Battle of the Bands BookLesson Plan . . . . . . . . . . . . . . . . . . . . . . 209Student Reproducibles . . . . . . . . . . . . . 212



Diagnostic Test . . . . . . . . . . . . . . . . . . .224

Culminating Activity . . . . . . . . . . . . . .232

AppendicesAppendix A: References Cited . . . . . . . . . . 246Appendix B: Interactive Mathematics Activities CD . . . . . . . . . . . . . . . . . . . . . . . . . 248Appendix C: Glossary . . . . . . . . . . . . . . . . . . 251Appendix D: Answer Key . . . . . . . . . . . . . . 253Appendix E: Contents of Teacher Resource CD . . . . . . . . . . . . . . . . . . . . . . . . . 263

÷

÷

=

+=

+

÷

÷

=

+=

+

÷

=+


Introduction

Research on Mathematics and LiteracyMeeting Needs in Today’s ClassroomsMore than ever before, there is a need to boost students’ understanding of mathematics in all grade levels . “We must expect all of our students to learn mathematics well beyond what we previously expected . We need all students to be more proficient than in the past, and we need many more students to pursue careers based on mathematics and science” (Seeley 2005) . There is also great need for more effective instruction in reading comprehension using nonfiction texts . In a study published in 2000 by Michigan State University education researcher Nell Duke, it was reported that first graders were exposed to an average of 3 .6 minutes of informational text per day . Students in low socioeconomic groups were exposed to less than two minutes of informational text per day (Collier 2006) . Today’s world is focused on information . The advent of the Internet has put countless informational resources at our fingertips . Students will be ill equipped in the real world unless they are exposed to informational texts in schools . Nonfiction texts are also prevalent on high-stakes tests . “Reading nonfiction materials would increase students’ depth of knowledge in the content areas, and probably help students score higher on the standardized tests that are of such concern to teachers and administrators” (Ivey and Broaddus 2000) .

Research by the National Council of Teachers of English shows that students have difficulty learning when subjects are taught in isolation (NCTE 1993) . “When language skills are embedded in meaningful contexts, they are easier and more enjoyable for children to learn . In the same way, numbers and their operations, when embedded in meaningful real-world contexts, give children the opportunity to make sense of mathematics and to gain mathematical power” (NCTM 2000) .

Mathematics Readers is a mathematics-based reading program . It combines effective instruction in nonfiction reading-comprehension strategies with standards-based mathematical content . Although literacy continues to be the primary focus in today’s schools, it is essential that teachers do not decrease instructional time spent in other crucial content areas . This program efficiently integrates instruction in mathematics and reading comprehension with a collection of engaging books that focus on mathematical concepts . Nonfiction writing assignments are also provided as extensions to what is being taught in the mathematics and reading lessons . Each book is written around real-life situations that are applicable to the students . The books include captivating photographs, interesting facts and captions, engaging questions, problem-solving scenarios, and leveled texts . Nonfiction features, such as tables of contents, glossaries, and indices, are also included . All of the books are organized by mathematical content strands to give the students a base of vocabulary and understanding on which to build comprehension .

This teacher’s guide offers lesson plans and teaching suggestions for both the reading and mathematics components . As a result, teachers are able to engage students, address different learning styles, and develop student understanding that leads to higher-level thinking . This program will support teachers’ effective mathematics instruction while boosting general reading skills .

÷

÷

=

+=

+

÷

÷

=

+=

+

÷

=+


÷

÷

=

+=

+

÷

÷

=

+=

+

÷

=+

O B J E C T I V E SO B J E C T I V E S


Teacher Resources Ratios and Proportions

Timeline for the UnitMathematics Language Arts

Day 1 Complete the Introduction to Mathematics Vocabulary and the Before Reading activities. (30 min.)

Complete the Before Reading activities. (30 min.)

Day 2 Begin the During Reading activities. Assign the student activity sheet. (30 min.)

Begin the During Reading activities. (60 min.)

Day 3 Finish the During Reading activities. Complete the After Reading activities. (45 min.)

Finish the During Reading activities. Complete the After Reading activities. (45 min.)

Day 4 Do the Focused Mathematics Lesson. (60 min.)

Have students reread the books or do the extension activities.

Day 5 Complete the Problem-Solving Lesson. (45 min.)

Reread, if necessary, or complete the extension activities.

On the Road and Our New Car

• Mathematics: Students will use ratio language to describe relationships and solve real-world problems, including rates and percent.

• Nonfictionreading: Students will visualize information from a text.

• Nonfictionwriting: Students will write persuasive paragraphs.

Timeline for the Unit This chart provides information to help you organize

your scheduling of the unit . It estimates how long each part of each lesson will take to complete with your class .

Objectives Listed here are the mathematics, reading, and writing

objectives for the lesson plans . Each pair of books has the same objectives so that students are focused on learning the same skills and concepts .

Introduction to Mathematics Vocabulary Each set of lessons has an activity to introduce the

mathematics vocabulary . This activity introduces the key mathematics words for the unit and is completed as a whole class .

÷

÷

=

+=

+

÷

÷

=

+=

+

÷

=+


On the Road and Our New Car (cont.)

Materials • chartpaper

Introduction to Mathematics Vocabulary 1. Write the vocabulary words on the chart

paper. As you introduce each word, write an example of the word on the chart paper.

2. Display the fraction 12 . Have one boy and

two girls stand up. Tell students that the ratio of boys to girls is 1:2. Explain that a ratio describes how two groups compare to one another. Have one more boy and two more girls stand up so that there are two boys and four girls. Ask students to give the ratio of boys to girls. When they say 2:4, have the students standing up separate into two groups of 1 boy and 2 girls. Explain that 1:2 and 2:4 are equivalent ratios. Ask students to give the ratio of girls to boys (4:2). The two parts describe the same general category—in this case, the category is people.

3. Have one girl and three boys stand up. Ask students to find the ratio of the number of girls to the total number of people (1:4). Ask how many girls there would be if this ratio were maintained for a total of 100 people (25:100). Explain that this is the meaning of percent—a ratio where a number is compared to 100.

4. Ask students what it means if a car travels at 50 mph. Explain that this is an example of a rate, where two numbers are compared that have different units of measurement. In this case, miles and hours are the units. Tell students that a runner travels 15 miles in 150 minutes. Ask them to find the speed of the runner in miles per minute.

Vocabulary • equivalentratios—ratios that have

the same value when simplified • percent—a part of a whole

expressed in hundredths • rate—a ratio comparing an amount

or distance to a period of time • ratio—a comparison of two

quantities

Differentiation Provide English language learners with picture cards that show ratios with pictures of boys and girls, showing boys:girls and the ratios.


÷

÷

=

+=

+

÷

÷

=

+=

+

÷

=+


Using the Books 1. Divide students into reading groups by readiness levels. Students on or above a

sixth-grade reading level should read the On the Road books. Students who are reading below a sixth-grade level should read the Our New Car books.

2. Within these groups, complete the activities described in each lesson plan on the following pages:

•On the Road book (pages 36–40) •Our New Car book (pages 41–45)

3. At the end of the lessons, bring students back together as a group to complete the Focused Mathematics Lesson on pages 46–51.

Using the Focused Mathematics Lesson Each Focused Mathematics Lesson uses concrete models, pencil and paper tasks, and application activities to develop mastery of the objective(s). The lesson starts and finishes with the books so that the mathematical learning is closely tied to the real-life aspects of the books.

Using the Problem-Solving TransparenciesThere are two problem-solving transparencies to support this unit of study. The first matches the problem-solving activity on pages 28–29 of the books, and the second supports the integration of mathematical skills and problem-solving strategies. Each can be used in a number of different ways. You can follow the specific lesson plans (pages 52–55) to analyze and discuss the real-life problems with your reading groups. Or, you can give copies of the lessons and the overhead transparencies to selected students and have those students teach the lesson to the rest of the class (or each student can teach a small group). You can also use the transparencies for whole-class lessons.

AssessmentThis mathematics lesson has a pre-test (page 46; page046.pdf) of the mathematical objective. Use the pre-test to determine the skills on which your students need to focus the most. This pre-test can be administered at any time prior to the teaching of this lesson so that results can be used to differentiate instruction. Also included is a Diagnostic Test (pages 224–231; page224.pdf) to assess student learning.

On the Road and Our New Car (cont.)


Using the Books This section begins the actual lesson plan for working

with the students as they read the books . This is the first page of the lesson plan . In total, there are three sections: Before Reading, During Reading, and After Reading . Many of the activities and questions can be used in any order that you would like . You do not need to follow the step-by-step directions to be successful with these activities .

How to Use This Product (cont.)

Introduction

Components of the Product

÷

÷

=

+=

+

÷

÷

=

+=

+

÷

=+


Student Reproducibles • There are many student guided practice pages

throughout the unit . These pages can be completed individually, in small groups, or as homework .

• Every book lesson has a page like this one, which relates directly back to a Let’s Explore Math activity in the book . Students may want to refer back to the book to get further information so they can solve the problems .


Name __________________________________ Date __________________________

Let’s Explore Math—On the Road

Directions: Answer the following questions.

On one day of the Elliot family’s trip, Malika observed 75 blue cars and Terell counted 50 green cars.

a. Give the following ratios of the cars in simplest form: blue to green, green to blue, blue to total cars, and green to total cars.

b. Suppose that they continued to count, and the ratio of blue to green cars remained the same. Terell counted 150 green cars. Write a proportion that could be used to find the number of blue cars. How many blue cars would Malika have counted?

c. Suppose they counted a total of 240 cars. If the ratio of green cars to total cars stays the same, write a proportion that could be used to find the number of green cars. How many green cars would Terell have counted?

d. Using the information from problem c, how many blue cars would Malika have counted? How did you find the number of blue cars? How else could you have found the number of blue cars?

a. A car is traveling at 60 mph. What is its speed in miles per day? (Hint: Think of how many hours are in a day.)

b. A truck is moving at 4,840 feet per minute. What is the speed in mph? (Hint: Think of how many minutes are in an hour and how many feet are in a mile.)

c. A car in Peru is traveling at 100 kilometers per hour. There are approximately 1.6 kilometers in a mile. About how fast is the car going in mph?

Student Reproducibles Ratios and Proportions

a =

2x +

4a

= 2x

+ 4


Learning ObjectiveMathematics: Students will use ratio language to describe relationships and solve real-world problems, including rates and percent.

Materials • copiesofRatios and Proportions Pre-test

(page 46; page046.pdf)

• On the Road and Our New Car books

• copiesofUps and Downs (page 50; page050.pdf)

• copiesofHands Full (page 51; page051.pdf)





quantities


Focused Mathematics Lesson: Ratios and Proportions


Book Warm-UpDistribute the On the Road and Our New Car books to students. Have students find at least three examples of percent problems in each book.

Focused Mathematics Lesson As students finish with the book, move into the

whole-class mathematics lesson . The lesson focuses on key mathematical skills and concepts . The activities can be completed during mathematics time in support of what you have done during reading instruction .

Using the Problem-Solving Transparencies • Each lesson has a problem-solving overhead

transparency . These transparencies can be used in small group lessons or for whole-class activities . The real-life problems on the transparencies support the mathematical concepts of the unit .

• There are a total of 16 transparencies . Eight of the transparencies match the problem-solving activities in the books . The other eight were created to support the integration of mathematical skills and problem-solving strategies .

a =

2x +

4a

= 2x

+ 4




(page 46; page046.pdf)



• copiesofHands Full (page 51; page051.pdf)





quantities




Book Warm-UpDistribute the On the Road and Our New Car books to students. Have students find at least three examples of percent problems in each book.


Introduction

Components of the Product (cont.)

÷

÷

=

+=

+

÷

÷

=

+=

+

÷

=+


Teacher Resource CD

Helpful reproducible resources and PDFs are provided on the accompanying CD . Find a detailed listing of the CD contents on pages 263–264 . The CD includes:

• Reproducible PDFs of all assessments

• Diagnostic Test Item Analysis Excel® spreadsheet

• PDFs and Word® documents of all books

• Reproducible PDFs of the problem-solving transparencies

• Reproducible PDFs of in-depth versions of the transparencies that include step-by-step directions for solving the problem

• Reproducible PDFs of all student activity sheets

• Reproducible PDFs of additional teacher resources

Interactive Mathematics Activities CD

Eight engaging CD-based mathematical games are provided on three CDs included in the kit . Find a detailed description of the activities and how to use them on pages 248–250 . Game titles include:

• Fair Game

• Extraterrestrial Equivalents

• Express Yourself

• Step Right Up!

• Picture This!

• Box It Up

• Measure Up

• Treasure Hunters

TCM 14446


Level 6© 2012 Teacher Created Materials, Inc.

For use with either Macintosh®

or Windows®

TCM 14446




or Windows®

TCM 14446




or Windows®


Introduction

Components of the Product (cont.)

÷

÷

=

+=

+

÷

÷

=

+=

+

÷

=+


Introduction

Assessment is an integral, important part of this unit of study . You can gain insight into students’ learning through written pre-tests, small-group observations, analysis of written assignments, the diagnostic test, and the culminating activity . These frequent formal and informal assessments provide the data needed to make informed decisions about what to teach and how to teach it . This is the best way to know who is struggling with various concepts and how to address the difficulties that students are experiencing with the curriculum .

There are several points throughout each lesson where useful evaluations can be made . Depending on the results, you can decide to continue with the lesson as planned or change gears to reteach or reinforce concepts .


Name __________________________________ Date __________________________

Ratios and Proportions Pre-test

Directions: Circle the best answer for each of the following questions.

A pet shelter is housing 8 dogs and 12 cats.

1. What is the ratio of cats to dogs in simplest form?

A. 3:4

B. 3:2

C. 2:3

D. 4:3

2. What is the ratio of dogs to total animals in simplest form?

A. 2:5

B. 5:2

C. 1:3

D. 3:1

3. In a school, the ratio of teachers to students is 3:64. If there are 15 teachers in the school, how many students are there?

A. 15 students

B. 192 students

C. 320 students

D. 915 students

4. A cricket chirps 1,200 times in 30 minutes. What is the rate of chirping in chirps per minute?

A. 20 chirps per minute

B. 30 chirps per minute

C. 40 chirps per minute

D. 50 chirps per minute

5. Maria purchased a shirt during a 30% off sale. If the regular price was $36, how much did she pay?

A. $10.80

B. $25.20

C. $29.00

D. $33.00

Ratios and Proportions Student Reproducibles • Before the Focused Mathematics Lesson—By giving the lesson pre-test, you can determine on which aspects of the lesson to focus . You can also use this assessment to differentiate instruction . Students who do well on the pre-test can complete the enrichment challenges, while students who do not get all of the questions correct should participate in the lesson and may need some reteaching opportunities .

a =

2x +

4a

= 2x

+ 4




(page46;page046.pdf)



• copiesofHands Full (page51;page051.pdf)


thesamevaluewhensimplified • percent—apartofawhole


ordistancetoaperiodoftime • ratio—acomparisonoftwo

quantities



AssessmentThismathematicslessonhasapre-test(page46;page046.pdf)ofthemathematicalobjective.Usethepre-testtodeterminetheskillsonwhichyourstudentsneedtofocusthemost.Thispre-testcanbeadministeredatanytimepriortotheteachingofthislessonsothatresultscanbeusedtodifferentiateinstruction.AlsoincludedisaDiagnostic Test (pages 224–231; page224.pdf)toassessstudentlearning.

Book Warm-UpDistribute the On the Road and Our New Car bookstostudents.Havestudentsfindatleastthreeexamplesofpercentproblemsineachbook.

• After Assessing Prior Knowledge—The warm-up mathematics vocabulary activity provides opportunities to assess students’ prior knowledge . During these activities, you may realize that students have a strong understanding of the concepts being introduced . Or, it may become clear that students are weak in these concepts . Analyzing students during these introductory activities will help you adjust lessons as necessary .

• During Guided Practice—Within these lessons, practice problems are provided for teacher modeling as well as student practice . Use this time to assess whether students have comprehended the lesson concepts and are on their way to mastery .

• Diagnostic Assessment—Use the Diagnostic Test as a pre-test and as a post-test to gauge students’ overall progress . If used as a post-test, the pre-tests from the individual units are great study guides . Have students review their pre-tests and re-solve the problems in preparation for the final test . A Diagnostic Test-Item Analysis is included on the CD (testitem .pdf; testitem .xls) .

• Final Authentic Assessment—A culminating activity has been included in this unit . The activity allows students to apply what they have learned throughout the unit in an engaging, interactive way . Students can take what they have learned and use that information to create new ideas in a real-life context .

Q U E S T I O N SQ U E S T I O N S


Name __________________________________ Date __________________________

Ups and Downs

Directions: Find the increase or decrease in the season attendance at football games for each school. Then find the percent of increase or decrease in attendance for each school. If there is a decrease, put a negative sign in front of the amount of decrease and the percent of decrease. Round your answers to the nearest whole percent.

High SchoolSeason

AttendanceLast Year

Season AttendanceThis Year

Amount of Increase or Decrease

Percent of Increase or Decrease

Washington 4,500 5,000

Adams 5,500 4,800

Jefferson 5,000 5,500

Madison 4,800 5,200

Monroe 5,000 4,500

Quincy 4,800 5,500

Jackson 5,500 5,000

Van Buren 5,200 4,800

1. Which school had the largest numerical increase in attendance? Which had the largest percent increase?

_________________________________________________________________

_________________________________________________________________

_________________________________________________________________

2. Why are the percents for Washington and Monroe different numbers?

_________________________________________________________________

_________________________________________________________________

_________________________________________________________________

Ratios and Proportions Students Reproducibles


Name __________________________________ Date __________________________

Diagnostic Test Student Reproducibles

Diagnostic Test

Directions: Circle the best answer for each of the following questions.

Use this information to answer questions 1 and 2.

A bag contains 9 blue marbles and 15 red marbles.

1. What is the ratio of blue marbles to red marbles in simplest form?

A. 3:8

B. 3:5

C. 8:3

D. 5:3

2. What is the ratio of red marbles to total marbles in simplest form?

A. 3:5

B. 8:5

C. 5:3

D. 5:8

3. In a zoo, the ratio of marsupials to mammals is 5:27. If there are 15 marsupials in the zoo, how many mammals are there?

A. 32 mammals

B. 81 mammals

C. 135 mammals

D. 243 mammals

4. A light flashes 1,800 in 45 minutes. What is the rate of flashing in flashes per minute?

A. 20 flashes per minute

B. 30 flashes per minute

C. 40 flashes per minute

D. 50 flashes per minute

5. Elias purchased a shirt during a 25% off sale. If the regular price was $38, how much did he pay?

A. $9.50

B. $28.50

C. $37.25

D. $38.25

6. 30% of the cars sold at a dealership were black. If the dealership sold 150 cars, how many were black?

A. 30 cars

B. 45 cars

C. 120 cars

D. 105 cars

÷

÷

=

+=

+

÷

÷

=

+=

+

÷

=+


Culminating Activity

Timeline for the Lesson

Mathematics Language Arts and Reading

Day 1 Begintheplanningofabicycletripforacyclingclub,includingthekindsofbicyclestobeusedorpurchased,thenumberofdaysfortravel,theroutetobetaken,decisions about overnight lodging, meals,transportationofsupplies,andplanningforinclementweather.Complete the math activity sheets to accompanythetrip.(90min.)

Review how to use the books as resourcesforplanningthetrip.

Day 2 Finishtherestofthemathsheetsandcreatealogforthetrip.(90min.)

Use the ExtensionIdea to create a pamphlet about promoting their cycling trips and their cycling clubs. (60min.)

Materials • allmathematicsbooks

• copiesofstudentreproducibles(pages236–241,243–244;page236.pdf;page237.pdf;page238.pdf;page239.pdf;page240.pdf;page241.pdf;page243.pdf;page244.pdf)

• mapsofyourstate

• Road Hazards Cards(page242;page242.pdf),cutalongthedottedlines

• scissors

• chartpaper

Differentiation • ProvideEnglishlanguagelearnerswithlistsofthevocabularywordsfromthe

previouslessonssothattheycanrefertothedefinitionsastheyreadtheguidelines,refreshingtheirmemoriesofthemathematicalconcepts.

• Haveabove-grade-levelstudentsstudythegearingsystemsondifferentkindsofbicyclesandexplainthemechanicaladvantagesofdifferentgears.

Culminating Activity Teacher Resources


Assessment Strategies

÷

÷

=

+=

+

÷

÷

=

+=

+

÷

=+

O B J E C T I V E SO B J E C T I V E S


Teacher Resources Writing, Simplifying, and Evaluating Expressions

Watch It Grow and Where Germs Lurk

Timeline for the UnitMathematics Language Arts

Day 1 Complete the Introduction to Mathematics Vocabulary and the Before Reading activities . (30 min .)

Complete the Before Reading activities . (30 min .)

Day 2 Begin the During Reading activities . Assign the student activity sheet . (30 min .)

Begin the During Reading activities . (60 min .)

Day 3 Finish the During Reading activities . Complete the After Reading activities . (45 min .)

Finish the During Reading activities . Complete the After Reading activities . (45 min .)

Day 4 Do the Focused Mathematics Lesson . (60 min .)

Have students reread the books or do the extension activities .

Day 5 Complete the Problem-Solving Lesson . (45 min .)

Reread, if necessary, or complete the extension activities .

• Mathematics: Students will write, simplify, and evaluate linear and exponential expressions .

• Nonfiction reading: Students will make inferences about the text .

• Nonfiction writing: Students will write short biographies of famous scientists, inventors, or mathematicians .

÷

÷

=

+=

+

÷

÷

=

+=

+

÷

=+



Where Germs Lurk BookLearning Objectives • Mathematics: Students will write, simplify, and

evaluate linear and exponential expressions .

• Nonfiction reading: Students will make inferences about the text .

• Nonfiction writing: Students will write short biographies of famous scientists, inventors, or mathematicians .

Materials • Where Germs Lurk books

• copies of student reproducibles (pages 92–93; page092 .pdf; page093 .pdf)

• paper

• chart paper

• sticky notes

• Where Germs Lurk electronic version (germs .pdf) (optional)

Using the BooksBefore Reading

1. Complete the Introduction to Mathematics Vocabulary activity (page 82) with the class . Then divide your students into readiness-based reading groups . This book is written for students at a fifth-grade reading level .

2. Reading Activity—Distribute the Where Germs Lurk books to students . Tell students that readers often make guesses based on what they read and what they already know . When they do that, they are making an inference . As an example, read the following sentences, one at a time, to the class: I am round. I have a president’s face on me. I am lucky when you pick me up. I am made of copper. I am a coin. I am worth one cent. As you read, have students write down a guess of the subject when they think they know what it is, changing their guesses as you read . When finished, discuss any incorrect guesses and when they knew for sure that their answers were correct . Explain that they have been making inferences—drawing conclusions from the clues .

3. Mathematics Activity— Have each student get out two pieces of paper . On one of the papers, have them make a two-column table, labeling the left column Folds and the right column Sections . In the Folds column, have them number from 0 to 7 . Tell them that they are going to fold a piece of paper repeatedly and write down the number of folds and sections they observe . Show them the blank piece of paper . Ask how many folds they have made (zero) and how many sections they see (one) . Show them how to fold the paper carefully, and make a sharp edge . Have them open the paper . Ask them how many sections they see on the paper (two) . Have them refold the paper and then fold again, so that there are two folds and then find the number of sections . Have them continue as many times as they can and save the papers for future use .

÷

÷

=

+=

+

÷

÷

=

+=

+

÷

=+


Writing, Simplifying, and Evaluating Expressions Teacher Resources

Where Germs Lurk Book (cont.)

Using the Books (cont.)

Before Reading (cont.)

4. Writing Activity—Write the following names on the chart paper: Elizabeth Blackwell, William Harvey, Jonas Salk, Florence Nightingale, Louis Pasteur, Alexander Fleming, Anton von Leeuwenhoek, Robert Koch, and Charles Drew . Tell the students that all of these people are famous in medical history . Ask students what questions they would ask these famous people about their lives and impact on medicine . Make a list of their questions on chart paper . Save for later use .

During Reading

1. On chart paper, make a list of the glossary words from the book, along with the chapter in which each appears, as a whole group . Because many of the words are unfamiliar scientific words, pay special attention to their pronunciations .

2. Reading Activity—Distribute the My Best Guess activity sheet (page 92) . Separate the class into small groups . Have each group choose a glossary word from each chapter and write each word on the activity sheet . Ask them to use the chapter title or any pictures in the chapter to make an inference about the meaning of the word . Have them write their inferences on the activity sheet . Then, have them take turns reading the book aloud .

3. After the group completes the first reading, have students read the book individually, placing a sticky note when they encounter the words on their lists .

4. Writing Activity—Have each student choose one of the people from the writing activity in the Before Reading section of the lesson . Make groups of three or four students who have chosen the same person . To help them research, have the group generate 10 questions that they would ask the person . Have them research to find the answers to the questions .

5. Mathematics Activity— Show the students that the number of sections can be expressed as powers of 2 . Show them that 23 means 2 • 2 • 2, which equals 8 and is the number of sections after three folds . Have them explain 22, 24, 25, 26, and 27 by using the folds and multiplication . Ask them how folding explains the value of 21 and 20 . Ask them to explain the values of 28 and 29 by using folds and multiplication .

6. Distribute copies of Let’s Explore Math—Where Germs Lurk (page 93) . This assignment can be used as classwork while you meet with other groups . Or, you can give it as a homework assignment and discuss the activity the following day .

÷

÷

=

+=

+

÷

÷

=

+=

+

÷

=+

N E X T S T E P SN E X T S T E P S



Where Germs Lurk Book (cont.)

Using the Books (cont.)

After Reading

1. Writing Activity—Have student groups make posters about the individual they chose for their research . The poster should include biographical information and the medical importance of the person . Display the posters around the room .

2. Reading Activity—Have students complete the My Best Guess activity sheet (page 92) by writing how further information showed their inferences to be true or not . Have students share their inferences with the students in their groups . Revisit the glossary to make sure that the students have found the correct definitions of the words . You may wish to use the digital version of the book (germs .pdf) to display the text and pictures as you discuss the vocabulary words .

3. Mathematics Activity— Review student work on the Let’s Explore Math activity sheet . Have students compare their solutions in groups . List different solution paths on the board .

4. To conclude the study of the book, have students discuss the different kinds of contributions made by the people on the posters . Ask them about any connections between the contents of the Where Germs Lurk book and the accomplishments of the individuals on the posters .

Mathematics • Pull students back together as a

whole group and present the Focused Mathematics Lesson on pages 94–99 .

• The lessons using the problem-solving transparencies (pages 100–103) are a great way to conclude the week’s study of writing, simplifying, and evaluating expressions .

Language ArtsHave students investigate the question of how many times a piece of paper can be folded . Have the class prepare a summary of their findings .

DifferentiationProvide below-grade-level students with cards with the nonmathematical words from the glossary used in a sentence . Where appropriate, show a picture of the item on the other side of the card .


Writing, Simplifying, and Evaluating Expressions Student Reproducibles

Name __________________________________ Date __________________________

My Best Guess

Directions: As you look through Where Germs Lurk, write down one glossary word you find in each chapter. Then, make an inference about how the word will be used in the book. After reading the book, write if your inference was true or false with supporting details from the book.

Chapter Glossary Word Inference Support for True/False

What Are Germs?

Louis Pasteur

Pasteurization

Germs on Your Hands

Germs in Your Mouth

Germs All Around


Name __________________________________ Date __________________________

Let’s Explore Math—Where Germs Lurk

Directions: Answer the following questions.

a. Dr. Ramirez takes five minutes to scrub in before a surgery. If she scrubs in s times per day, write an expression to show how many minutes she spends scrubbing in each day.

b. Evaluate the expression you wrote in problem a if Dr. Ramirez scrubs in three times per day.

c. Evaluate the expression you wrote in problem a if Dr. Ramirez scrubs in 10 times per day.

Each week, Jermaine stocks alcohol wipes at the hospital on Mondays, Wednesdays, and Fridays. He stocks x cases on Mondays. On Wednesdays, he stocks three times as many cases as he does on Mondays. On Fridays, he stocks double the amount that he stocks on Wednesdays.

a. Write an expression to show the number of cases Jermaine stocks on Wednesdays.

b. Write an expression to show the number of cases Jermaine stocks each Friday.

c. Write an expression to show the total number of cases Jermaine stocks each week. Simplify the expression.

d. Evaluate the expression you wrote in problem c when x = 6.

Student Reproducibles Writing, Simplifying, and Evaluating Expressions

a =

2x +

4a

= 2x

+ 4



Focused Mathematics Lesson: Writing, Simplifying, and Evaluating Expressions

Learning ObjectiveMathematics: Students will write, simplify, and evaluate linear and exponential expressions .

Materials • copies of Writing, Simplifying, and

Evaluating Expressions Pre-test (page 94; page094 .pdf)

• Watch It Grow and Where Germs Lurk books

• copies of Cross Match (page 98; page098 .pdf)

• copies of Trading Places (page 99; page099 .pdf)

AssessmentThis mathematics lesson has a pre-test (page 94; page094 .pdf) of the mathematical objective . Use the pre-test to determine the skills on which your students need to focus the most . This pre-test can be administered at any time prior to the teaching of this lesson so that results can be used to differentiate instruction . Also included is a Diagnostic Test (pages 224–231; page224 .pdf) to assess student learning .

Book Warm-UpDistribute the Watch It Grow and Where Germs Lurk books to students . Have students work in pairs to find examples of how the order of operations is used . Then, as a class, compile the rules they discovered .

Vocabulary • base—the number used as a factor

in exponential form • evaluate—to find the value of • exponent—a number that tells how

many times to multiply a base by itself; in ab, b is the exponent

• exponential form— the form ab, which shows the number of times (b) that a number (a) is to be multiplied by itself

• numerical expression—a mathematical phrase that is a combination of one or more numbers and one or more operations, or combinations of the two

• order of operations—rules describing the order to use when evaluating expressions

• terms—the parts of an algebraic expression or equation, such as numbers, variables, or combinations of the two

a =

2x +

4a

= 2x

+ 4

a =

2x +

4a

= 2x

+ 4



Focused Mathematics Lesson: Writing, Simplifying, and

Evaluating Expressions (cont.)

Teaching the Skills and Concepts 1. Write an expression such as 10 ÷ 2 + 3 • 8 – 5 on the board . Ask students to think of

all the possible values for the expression that they might come up with if they did not know the correct mathematical order of operations . Discuss why it is important that everyone uses the same rules for evaluating expressions .

2. Tell students that many people use the letters PEMDAS (or GEMDAS) to remember the correct order of operations . Remind them that although M precedes D, multiplication and division are performed from left to right as they appear in the expression . Show them that addition and subtraction are also performed from left to right as they appear in the expression .

3. Write the algebraic expression 3m – 7 + 4m + 5 on the board . Have students choose values for m. Then, have students simplify the expression and evaluate the simplified expression using the chosen numbers . Discuss why the answers should be the same . Ask why simplifying the expression first is a good idea .

4. Distribute copies of the Cross Match activity sheet (page 98) . Pair students . In each pair, have one student complete the top part of the sheet and the other complete the bottom part . Have them match up their answers to locate the simplified form of each expression .

Differentiation • Help English language learners write examples using the order of operations, one

step at a time, labeling each step with the part of PEMDAS used—parentheses/grouping symbols, exponents, multiplication, etc .

• Have the above-grade-level students create a riddle, using the values of the expressions as a code for finding the answer .

a =

2x +

4a

= 2x

+ 4

a =

2x +

4a

= 2x

+ 4

E X T E N S I O N I D E AE X T E N S I O N I D E A



Focused Mathematics Lesson: Writing, Simplifying, and


Application of the Skill 1. Distribute the Trading Places activity sheet (page 99) . For homework, have them create

expressions that can be simplified and choose three numbers for each expression . On another piece of paper, evaluate each expression using the numbers chosen, simplify the expression, and evaluate the simplified expression .

2. The next day, have students exchange papers with partners and simplify and evaluate the expressions . Then, have them compare their answers and make a note of any difficulties .

3. As a class, discuss expressions that caused difficulty .

Book ConclusionDistribute the Watch It Grow and Where Germs Lurk books . Group students so that they have both books available . Have students look at pages 25 and 26 in Watch It Grow and the Let’s Explore Math on page 25 in Where Germs Lurk . Ask the groups to model the solution to the Let’s Explore Math with the explanation in Watch It Grow.

Have students look at the tables on page 12 of the Where Germs Lurk book and page 10 of the Watch It Grow book . Ask them to make graphs of the data, using the data in the left column for the horizontal axis and the data in the right column for the vertical axis . Ask students if they have heard of something increasing exponentially . Have them discuss what that means .


Name __________________________________ Date __________________________

Cross Match

Directions: Complete the top or the bottom table as directed by your teacher. For each table, evaluate the expression for the numbers given.

Expression Valuen = 2

Valuen = 3

Valuen = 10

1. 2n + 5 + 4n + 3

2. 4(n + 6)

3. 4n – 3 + 7n – 10

4. 8n + 3(n – 2)

5. 10 + 2(7n + 2) – 5n

6. 2n – 7 + 3n – 3

7. 5 – 4n + 6n

Expression Valuen = 2

Valuen = 3

Valuen = 10

A. 11n – 6

B. 4n + 24

C. 11n – 13

D. 2n + 5

E. 5n – 10

F. 9n + 14

G. 6n + 8


÷

÷

=

+=

+

÷

÷

=

+=

+

÷

=+



Using the Problem-Solving Transparencies: Writing, Simplifying, and Evaluating Expressions

Materials • Watch It Grow and Where Germs Lurk books

• E. Coli Outbreak overhead transparency (outbreak1 .pdf)

• Small Change overhead transparency (change1 .pdf)

• copies of Disease Control activity sheet (page 102; page102 .pdf)

• copies of Add It Up activity sheet (page 103; page103 .pdf)

E. Coli Outbreak

Summary

Students follow the progress of an E. coli outbreak .

Problem-Solving Steps

1. Ask students to discuss how airborne diseases are transmitted . Explain that they will be solving problems about a disease outbreak .

2. Display the E. Coli Outbreak transparency . Explain that they will be looking at the occurrence of the disease in different towns .

3. Distribute copies of the Disease Control activity sheet (page 102) . Group students in pairs . Ask them to explain the first problem in the Solve It! section . Discuss the application of the distributive property with the entire class .

4. Then, ask students to solve the rest of the problems from the transparency, recording their answers on the activity sheet .

5. When everyone is finished, discuss the answers with the class .

DifferentiationFor below-grade-level students, an in-depth version of the problem-solving transparency is provided (outbreak2 .pdf) on the Teacher Resource CD . This version includes step-by-step directions for solving the problem .

÷

÷

=

+=

+

÷

÷

=

+=

+

÷

=+



Using the Problem-Solving Transparencies: Writing, Simplifying, and


Small Change

Summary

This problem asks students to write expressions representing the value of coins and evaluate the expressions .

Problem-Solving Steps

1. Ask students to imagine that they have dumped out the contents of a large piggy bank and they need to find the value of the money .

2. Display the Small Change transparency . Have students read the problem silently as you read it aloud . Discuss the difference between the number of coins and the value of the coins .

3. Distribute copies of the Add It Up activity sheet (page 103) . Group students in pairs . Have them complete the Solve It! section on the activity sheet . When they have finished, discuss their answers .

4. Have each student complete the rest of the activity sheet . As a class, discuss the answers .

DifferentiationFor below-grade-level students, an in-depth version of the problem-solving transparency is provided (change2 .pdf) on the Teacher Resource CD . This version includes step-by-step directions for solving the problem .


Name __________________________________ Date __________________________

Directions: Answer the questions in each section below.

Think About It!

1. Do you remember a flu outbreak? What measures did public health officials recommend?

_________________________________________________________________

_________________________________________________________________

Solve It!

2. Solve the problems from the problem-solving activity, E. Coli Outbreak.

a. Write expressions that show the number of cases reported by Sick Town in weeks 1 and 2, based on the number of cases in Queasy Town.

_______________________________________________________________

b. Write an expression that shows the number of cases reported in week 3. Let a represent the number of cases first reported by Ailment Town. Let u represent the number of cases first reported by Unwell Town.

______________________________________________________________

c. Evaluate the expression you wrote in problem b if a = 30 and u = 20.

______________________________________________________________

d. One E. coli bacterial cell divided three times in one hour. Write an expression to represent the number of bacteria after n hours. How many would there be after 3 hours?

___________________________________________________

Describe It!

3. On a separate piece of paper, describe how the distributive property applies to your solution of problems a and b.

Extend It!

On a separate piece of paper, make a chart showing the division of the E. coli sample in problem d over 5 hours. Make a table showing the number of bacteria each hour.

Disease Control



Name __________________________________ Date __________________________

Student Reproducibles Writing, Simplifying, and Evaluating Expressions

Directions: Answer the questions in each section

Think About It!

1. Suppose you had to find the value of a large collection of different kinds of coins. How would you do it?

________________________________________________

_________________________________________________________________

Solve It!

2. Solve the problems from the problem-solving activity, Small Change.

a. One of her piles has 10 dimes and 10 nickels. Using n for the value of a nickel and d for the value of a dime, write an expression for the total amount of money she has in the pile.

_________________________________________

b. Using n = $0.05 for the value of each nickel and d = $0.10 for the value of each dime, evaluate the expression you wrote for problem a to find out how much money is in her pile.

_________________________________________

c. Suppose that you have five pennies on Monday. On Tuesday morning, each penny has doubled magically. This happens Tuesday night and again on Wednesday night. Using n to represent the number of days that have passed, write an expression to represent the number of coins. How many pennies do you have on Thursday morning?

____________________________________

Describe It!

3. Describe how the distributive property describes your solution to problems a and b.

_________________________________________________________________

_________________________________________________________________

Extend It!

Suppose your sister saved a total of $1 during the first month she had her piggy bank, $5 during the second month, and $25 during the third month. Write an expression that describes how much she would have at the end of each month. If this pattern continues, how much would she have at the end of a year?

Add It Up

Algebra and Algebraic Thinking

Germs are everywhere. They’re on your hands, your school supplies, and even in your mouth! But what exactly are germs, and how do they spread? Write, simplify, and evaluate algebraic expressions to explore how fast germs can spread. Learn about scientists who study germs, and simple things that you can do to keep them from spreading.

TCM 14455 ●W

here

Ge

rms Lurk

Ba

rker

Where Germs Lurk

Lori Barker

Writing, Simplifying, and Evaluating Expressions

Writing, Simplifying, and Evaluating Expressions

Where Germs Lurk

What Are Germs? 4

Louis Pasteur 6

Pasteurization 10

Germs on Your Hands 14

Germs in Your Mouth 20

Germs All Around 24

Problem-Solving Activity 28

Glossary 30

Index 31

Answer Key 32

Table of Contents

3

What Are Germs? “Cover your mouth when you cough!”Sound familiar? We have all been told to cover our

mouths when we cough or sneeze. You know to wash your hands after using the restroom and before eating, and not to put your mouth on a drinking fountain. We do these things to prevent the spread of germs. But what are germs anyway?

Germs are tiny, living things that you can only see with a microscope. They are microbes, or microorganisms (mahy-kroh-AWR-guh-niz-uhmz). Some germs are made up of only one cell. Others are not even a complete cell and need to be inside another living organism in order to survive.

Many microbes are necessary to help us stay healthy. Unfortunately there are germs that lurk all around us that can make us very sick.

Covering a cough or sneeze helps prevent the spread of germs. It is best not to use a bare hand to cover your mouth since germs are easily spread through contact with hands.

4

Different Ways to Show It Multiplication expressions can be shown in different ways:

2 × 46 2 • 46 2(46) (2)(46)

As much as we try to prevent the spread of germs, most people get sick once in awhile. Sometimes students must be absent from school due to illness. Schools keep track of students’ absences by collecting data.

Numerical expressions can be used to help understand data. A numerical expression is a combination of numbers and operations that has not been evaluated. Suppose in Mr. Marin’s fifth period class, there were twice as many absences as in his third period class. The numerical expression 2(46) represents the first semester absences from Mr. Marin’s fifth period class.

First Semester Absences in Mr. Marin’s Math Classes

Class Number of Absences

1st period 75

3rd period 46

5th period 2(46)

5

by for teachers and students thanks for checking us out ... · assignments are also provided as...

Documents