Using Interactive Notebooks in the Mathematics...

Sherry Olivares Region 4 Education Service Center

www.theansweris4.net [email protected]

713.744.6330

Permission to copy classroom-ready materials granted to attendees of this session.

© 2011 Region 4 Education Service Center All rights reserved.

Using Interactive Notebooks in the Mathematics Classroom

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Interactive Notebooks are characterized by

RIGHT SIDE Input and LEFT SIDE Output!

An Interactive Notebook gives students a place to:

Set Goals Plan Study Strategies Document Learning

Track Success

Left Side Examples Right Side Examples Poems Vocabulary Cartoons Word Puzzles Analogies Graphics Sketches Practice problems or examples Paraphrases Pictures Articles Lyrics to a song Web information Memory tips and techniques Brainstorming Concept maps/flow charts Study plan Reflections Goal setting Communication with parent/teacher

Lecture Notes Daily and homework assignments Tests Quizzes Lab activities Hand outs Vocabulary Assignments Focus or warm-up activities Foldables Pre-lab notes Book notes Graphic organizers Film notes

Left Side Characteristics

Colorful, creative, unique to student, demonstrates understanding, entered on even numbered pages, date and subject

title at top of each page

Right Side Characteristics

Content and concepts of curriculum, notes in Cornell style, teacher or text driven, entered on odd numbered pages, date and

subject title at top of page

Interactive Notebook and Parent Communication

Math Student: Each 6 weeks, schedule a time to meet with your parent or significant adult. Show them your INB and let them know what is going on in class. Write down a few comments made.

Dear Parent or Significant Adult,

Your student is keeping an Interactive Notebook in Mathematics. Please look through it and respond to the following questions. Thank you for supporting our science program.

1) The work I found most interesting was…….. because…….

2) What does the notebook tell you about your student’s learning habits?

3) Do you have any comments, questions, or concerns?

Print Name_______________________________

Signature_________________________________

Student’s Name____________________________

Date_______________________________

Suggested First Pages Title Page (1st actual page)

• Name • Course • Class period • Year • Instructor

Table of contents • Have students draw their own TOC chart • Start on the front of the 2nd actual page • First entry is a right side Content • Student use three consecutive pages front and back

The following documents may be entered on the front and back of the next few pages. Have the students use staples or tape. Handouts

• Course syllabus • Expectations/norms • Honor code • Other

Goal Page • Students write goals stating what they want to accomplish or gain from the

course • May be written in process or performance terms • Goals should be revisited/rewritten when analyzing grade reports/test scores

Planning page • Students state the strategies needed to accomplish their goals • Strategies should be revisited/rewritten when analyzing grade reports/test scores

Tracking Page • Students create data table for grade reports or exam grades • Students graph their progress

First Content Page • Page one on the next available right side.

Table of Contents

Page # Left Side Page # Right Side

This Table of Content is designed to fit a standard composition book.

Cut along the dotted lines.

Table of Contents

Page # Date Left Side Page # Date Right Side

My Math Interactive Notebook You are a mathematician. Mathematicians use notebooks and journals to record data, illustrations, charts, graphs, and their thinking. You can also use it to record your questions and ides. We will follow guidelines when using our notebooks to make them informative and interesting. Your notebook should reflect your experiences, your thinking, and your creativity, but it should be easily understood by others. Guidelines:

• Write neatly and legibly – across out mistakes with a single line or carefully erase

• Do not tear out pages • Create a title page • Number each page • Create a table of contents • Title each activity and add to the table of contents • Label drawings, graphs, and charts • Use sentences to communicate observations, plans,

explanations, conclusions, and applications Getting Started with Writing:

• This reminds me of . . . • I see a pattern . . . • What would happen . . . • I observed that . . . • This problem . . . • How many . . .

INTERACTIVE CAFÉ DAILY SPECIALS

This Interactive Café is designed to fit a standard composition book.

APPETIZERS– EASY PICKINGS Digital photos Magazine pictures Web information Research notes Articles News feeds

0.00

ENTRÉES– MEATY MATTERS Graphic organizer Thinking maps Real world applications Career connections Goal setting Study plan

0.00

SIDES– CROSS-CURRICULAR

Practice problems Historical connections Acrostics Acronyms Analogies Sketch

0.00

DESSERTS– CREATIVE FLAIR Nonlinguistic representation Innovative application Cartoon Game Song Folding model

0.00

BEVERAGES– THE FLOW Reflection Summary of Understanding AHAs!

Where meetings of the mind are always the special of the day!

0.00


INTERACTIVE CAFÉ DAILY SPECIALS

INTERACTIVE CAFE Where meetings of the mind are always the special of the day!

APPETIZERS– EASY PICKINGS Digital photos Magazine pictures Web information Research notes Articles News feeds

0.00

ENTRÉES– MEATY MATTERS Graphic organizer Thinking maps Real world applications Career connections Goal setting Study plan

0.00

SIDES– CROSS-CURRICULAR

Practice problems Historical connections Acrostics Acronyms Analogies Sketch

0.00

DESSERTS– CREATIVE FLAIR Nonlinguistic representation Innovative application Cartoon Game Song Folding model

0.00

BEVERAGES– THE FLOW Reflection Summary of Understanding AHAs!

0.00

Authors Page

Name: ________________________________

Nickname: _____________________________

Birthday: ______________________________

Food: ____________________

Music: ___________________

Sport: ___________________

Color: ___________________

Movie: ___________________

Book: ___________________

Place: ___________________

Three words I would use to describe myself are: I would like to take a vacation to: In the future I would like to be a(n):

Authors Page

Name: __________________________

Nickname: _______________________

Birthday: ________________________

Food: ____________________

Music: ___________________

Sport: ___________________

Color: ___________________

Movie: ___________________

Book: ___________________

Place: ___________________

Three words I would use to describe myself are: I would like to take a vacation to:

In the future I would like to be a(n):

Notebook Labels

Name: _________________ Please return to _________________________ Room: __________








Interactive Notebook Rubric

6 Excellent

Notebook contents are complete, dated, and labeled Pages are numbered (odd: Right side, even: Left-side) Right-side/Left-side topic are correct and organized Notes and writing go beyond basic requirements Uses color and effective diagrams Notebook is neat and shows attention to detail Shows impressive and in-depth self-reflection about work

5 Above Average

Notebook contents are complete, dated, and labeled Pages are numbered (odd: Right side, even: Left-side) Right-side/Left-side topic are correct and organized Most areas meet requirement but don’t go beyond Uses color and effective diagrams Includes traits of a six, but lacks excellence Shows in-depth self-reflection

4 Average

Notebook contents are 90% complete, dated, and labeled Pages are numbered (odd: Right side, even: Left-side) Right-side/Left-side topic are correct and organized Information shows a basic understanding of content and topics Uses color and some diagrams Some areas meet requirements but don’t go beyond Shows limited but real self-reflection

3 Below Average

Notebook contents are 80% complete, dated, and labeled Pages are numbered (odd: Right side, even: Left-side) Right-side/Left-side topic are somewhat organized Information shows limited understanding of content and topics Uses minimal color and few diagrams Few areas meet all requirements Shows some real self-reflection

2 Inadequate

Contents are incomplete Some attempt at dating an labeling is evident R side/L side inconsistent an unorganized Information shows superficial understanding and inaccuracies Sloppiness prevails Shows little self reflection

1 Incomplete

Too incomplete to grade

This Interactive Notebook Rubric is designed to fit a standard composition book.



6 Excellent

Notebook contents are complete, dated, and labeled Pages are numbered (odd: Right side, even: Left-side) Right-side/Left-side topic are correct and organized Notes and writing go beyond basic requirements Uses color and effective diagrams Notebook is neat and shows attention to detail Shows impressive and in-depth self-reflection about work

5 Above Average

Notebook contents are complete, dated, and labeled Pages are numbered (odd: Right side, even: Left-side) Right-side/Left-side topic are correct and organized Most areas meet requirement but don’t go beyond Uses color and effective diagrams Includes traits of a six, but lacks excellence Shows in-depth self-reflection

4 Average

Notebook contents are 90% complete, dated, and labeled Pages are numbered (odd: Right side, even: Left-side) Right-side/Left-side topic are correct and organized Information shows a basic understanding of content and topics Uses color and some diagrams Some areas meet requirements but don’t go beyond Shows limited but real self-reflection

3 Below Average

Notebook contents are 80% complete, dated, and labeled Pages are numbered (odd: Right side, even: Left-side) Right-side/Left-side topic are somewhat organized Information shows limited understanding of content and topics Uses minimal color and few diagrams Few areas meet all requirements Shows some real self-reflection

2 Inadequate

Contents are incomplete Some attempt at dating an labeling is evident R side/L side inconsistent an unorganized Information shows superficial understanding and inaccuracies Sloppiness prevails Shows little self reflection

1 Incomplete

Too incomplete to grade


Excellent Satisfactory Need

Improvement Weak

Output

All work is: ∗ Finished ∗ Thoughtful ∗ Making

connections ∗ Clear ∗ Creative

Majority of work is: ∗ Finished ∗ Thoughtful ∗ Making


Some work is: ∗ Finished ∗ Thoughtful ∗ Making


Little/No work is: ∗ Finished ∗ Thoughtful ∗ Making


Points 20 15 10 5

Input

All work is: ∗ Finished ∗ Thoughtful ∗ Thorough ∗ Consistently

done with good effort

Majority of work is: ∗ Finished ∗ Thoughtful ∗ Thorough ∗ Consistently


Some work is: ∗ Finished ∗ Thoughtful ∗ Thorough ∗ Consistently


Little/No work is: ∗ Finished ∗ Thoughtful ∗ Thorough ∗ Consistently


Points 20 15 10 5

Organization and Neatness

∗ Pages are numbered

∗ Table of Contents complete with titles

∗ Work is neat and legible

∗ Contents is organized and in its proper place

Less than 4 items are missing.

Five to Eight items are missing.

Nine or more items are missing.

Points 10 8 6 4

Teacher Comments: _________________________________________________

_________________________________________________

_________________________________________________

_________________________________________________

_________________________________________________

Score: Rubric Points: ________

50= %

Inte

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N

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Wea

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Outp

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All w

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is:

∗

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∗

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∗ M

akin

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onnec

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∗ Cle

ar

∗ Cre

ativ

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Majo

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of

work

is:

∗

Finis

hed

∗

Thoughtf

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∗ M

akin

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onnec

tions

∗ Cle

ar

∗ Cre

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So

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ork

is:

∗

Finis

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∗

Thoughtf

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∗ M

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∗ Cle

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∗ Cre

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Lit

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∗

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∗

Thoughtf

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∗ M

akin

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∗ Cle

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∗ Cre

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ints

20

15

10

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Input

All w

ork

is:

∗

Finis

hed

∗

Thoughtf

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∗ Thoro

ugh

∗ Consi

sten

tly

done

with

good e

ffort

Majo

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of

work

is:

∗

Finis

hed

∗

Thoughtf

ul

∗ Thoro

ugh

∗ Consi

sten

tly

done

with g

ood e

ffort

So

me w

ork

is:

∗

Finis

hed

∗

Thoughtf

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∗ Thoro

ugh

∗ Consi

sten

tly

done

with

good e

ffort

Lit

tle/

No w

ork

is:

∗

Finis

hed

∗

Thoughtf

ul

∗ Thoro

ugh

∗ Consi

sten

tly

done

with

good e

ffort

Poin

ts

20

15

10

5

Org

aniz

atio

n a

nd

Nea

tnes

s

∗ Pa

ges

are

num

ber

ed

∗ Tab

le o

f Conte

nts

co

mple

te w

ith t

itle

s ∗

Work

is

nea

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d leg

ible

∗

Conte

nts

is

organ

ized

an

d in its

pro

per

pla

ce

Less

than

4 ite

ms

are

mis

sing.

Five

to E

ight

item

s ar

e m

issi

ng.

Nin

e or

more

ite

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are

mis

sing.

Poin

ts

10

8

6

4

Tea

cher

Com

men

ts:

_________________________________________________

_________________________________________________

Score

:

Rubric

Poin

ts:

________

50

=%

Name:___________________________


Title Page: 5 pts. ______

Student Name, Course, Period, Year, Teacher

Table of Contents: 15 pts. ______ LS/RS correct designation, entries complete

Grade Sheet/Graph Updated: 5 pts. ______ Pages Titled: 5 pts. ______ Pages Numbered: 10 pts. ______ Entries Secure: 5 pts. ______ Daily Focus: 15 pts. ______ All Assignments Entered: 10 pts. ______ L Sides: 30 pts. ______

Appropriate, colorful, creative, shows interaction with content

Extra Credit: 5 pts. ______

Work is neat and organized

Total points: ______ Teacher Comments:

Name:___________________________


Title Page: 5 pts. ______

Student Name, Course, Period, Year, Teacher

Table of Contents: 15 pts. ______ LS/RS correct designation, entries complete

Grade Sheet/Graph Updated: 5 pts. ______ Pages Titled: 5 pts. ______ Pages Numbered: 10 pts. ______ Entries Secure: 5 pts. ______ Daily Focus: 15 pts. ______ All Assignments Entered: 10 pts. ______ L Sides: 30 pts. ______

Appropriate, colorful, creative, shows interaction with content

Extra Credit: 5 pts. ______

Work is neat and organized

Total points: ______ Teacher Comments:

Algebra 1 Course Syllabus and Expectations

Teacher: XXXXXXXXXXXX Room XXX XXXXX Middle School School Phone: XXX-XXX ext: XXX Home Phone: XXX-XXXX email: XXXXXXXXXXXXXXX Course Description: Algebra 1 is a required yearlong course for advanced middle school students. It is the study of expressions, equations, functions and inequalities. Students will solve linear equation, use proportional reasoning, graph relations and functions, analyze linear equations solve linear inequalities and systems of linear equations and inequalities, explore polynomials and quadratic/exponential functions. They will also explore rational and radical expressions and equations. Credit: Students successfully completing this course are eligible for one high school credit. Classroom Instruction and group work: Students will work in collaborative groups on a regular basis and approach problems conceptually. The only way students will master the concepts is by being actively involved in their learning. I will be responsible for guiding, supporting and summarizing at all times. Daily assignments will be given to practice and master the skills we have learned in class. Student Assessments will be given at the end of each chapter and may include multiple choice, short answer and extended response questions. This is a balanced program where skill development is based upon problem solving and understanding. Most of the 8th grade student expectations (TEKS) are embedded in the curriculum but some are not because it is a high school curriculum. Any 8th grade SEs not covered by the high school Algebra 1 curriculum will be included in some other manner throughout the school year. Parent Involvement: Parents, the following suggestions will help students be successful and have a positive experience in Algebra 1.

• Encourage and support risk taking on homework and while working in groups. • Talk on a regular basis about the concepts being taught. • Read and discuss student toolkit and journal entries on occasion. • Create an atmosphere at home where there is a designated study space and study time. • Be open to math groups working together at homes in evenings and weekends. • When students are asked to teach new concept to parents, be enthusiastic and attentive. • Offer help with homework and suggest that students get help at school when necessary. • Look through the geometry binder on occasion and ask about organizational strategies. • If your student needs help, start by asking them to read the problem out loud.

Textbook: College Preparatory Mathematics (CPM) Algebra Connections: www.cpm.org. This web site has all of the problems from the student textbook as well as solutions to the out-of class portion of each assignment for Algebra Connections. Any resource pages that we have used in class are also available for the students that have been sick or have missed class.

Classroom Supplies: Students will need these materials for math by Friday of the first week of school.

1. 5-Star Notebook (college rule) 2. Pencil pouch with two pencils, one red pen for correcting, colored pencils, eraser, six-inch ruler. 3. A scientific calculator in pencil pouch. (TI 30xa is the least expensive and is excellent.) 4. A bound quad rule notebook (with holes punched in it) of graph paper. We have asked the office

supply stores to have these books available for the high school and the middle school math students.

Attendance: Attendance is required in accordance with XXXX's Policy (see XXXX Handbook in the “Planner”. A student will not be successful without regular attendance. Classroom Management: “Make Your Day” is a citizenship program that encourages students to “Do what is expected” and “Do their best” each period of the day. Students have an opportunity to earn points, which enables them to “MYD” each school day. Assessments and Evaluation: Grades will be given at the end of each quarter. Grades will be updated weekly on line at: http://fms.wsd.wednet.edu. Please check student grades on line regularly.

Assessments: Team and Individual exams 65% Daily Assignments and group presentations 25% Performance Expectations 5% Parent signatures and attendance at open house 5%

The only extra credit will be applied from the bathroom passes and it will not exceed 1% of total grade.

Grading Scale: A 93-100 C+ 76-79 A- 90-92 C 73-75 B+ 86-89 C- 70-72 B 83-85 D+ 66-69 B- 80-82 D 60-65

F 0-59

------------------------------------------------------------------------------------------------------------ Please sign and return this section of the Algebra 1 Syllabus to school with you student. Keep the syllabus as a reference. Thank you! Student Signature: ______________________________ _________________________________ (Please print and sign clearly.) Parent signature: ______________________________ Home or Cell Phone # __________________ Please clearly print email address below.

Clo

ck P

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ers

Clo

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My Clock Partners My Clock Partners

Concept Definition Map

Provided by Region 4 Education Service Center

Concept

Definition

Attributes

Examples

My Concept Map: _____________________

My definition:

Important facts to remember:

______________

My example:

_____________

My example:

______________

My example:

My Concept Map: ____________________

____________

My example:

___________

My example:

____________

My example:

Important facts to remember:

My Concept Map: ____________________

My example: My example: My example:

Attributes:

Category:

Another work in the Category:

Another work in the Category:

Title:

Questions Notes

Summary:

Title:

Questions Notes

Summary:

Cornell Note Taking (Content title here)

Questions Notes

Questions, comments, thoughts about content

notes Fold at line or cover notes

and use questions as a study tool

Students take notes in the style you model or in the style that makes sense to them

Summary: Students summarize concepts and content and/or connect to real world or their own experiences. Can use as a checkpoint for understanding.

Provided by

Definition (in your own words)

Facts/Characteristics

Examples

Non-Examples

Definition (in your own words)

Facts/Characteristics

Examples

Non-Examples

Lesson 2 Grade 9

© 2007 Region 4 Education Service Center Closing the Distance: A Flexible Tutorial for TAKS™ All Rights Reserved 31

Transparency: Posing the Problem

Kim is standing by her desk. She starts walking away from her desk at a rate of 2 feet per second and walks for 10 seconds.

1TEXTEAMS Rethinking Middle School Mathematics: Algebraic Reasoning

Movin' on Down the Line

Institute Notes

Concept: Use a graph to explore relationships between thequantities time and distance.

Overview: Participants actively collect distance data in relation totime and graph it. Through questioning and richdiscussion, participants make the connection betweenthe motions observed during the activity and therelationship shown in the graph. This activity requiresextra physical space and can be done in a hallway orgym but gives the perfect opportunity to go outdoorson a day that weather permits.

TEKS Focus: 6.13— The student uses logical reasoning to makeconjectures and verify conclusions.7.15— The student uses logical reasoning to makeconjectures and verify conclusions.8.16— The student uses logical reasoning to makeconjectures and verify conclusions.

Materials: Stop watches or watches with a second hand (one pergroup), 100’ or 150’ Measuring tapes (one per group),Data Collection Cards, Secret Instruction Cards, 1”grid wall charts, Peel-and-stick dots or markers

Procedure: 1. To prepare for this activity make a copy of the DataCollection Cards and Secret Instruction Cardssheets for each group and cut the cards apart.You may wish to laminate the cards.

2. Go over the directions on a transparency ofActivity 1 - Instruction Sheet with the whole group.Do a quick demonstration and allow participants toask questions about the procedure.

3. Divide the participants into groups of 12, distributesupplies, and have them complete Activity 1 byrecording the distance data for the five movers.

4. Once the participants return to the room, havethem complete Activity 1 by compiling their data

into the tables and graphing the data on the grids.

Also:

Grade 6

4A, 7, 8B, 10D, 12A, 13AGrade 7

2G, 4B, 7A, 11B, 14A, 15AGrade 8

4, 5A, 12B, 15A, 16AAlgebra I

b.1A, 1D, 1E, b.2C, 2D,c.1B, c.2B, 2F



5. Have participants do Activity 2 by graphing the dataon 1” grid wall charts. Label each graph with thename and number of the mover. You may wish toassign a mover (1 – 5) to each group so that thedata for each mover is graphed only once.

6. When all graphs are completed, use the Reason andCommunicate questions to discuss the informationyou can determine from the graphs.

7. Have participants work in their groups of twelve todiscuss the graphs and determine the writteninstructions that each mover was given.

8. With the whole group, use a transparency of theSecret Instruction Card sheet to compare theinstructions written by the groups to the actual secretinstructions given to each mover.

9. Have participants reverse the process by doingActivity 2. Discuss using the Reason and Communi-cate questions.

10.Have participants use the rules they have formed toanalyze the graphs in Activity 3. Discuss using theReason and Communicate questions.

Extensions: Write a story about a person or some people moving.Draw a graph to illustrate it. The graph should showthe relationship between the distances of the personor people from some fixed place at different times.Exchange graphs with another group. Write a story togo with the graph drawn by the other group. Compareyour story with the other group’s story.

Select a straight line section of one of the “Movin’ onDown the Line” graphs and determine the speed ofthe mover and the direction in which he or she wasmoving. Repeat for several different sections. Write abrief description explaining how you determined thespeed and direction.

Graph the data in both inches and feet and comparethe graphs.



Assessment: Illustrate the following situation with a graph thatshows distance from the bus stop in relation to time:

Ann was walking toward the bus stop when shesaw the bus coming. She ran as fast as she couldtoward the bus stop, but the bus left before she gotthere. She walked slowly the rest of the way to thestop and sat down to wait for the next bus.

Write a brief statement describing how you can deter-mine the following when looking at a graph of distancefrom a fixed place over time.

• How can you tell when the mover is travelingfast, slow, or standing still?

• How can you tell if the mover is traveling towardor away from the beginning of the measuringtape?

Notes:

TEXTEAMS Rethinking Middle School Mathematics: Algebraic Reasoning Activity-4

Movin' on Down the LineSecret Instruction Cards

Movin’ on Down the Line

Secret Instruction Card for Mover 1

Do not show this card to anyone.

Start at the beginning of the measuringtape. Walk forward slowly at a constantrate. When the timekeeper calls the10th second, stand still. When youhear 16, walk at a faster rate until timeruns out.




Start at the far end of the measuringtape. Walk fast toward the beginningof the measuring tape. Keep yourspeed as constant as you can. Whenthe timekeeper says 10, walk veryslowly. Continue to walk very slowlytoward the beginning of the tape.




Start at the 10 foot mark of the mea-suring tape. Walk very, very slowly atfirst. Then very gradually increaseyour speed until you are running.When you reach the end of the tape,

stop running and stand still.




Start at the 25 foot mark of themeasuring tape, facing the beginningof the measuring tape. Stand still for 6seconds. When the timekeeper callsthe 6th second, walk along the tapetoward the beginning of the tape at aconstant speed. When you hear 12,stand still. When the timekeeper says

18, walk again until time runs out.




Start at the beginning of the measuringtape. Jog along the tape at a moder-ate speed for 10 seconds, keepingyour speed as constant as you can.When the timekeeper calls the 10th

second, walk back toward the startingpoint at a slow, steady pace until timeruns out.



Data Collection Cards

Mover

1

2

3

4

5

Position at:Mover

1

2

3

4

5

Position at:

Mover

1

2

3

4

5

Position at:Mover

1

2

3

4

5

Position at:

Mover

1

2

3

4

5

Position at:Mover

1

2

3

4

5

Position at:

0 seconds 2 seconds 4 seconds 6 seconds




Movin' on Down the LineActivity 1 - Instruction Sheet

Purpose: Collect data about the relationship between the distance of a personfrom the beginning of a measuring tape and the elapsed time.

In each group identify: 1 Timekeeper with a stopwatch or a watch with a second hand5 Movers, each with a different Secret Instruction Card6 Data collectors, each with a Data Collection Card

Description of the activity:

Each data collector will be given a Data Collection Card with two times writtenon the top. Each is responsible for recording the position of the mover at eachtime on his or her card. For example, if your card has 4 and 6 seconds on it,you are responsible for recording the position of each mover when the time-keeper calls 4 seconds and 6 seconds.

Each mover will be given a Secret Instruction Card. One at a time, follow thesecret instructions on your card without showing others your card. The time-keeper will give the start signal and then call out each second for 22 seconds.(“Go,…1,…2,...”)

First, mover 1 will practice moving down the line to give the data collectors theopportunity to position themselves where the mover will be at their assignedtime. The second time Mover 1 moves down the line, each data collector willrecord the position of the BACK of the mover’s back foot at his or her assignedtime, rounding to the nearest foot.

Repeat this procedure for each mover.

Once all of the data is collected, return to the classroom.



Math Notes:

In this activity, participants have recorded movers' distances at certaintimes, organized this data into a table, and then represented the data witha graph. From the data and graphs, they made conjectures about themovers’ instructions. In the next activity, they will reverse the process.We call this habit of mathematical (algebraic) thinking doing and

undoing. One of the processes we want to help develop during theinstitute and in our students is this notion of reversibility. That is, once wedo something, often we can work backwards and gain new insight, abetter understanding of what we have done, and a concrete knowledge ofthe concepts.

Also, one goal of this activity is for participants to form ideas about howthe graph of a mover’s movement looks for different instructions. Ineffect, we are building intuition for what motion looks like graphically as arelationship between distance and time. This is the first step towarddeveloping algebraic reasoning by generalizing rules from data. We havenot moved to a symbolic form with variables and equations yet, but wehave begun to move from one representation to another. We call thishabit of mathematical (algebraic) thinking patterns to rules (Driscoll).

Reason and Communicate:

• What does the ordered pair (x,y)mean in these graphs? (time,distance)

• In which graphs did the moverstand still for some period of time?How can you tell? Graphs 1, 3, and5. They have a horizontal line,which indicates that for more thanone second the mover was at thesame distance from the beginning ofthe tape.

• In which graphs did the moverstart at the beginning of the tape?Graphs 1 and 2.

• If the mover starts at the beginningof the tape, at what point does thegraph start? (0,0)

• If the mover did not start at thebeginning of the tape, where did heor she start? In Graph 3, the moverstarted 25 feet from the beginning ofthe tape since the distance at t=0 is25 feet (300 in.). In Graph 4, themover started at the end of the tapesince the distance from the begin-ning of the tape at t=0 is equal to thelength of the tape. In Graph 5, themover started 10 feet (120 in.) fromthe beginning of the tape since thedistance at t=0 is 10 feet.

• In which graphs is the mover

moving away from the beginning ofthe tape? How can you tell? InGraphs 1 and 5, the mover movesaway from the beginning of the tapesince the distance from the begin-ning of the tape is increasing overtime. In Graph 2, the mover ismoving away from the beginning ofthe tape at first.

• In which graphs is the mover

moving toward the beginning of thetape? How can you tell? In Graphs3 and 4, the mover is moving towardthe beginning of the tape since thedistance from the beginning of thetape is decreasing over time. InGraph 2, the mover moves towardthe beginning of the tape in thesecond part.


Movin' on Down the LineActivity 1, cont.

Enter the data for each mover into the tables below. Graph the data on the corre-sponding grids below and then transfer to the 1" grids to display on the wall.Based on each graph, write a description of the instructions the mover followed.

Dis

tan

ce

Dis

tan

ce

Time

Time

Mover 2

Time Distance

Mover 1

Time Distance


Movin' on Down the LineReason and Communicate, cont:

• What does the graph look like if

the mover moves away from thebeginning of the tape? The graphrises from left to right.

• What does the graph look like if

the mover moves toward thebeginning of the tape? The graphfalls from left to right.

• In Graph 1, during which part is

the mover moving the fastest? Themover is moving fastest in the thirdsection of the walk because then thechange in his or her distance overone second is the greatest .

• In Graph 2, when is the mover

moving the slowest? The mover ismoving the slowest in the secondsection because the change in his orher distance over one second is theleast then.

• Comparing all five graphs, in

which one is the mover moving thefastest? How can you tell? Look forthe steepest segment.

• Comparing all five graphs, in

which one is the mover moving theslowest? How can you tell? Lookfor the most shallow segment.

• Which graph does not look similar

to the others? Why? Graph 5 has acurved line instead of a straight line.The mover’s rate is changing.

• Should you connect the data

points? Is the data discrete orcontinuous? Discuss that the onlyway you would have a break in thegraph is if the mover left the courseand then came back.

• The graph represents a relation-

ship between what two quantities?Elapsed time and distance from thebeginning of the measuring tape.



Dis

tan

ce

Time

Time

Mover 3

Time Distance

Mover 4

Time Distance

Dis

tan

ce


Dis

tan

ce

Time


Mover 5

Time Distance



Math Notes:

Point out that in Activity 1 participants recorded movers' distances atcertain times, organized the data into a table, and represented the data ona graph. From the data and graphs, we made conjectures about themovers’ instructions. Now in Activity 2, we have reversed the process.We are undoing by taking the verbal description of a mover's walk andrepresenting it with a graph.

Also, we used the algebraic thinking skill of patterns to rules by applyingthe rules we found in Activity 1. For example, a faster pace is representedby a steeper line.


• How are the graphs alike? How

are they different?

• Which graph has a horizontal

section? Graph 1

• How do you represent on the

graph a mover standing still? Ex-plain why. By drawing a horizontalline to show that the distance isstaying the same as the timechanges.

• Which graph slopes down from left

to right? Why does it slope thatway? Graph 2 slopes down from leftto right because the mover started atthe end and walked toward thebeginning. Thus, the distance fromthe beginning of the tape decreasedin relation to time. Also, Graphs 3and 4 had segments where themover turned around and walkedtoward the beginning, so they havesegments that slope down from leftto right.

• Which graph has the steepest

segment? Why? Graph 3, becausethe mover ran and there was agreater change in distance persecond.

• How did you represent a mover

walking at a slow pace? Why? Bydrawing a shallow line to show asmall change in distance for eachsecond of time.

• Does it matter how shallow you

draw the line? At this point, we arenot overly concerned with findingspecific rates of change. We justwant participants to draw things slowand fast relative to one another.


Movin' on Down the LineActivity 2

Some students in another class were given different Secret Instruction Cards for“Movin' on Down the Line.” Data was collected for 20 seconds. Below is a list ofwhat was on their cards. Draw a sketch of what you think the graph should looklike for each one.

1. Start at the beginning of themeasuring tape. Walk forward at asteady, slow pace for 5 seconds.Then stand still for the next 5 sec-onds. Repeat these steps until timeruns out.

2. Start at the end of the tape andwalk towards the beginning of thetape at a steady pace.

3. Start at the beginning of themeasuring tape and walk slowly for8 seconds then run for 8seconds. Then turn around andwalk slowly back towards the begin-ning of the tape.

4. Start at the 50 foot mark on themeasuring tape. Walk forwardquickly for 7 seconds. Then turnaround and walk slowly backtoward the beginning of the tape for7 seconds. Turn around again andwalk away at a medium rate fromthe beginning of the tape until timeruns out.


Answers:

1. Start about in the middle of the tape measure, walk further away for ashort while, and then stand still for the remainder of the time.

2. Start at the beginning of the tape measure and stand still for a fourthof the time. Then walk away from the beginning of the tape measure untiltime runs out.

3. This graph is not possible for this activity. At one time, the mover isthree different distances from the beginning of the tape. This implies thatthe walker was in three places at once. Note that Exercises 1 and 2 arefunctions and Exercise 3 is not a function.

Math Notes:

Remember that we are looking atthe relationship between the twoquantities time and distance fromthe beginning of the tape. Thegraphs represent these relation-ships. The graphs do not representa picture of the path taken. Themover did not walk a course thatlooks like the graph.

In Activity 2, we went from a descrip-tion to a graph. In Activity 3, wemove from a graph to a description.This idea of going back and forthbetween representations, doing and

undoing, is a major mathematicalhabit of thinking that builds algebraicreasoning. Keep looking for itthroughout the institute.

In Activity 3, we build intuition for thealgebraic concept of function.Algebra students will need todifferentiate between relations thatare functions and relations that arenot functions.


• Which graphs are possible graphs

for Secret Instruction Cards? Why?Graphs 1 and 2 show that eachmoment the mover is only at onedistance from the beginning of the

measuring tape.

• Which graph is not a possible

graph of distance from the beginningof the measuring tape in relation toelapsed time? Why? Graph 3 is notpossible because to produce thisgraph, the mover would have to bein up to three places at the samemoment in time.

• What do we mean by doing and

undoing? Doing and undoing is amathematical (algebraic) habit ofmind. It is the idea of reversibility,strengthening of mathematicalconnections by going backwards.Activity 2 reverses Activity 1. Activ-ity 3 reverses Activities 1 and 2.



Movin' on Down the LineActivity 3

Study the graphs below made by a group of students in another class. Are thesegraphs possible graphs for other Secret Instruction Cards for “Movin’ on Downthe Line”? If not, explain why. If possible, write a description of how the personwas moving.

1.

2.

3.

Movin’ on Down the Line Adapted for Interactive Notebook Cut along the dotted lines, and then fold along the solid line. Attach to your notebook. Then draw a sketch of what you think the graph should look like for each scenario.

Adapted from TEXTEAMS (Movin’ on Down the Line)

Start at the beginning of the measuring tape. Walk forward at a steady, slow pace for 5 seconds. Then stand still for the next 5 seconds. Repeat these steps until time runs out.

Start at the end of the tape and walk towards the beginning of the tape at a steady pace.

Start at the beginning of the measuring tape and walk slowly for 8 seconds then run for 8 seconds. Then turn around and walk slowly back towards the beginning of the tape.

Start at the 50 foot mark on the measuring tape. Walk forward quickly for 7 seconds. Then turn around and walk slowly back toward the beginning of the tape for 7 seconds. Turn around again and walk at a medium rate from the beginning of the tape until time runs out.

Plot each point.

On what part of the coordinate plane does each point fall?

A (2,2) B ( 3,1)

C ( 4, 5) D (2, 3)

E (0, 3) F (5,0)

Engaging Mathematics: Algebra I TEKS-Based Activities

© Region 4 Education Service Center All rights reserved.

Linear Relationship Cards Cut along the dotted lines. Four sets of cards are provided.

The graph of the line passes through the origin.

Equation is not of the form y = kx.

The video game rental fee is $15 plus $3 per day.

There is a constant rate of change.

The cell phone rate is $9.99 each month and 3 cents a

minute.

The graph does not pass through the origin.

Angelica earns $6 an hour babysitting. The graph is a line. Equations fit the form y = kx.

The graph of the line passes through the origin.

Equation is not of the form y = kx.

The video game rental fee is $15 plus $3 per day.



minute.



The graph of the line passes

through the origin. Equation is not of the

form y = kx. The video game rental fee is

$15 plus $3 per day.



minute.



The graph of the line passes

through the origin. Equation is not of the

form y = kx. The video game rental fee is

$15 plus $3 per day.



minute.



26

Prop

ortio

nal

A candy necklace costs $1.20. Jaiden wants to buy candy necklaces for all of her friends, but only has $15.00 to spend. How many necklaces can Jaiden purchase with $15?

A health club charges $30 per month as a membership fee. Members can enroll in fitness classes for $10 per class. How many classes could Monica take in one month for $100?

Non-Proportional

Table A Table B Number of

Books Height of Stack of

Books From Floor (in.) Number of Books

Height of Stack of Books From Floor (in.)

1 1.25 1 9.5

2 2.5 2 10.75

3 3 12

5 6.25 4

10 17

10 9

x x





1 1.25 1 9.5

2 2.5 2 10.75

3 3 12

5 6.25 4

10 17

10 9

x x





1 1.25 1 9.5

2 2.5 2 10.75

3 3 12

5 6.25 4

10 17

10 9

x x



Quilt Pieces Cut along the bold lines.

2x

3x –

2

x

x x + 1

x + 2

2x – 2

5 – x

2

1

x +

2

2

1

64



Student Name: ________________________________________ Date: ________________

Technology and Scatterplots Enter the data below into Ω and æ of your graphing calculator to create a scatterplot.

Miles Driven Gallons of Gasoline Used

285 8.9 378 11.8 341 10.7 454 14.2 272 8.5 422 13.2 319 10

1. Determine an appropriate viewing window.

Record your window settings. 2. View the graph and sketch the scatterplot that appears. Determine the trend.

Trend: _______________________ Communicating About Mathematics Interpret the meaning of the trend in the problem above.

_______________________________________________________________

_______________________________________________________________

_______________________________________________________________

_______________________________________________________________

_______________________________________________________________

Miles

Gal

lons

of G

as

49

Star Coordinates – one per student

Point A (2, 0) Point B (3, 4) Point C (0, 6) Point D (4, 6) Point E (5, 10) Point F (6, 6) Point G (10, 6) Point H (7, 4) Point I (8, 0) Point J (5, 3)





Point A (2, 0) Point B (3, 4) Point C (0, 6) Point D (4, 6) Point E (5, 10) Point F (6, 6) Point G (10, 6) Point H (7, 4) Point I (8, 0) Point J (5, 3))







Vocabulary List: Acute

Angle

Degree

Obtuse

Protractor

Right

an angle with a measure between

0° and 90°

an angle with a measure between

90° and 180°

an angle with a measure of 90°

a unit of measure the symbol a tool used to measure degrees

Vocabulary Word Question Vocabulary Word

Which word goes with

______________________

______________________?


______________________

______________________?


______________________

______________________?


______________________

______________________?


______________________

______________________?


______________________

______________________?

Vocabulary Word Question Vocabulary Word

Which word goes with . . .








Information Cards Cut along the dotted lines. Two sets of cards are provided.

Data that is only defined for the given values. The values in between are not included (usually because fractional data is not possible).

Data that is defined for given values and the interval between the values

Graphs as separate points

Usually things you count (ex: number of books or people)

Graphs as a line or curve

Usually things you measure (ex: time, temperature)

This space intentionally left

blank.

Data that is only defined for the given values. The values in between are not included (usually because fractional data is not possible).

Data that is defined for given values and the interval between the values

Graphs as

separate points Usually things

you count (ex: number of books or people)

Graphs as a line or curve

Usually things you measure (ex: time, temperature)

This space intentionally left

blank.

36



Student Name: ________________________________________ Date: ________________

Vocabulary Organizer Cut apart the Information Cards and paste the items in the appropriate box in the vocabulary organizer.

Definition

Characteristics

Example Nonexample

Communicating About Mathematics Give an example of continuous data and explain why it is continuous.

Definition

Characteristics

Example Nonexample

Discrete Data

Continuous Data

_______________________________________________________________

_______________________________________________________________

_______________________________________________________________

_______________________________________________________________

_______________________________________________________________

35

Using Interactive Notebooks in the Mathematics...

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