Middle School Math Strategies: Teaching the Standards in

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Middle School Math StrategiesTeaching the
Standards in

• Lois Coles
• 8th Grade
• Brentwood Middle School
• loisc_at_wcs.edu

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NCTM Process Standards

• Problem Solving
• Communication
• Connections
• Reasoning and Proof
• Representation

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TN Process Standards

• Use mathematical language, symbols, and
  definitions while developing mathematical
  reasoning.
• Apply and adapt a variety of appropriate
  strategies to problem solving, including
  estimation, and reasonableness of the solution.
• Develop independent reasoning to communicate
  mathematical ideas and derive algorithms and/or
  formulas.
• Move flexibly between concrete and abstract
  representations of mathematical ideas in order to
  solve problems, model mathematical ideas, and
  communicate solution strategies.
• Use mathematical ideas and processes in different
  settings to formulate patterns, analyze graphs,
  set up and solve problems and interpret
  solutions.
• Read and interpret the language of mathematics
  and use written/oral communication to express
  mathematical ideas precisely.
• Recognize the historical development of
  mathematics, mathematics in context, and the
  connections between mathematics and the real
  world.
• Use technologies/manipulatives appropriately to
  develop understanding of mathematical algorithms,
  to facilitate problem solving, and to create
  accurate and reliable models of mathematical
  concepts.

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Instructional Strategies for Middle School

• Know Your Students
• Motivations/Interests/Relevance
• Discourse/Questioning
• Stations/Group work/Problem Solving
• Multiple Representations
• Differentiation/Kinesthetic/Hands-on
• Reading/Writing/ Vocabulary
• Integrating Technology
• Test Prep/Assessment
• Rigor/Webb Levels/Going Deeper/Extensions

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Know Your Students Motivations/Interests/Relevanc
e

• Human Graphs Great getting to know you activity
  at the beginning of the year

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FYI - Statistically, on average two people in a
group of 23 will share the same birthday.
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Write Your Math Autobiography

• Your strengths and weaknesses
• Hopes/fears for this year
• Goals for this year
• What helps you learn the best
• What bothers you most in a classroom
• Past experiences with math
• Future plans
• Anything else you feel is relevant

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Problem Solving with Apollo 13

• Brainstorm list of Problem Solving Strategies

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Realplayer Video Clips
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Houston, we have a problem
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We gotta find a way to make this... fit into the
hole for this... usin' nothin' but that. ...
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Real World Applications

• Career Fair
• Junior Achievement

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Discourse/Questioning

• Mathematical Processes/Questions
• Socratic Seminar
• Pick one activity to work with a partner report
  out!
• ABC123/Perplexing Hexagons
• Which Doesnt Belong and Why?
• Fuel Gauge/Highway Grade

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What is a Socratic Seminar?

• Socratic named for Socrates, a classical
  Greekphilosopher470-399 B.C who developed a
  Theory of Knowledge. He was convinced that the
  surest way to attain reliable knowledge was
  through the practice of disciplined
  conversation.  He called this method dialectic.
  Di-a-lec-tic (noun) means the art or practice of
  examining opinions or ideas logically, often by
  the method of question and answer, so as to
  determine their validity.

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Procedure

• Respect one another's opinions
• Avoid interrupting, but there is no need to raise
  hands
• Address classmates by name
• Take notes
• Comments should address the topic and not digress
  
• Points of disagreement are settled among
  participants the teacher is not a resource
• Sit in a circle so that everyone can be seen (or
  a semicircle at the board)

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Why have a Socratic Seminar in Math?

• Students are given opportunities to "examine"
  text or problem
• After "reading" the text open-ended questions
  are posed
• Open-ended questions allow students to
• think critically
• analyze multiple meanings/solutions/viewpoints
• express ideas with clarity and confidence

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Research

• Socratic seminars (encouraged) students to
  assume responsibility for reasoning and
  communicating convincingly about
  mathematicshelped the teacher assess students
  conceptual understanding of functions
  (Koellner-Clark)
• We saw repeatedly that when students discussed
  their ideas with others, they continued to
  revise, refine, and improve them. (Borasi 1992
  Moschvich 1998)

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Socratic seminars

• Involve all kids
• Find situations that use math but dont have
  right answers
• Get kids away from computation-based math
  problems
• Build a thinking and reflecting community of
  learners

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Rundown of Rules

• EVERYONE participates
• No idea is a bad idea
• Think outside the box and dont be afraid to be
  creative
• Show respect - No criticism allowed
• No right/wrong answers
• Acknowledge others comments
• Student-Led!

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Practice SeminarSkin Scare

• Imagine for one moment that you have been
  involved in a car accident. There was a fire and
  you were burned. You were taken by ambulance to
  the emergency room and are being treated by
  several doctors.

Dr. Steve Leinwand, Principal Research Analyst,
American Institutes for Research (AIR),
Washington, D.C
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Skin Scare

• You are fully aware of what is going on around
  you, but as is often the case, no one is telling
  you what is happening. You have to gather
  information from what you hear and observe. You
  know you have been given medication, so you
  cannot judge the extent of your injuries by the
  amount of pain you feel. You know that you are
  burned, but cannot tell how badly.

Dr. Steve Leinwand, Principal Research Analyst,
American Institutes for Research (AIR),
Washington, D.C
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Skin Scare

• You hear the doctors talk about skin grafts and
  then an order is made for 800 in2 of skin for the
  procedure.
• At this point, how serious are your injuries? Do
  you think, Oh good, they will take care of me
  or Oh NO! Im in trouble? Why?

Dr. Steve Leinwand, Principal Research Analyst,
American Institutes for Research (AIR),
Washington, D.C
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Student Comments

• When are we going to have another discussion? I
  love those!
• Im glad that there arent right answers and
  that there are lots of ways of looking at the
  problem.
• Its fun to see how what we are studying
  connects to the world.

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Brainstorm ideas for questions

• Open ended, but not huge (can tackle in one class
  period)
• Problems that can have a variety of approaches
• Problems that have less computation and more
  reflection/application
• Problems that can have very different
  strategies-create debate!

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Stations/Group Work/Problem Solving

• Whose Line Is It Anyway?
• Cents
• A Tall Fish Tale

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Multiple Representations

• TWANG
• Technology, Written Word, Algebraic, Analysis,
  Algebra Aerobics, Assessment, Numeric, NUMB3RS,
  Graphical, and Geometry
• Rates are a SNAP!
• Function Family Trees
• Equipment Costs

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Differentiation/Kinesthetic/Hands-on

• Reading a Ruler
• Venn Diagram Foldable
• Two-Color Counters/Songs
• Algebra Tiles
• X- in the Box
• Coordinate Plane foldable
• Wikki Stix
• Algebra Aerobics
• Real Number Box

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Two-Color Counters
YELLOW represents POSITIVE RED represents
NEGATIVE ZERO PAIR 0 Model Problems
with a Partner
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Algebra Tiles

• Virtual Manipulatives

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Algebra Aerobics

• Your instructor Mrs. Coles
• Be prepared to move and
• groove to the math beat!
• So get off your seat!

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Algebra Aerobics
Y x
Y -x
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• Y mxb
• Math class, theres no need to feel down,
• I said math class, get yourselves off the
  ground.
• Come on math class, if theres a line to be
  found, its so easy when you sing out.
• Math class, come on get in the swing,
• I said math class, its more fun when you sing.
• Come on math class, naming lines is your thing,
  its so easy when you sing out (5 beats)
• YMXB, (rpt)

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• Its so easy to do and it earns high grades to,
• you can catch up with all the smart kids,
• YMXB (rpt)
• Its so simple you see come on and listen to me,
• you can do math as well as the re-est.
• Math class, you know the M stands for slope,
• I said math class now you dont have to mope,
• come on math class you have reason to hope,
• its so easy when you sing out..
• Math class, Bs the y-intercept.
• Come on admit now, its not hard to accept.
• Math class, youll do your math with more pep.
• Its so easy when you sing out (5 beats)
• YMXB (rpt)

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Algebra Aerobics

• U, U, U
• let
• the dawgs out!

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Algebra Aerobics

• U, U, U
• let
• the dawgs out!
• NOT!!!!!

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Algebra Aerobics

• V-i-c-t-o-r-y
• Thats our
• Absolute Value Cry!

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Algebra Aerobics

• V-i-c-t-o-r-y
• Thats our
• Absolute Value Cry!
• NOT!!!!!!!!

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Algebra Aerobics

• I, I, I, I
• I am cubed.
• I am cubed.
• I, I, I, I,
• I am cubed
• I am cubed!!!

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Algebra Aerobics

• Im a little
• Square root
• short and stout.
• I dont have a handle but here is my spout!

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Algebra Aerobics

• When you tip me over, I wont pout.
• Cause Im a little
• square root, short and stout!

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Real Number Box
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Reading/Writing/Vocabulary

• Concept Cards
• Word Whacker
• Unit Vocabulary review
• Journaling
• Exit Cards
• Reasoning
• The Answer Is
• Trade Books/Newspaper
• Famous Mathematician Trading Cards

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Math History

• Cross-curricular
• Reaches all learners
• Mathematicians were people too
• Relevance
• Interesting trivia

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Childrens Literature

• Grandfather Tangs Story A Tale Told with
  Tangrams Ann Tompert
• The Librarian Who Measured the Earth Kathryn
  Lasky
• The Fly on the Ceiling Dr. Jullie Glass
• One Grain of Rice Demi

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Tangram Geometry Vocabulary

• Square
• Parallelogram
• Trapezoid
• Isoceles Right Triangle
• Midpoint
• Hypotenuse

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Integrating Technology

• Textbook Resources
• Personal Tutors
• Workbooks
• BRAINPOP
• Graphing Calculator
• TI-84
• TI- Nspire

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Creative Writing with the TI-84

• 0 1 2 3 4 5 6 7 8 9
• o I z e h s g L B G
• Did you have ________ for breakfast this morning?
  
• 5 x 103 6 x 102 6 x 10 3
• Turn your calculator up-side down for the answer!
• Now you try one!

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Graphing Calculator Scavenger Hunt

• This activity helps to familiarize students with
  the many keys, menus and functions of the TI-84
  and the TI-Nspire.

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Scientific Notation on the TI-84

• Cross Curricular Activity Do in conjunction
  with Physical Science or Integrated Science
• Objective - In this lesson students will learn to
  perform computations involving scientific
  notation using the graphing
  calculator.

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• Examples
• Express 6,184,000 in scientific notation.
• To access the scientific mode, press ?Sci
  and press . Press to return to
  home.
• Type in 6184000 and press
• 6.184E6 will appear on the calculator screen,
  so the answer is 6.184 x 106
• Express 0.00004637 in scientific notation.
• Repeat procedure.
• Type in 0.00004637 and press
• 4.637E ?5 will appear on the calculator
  screen, so, the answer is 4.637 x 10-5

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Let Me Nspire You
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Home Screen

• Calculator
• Graphs and Geometry
• Lists and Spreadsheets
• Notes
• Data and Statistics
• New Document
• My documents
• System Info
• Hints

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Test Prep/Assessment

• Lotus Grahic Organizer
• Foldables
• Exponents PBT Attn to Common Errors
• Color Change Marker
• I Have, Who Has
• ACT/SAT Question of the Day

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Rigor/Webb Levels/ Going Deeper/Extensions

• Your Age by Chocolate Math
• NUMBER JUMBLERS

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Other

• Organizations
• NCTM
• TMTA
• (MT)²
• TI-User Group

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Math Takes a Holiday

• Halloween
• Thanksgiving
• Christmas
• Hanukah
• Valentines Day
• Pi Day

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Reflections in the Coordinate Plane A
Performance Task
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Tangram Thanksgiving

• In 1620, the Pilgrims boarded the Mayflower and
  set sail for America. The journey across the
  ocean was often treacherous. After many months,
  they tired of eating fish. Upon safely reaching
  dry land, they fell to their knees in prayer.

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What would the process be for finding the area of
this heart?
If the side of the square is 5 units, what is the
area of the heart?
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App-p-tizingPi Day Activities

• On or around March 14
• Parent and community involvement
• Students rotate through centers
• Serve Moon pies, pizza pies, homemade pies and
  decorated cakes, Eskimo pies

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Even the teacher had fun!
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Pi Day Activities

• Pi Day History
• Einstein Maze
• Pi Day Online Greeting Card
• Find your Birthday in Pi online activity
• Pi Karaoke
• Pi Poetry Cross Curricular Activity
• Pi Jokes
• Pi Cartoons
• Finding Pi
• Its Probably Pi Buffons Needle Experiment
  Math History
• Pie Bake-off!
• Pi Aerobics Kinesthetic learner
• Read Sir Cumference and the Dragon of Pi
• Pi Jeopardy!
• Pi Day Webquest/Scavenger Hunt

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What is pi?

• Pi, which is denoted by a Greek letter, is the
  most famous ratio in mathematics, and is one of
  the most ancient numbers known to humanity.
• Pi possibly first entered human consciousness in
  Egypt. The earliest known reference to pi occurs
  in a papyrus scroll, written around 1650 BC by a
  scribe named Ahmes.
• Around 200 BC, Archimedes of Syracuse found that
  pi is about 22/7 (Greeks did not use decimals).
• The first person to use the Greek letter for the
  number was William Jones, an English
  mathematician, who coined it in 1706.

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Happy Birthday
Albert Einstein
Waclaw Sierpinski
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A-Mazing Mr. Einstein
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pPi Day Greeting Card

• Click here to send a Pi Day greeting card via
  email
• http//www.123greetings.com/events/pi_day/

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Find YOUR birthday in Pi!

• Click on the link below to find your birthday in
  the digits of Pi
• http//www.facade.com/legacy/amiinpi/

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Pi Karaoke

• Bob Garvey tapes bgarvey_at_aol.com
• Pi equals 3141592
• 65358
• 979 323 846 264

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• Oh Number Pi
• Oh, number Pi, Oh, number Pi
• Your digits are unending.Oh, number Pi, Oh,
  number Pi
• No pattern are you sending.You're three point
  one four one five nine,And even more if we had
  time,Oh, number Pi, Oh, number Pi
• for circle lengths unbending.Oh, number Pi,
  Oh, number Pi
• You are a number very sweet,Oh, number Pi,
  Oh, number Pi
• Your uses are so very neat.There's 2 Pi r and
  Pi r squared,A half a circle and you're
  there,Oh, number Pi Oh, number Pi
• we know that Pi's a tasty treat.(to the tune of
  "Oh, Christmas Tree")

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Pi Poetry

• Simple Simon met a pi manGoing to the fair.Said
  Simple Simon to the pi man,You have unusual
  ware.The pies Ive seen before were roundBut,
  gosh, your pis r2.

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Piaku

• Piaku Poetry in which the number of syllables in
  each sentence correspond to the consecutive
  digits of Pi.
• The Storm by Mike Rollins
• 3 Flash, Rumble
• 1 Rain
• 4 Awesome thunder
• 1 Wind
• 5 The wind will plunder
• 9 As did the pirates from on yonder
• 2 Raid, fall
• 6 Pillage! My ship sinks deep
• 5 The water stinging
• 3 Quivering
• 5 The storm moves onward
• 8 I'm tired, I'm cold, I sink, I die.

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Pi Jokes

• Q What do you get if you divide the
  circumference of a jack-o-lantern by its
  diameter?

A Pumpkin pi.
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• Q What do you get when you take green cheese
  and divide its circumference by its diameter?

A Moon pi.
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• Q What do you get when you take a native
  Alaskan and divide its circumference by its
  diameter?

A Eskimo pi.
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• Q What do you get if you divide the
  circumference of a bowl of ice cream by its
  diameter?

A Pi a'la mode.
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• What kind of pie are you ordering when you ask
  the waiter for
• p z2 a

pizza
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Pi Cartoons
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Pi Cartoons
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Pi Comics
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Finding Pi
?

• CAREFULLY measure the diameter and circumference
  of 10 circular objects and fill in the chart.
• Enter the circumference into L1 in your graphing
  calculator. Enter the diameter into L2 in your
  graphing calculator.
• In L3 divide L1 by L2
• Do you recognize the numbers in L3?

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Georges-Louis Leclerc, Comte de Buffon

• Comte de Buffon discovered this result in the
  16th century if you drop a needle on a grid of
  parallel lines which are spaced the length of the
  needle apart, the probability that the needle
  will land on a line is 2/p.

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Buffons Needle ExperimentIts Probably Pi

• 1. Drop a bunch of toothpicks on the parallel
  lines. Write down the number of toothpicks you
  dropped in "Number of Drops" column.
• 2. Count the number which crossed a line and
  write it in the "Number of Crossings" column.
• 3. Add your number of drops to the "Cumulative
  Drops" and write the total on the data sheet.
• 4. Add your number of crossings to the
  "Cumulative Crossings" and write the total on the
  data sheet.
• 5. Calculate a new value for p by dividing the
  "Cumulative Drops" by the "Cumulative Crossings"
  and multiplying your result by 2.

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Pie Bake-Off

• Teachers serve as judges! Yummy!

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Pi Aerobics
Diameter
Pi
Circumference
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Sir Cumference and the Dragon of Pi
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"Math's never a piece of cake, but sometimes it's
just as easy as pi"
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Ticket Out the Door
TICKET out the door Name one valuable thing
you learned today that you will use in your
classroom A question I still have is