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NCTM Process Standards. Problem SolvingCommunicationConnectionsReasoning and ProofRepresentation. 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

Middle School Math Strategies: Teaching the Standards in

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**1. **Middle School Math Strategies: Teaching the Standards in Lois Coles
8th Grade
Brentwood Middle School
[email protected]

**2. **NCTM Process Standards Problem Solving
Communication
Connections
Reasoning and Proof
Representation

**3. **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.

**4. **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

**5. **Know Your Students Motivations/Interests/Relevance Human Graphs – Great getting to know you activity at the beginning of the year

**7. **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

**8. **Problem Solving with Apollo 13 Brainstorm list of Problem Solving Strategies

**9. **Realplayer Video Clips

**10. **

**11. **Houston, we have a problem

**12. **We gotta find a way to make this... fit into the hole for this... usin' nothin' but that. ...

**13. **Real World Applications Career Fair
Junior Achievement

**14. **Discourse/Questioning Mathematical Processes/Questions
Socratic Seminar
Pick one activity to work with a partner & report out!
ABC123/Perplexing Hexagons
Which Doesn’t Belong and Why?
Fuel Gauge/Highway Grade

**15. **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.

**16. **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)

**17. **Why have a Socratic Seminar in Math?

**18. **Research “Socratic seminars (encouraged) students to assume responsibility for reasoning and communicating convincingly about mathematics…helped 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)

**19. **Socratic seminars Involve all kids
Find situations that use math but don’t have “right” answers
Get kids away from computation-based math problems
Build a thinking and reflecting community of learners

**20. **Rundown of Rules
EVERYONE participates
No idea is a bad idea
Think outside the box and don’t be afraid to be creative
Show respect - No criticism allowed
*No right/wrong answers
*Acknowledge others’ comments
Student-Led!

**21. **Practice Seminar: Skin 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.

**22. **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.

**23. **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! I’m in trouble”? Why?

**24. **Student Comments “When are we going to have another discussion? I love those!”
“I’m glad that there aren’t right answers and that there are lots of ways of looking at the problem.”
“It’s fun to see how what we are studying connects to the world.”

**25. **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!

**26. **Stations/Group Work/Problem Solving Whose Line Is It Anyway?
Cents
A Tall Fish Tale

**27. **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

**28. **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

**29. **Two-Color Counters

**30. **Algebra Tiles Virtual Manipulatives

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

**33. **Algebra Aerobics

**34. **
Y = mx+b
Math class, there’s no need to feel down,
I said math class, get yourselves off the ground.
Come on math class, if there’s a line to be found, it’s so easy when you sing out.
Math class, come on get in the swing,
I said math class, it’s more fun when you sing.
Come on math class, naming lines is your thing, it’s so easy when you sing out (5 beats)
Y=MX+B, (rpt)

**35. **It’s so easy to do and it earns high grades to,
you can catch up with all the smart kids,
Y=MX+B (rpt)
It’s 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 don’t have to mope,
come on math class you have reason to hope,
it’s so easy when you sing out..
Math class, B’s the y-intercept.
Come on admit now, it’s not hard to accept.
Math class, you’ll do your math with more pep.
It’s so easy when you sing out (5 beats)…
Y=MX+B (rpt)

**36. **Algebra Aerobics U, U, U
let
the dawgs out!

**37. **Algebra Aerobics U, U, U
let
the dawgs out!
NOT!!!!!

**38. **Algebra Aerobics V-i-c-t-o-r-y
That’s our
Absolute Value Cry!

**39. **Algebra Aerobics V-i-c-t-o-r-y
That’s our
Absolute Value Cry!
NOT!!!!!!!!

**40. **Algebra Aerobics I, I, I, I
I am cubed.
I am cubed.
I, I, I, I,
I am cubed
I am cubed!!!

**41. **Algebra Aerobics I’m a little
Square root
short and stout.
I don’t have a handle but here is my spout!

**42. **Algebra Aerobics When you tip me over, I won’t pout.
Cause I’m a little
square root, short and stout!

**43. **Real Number Box

**44. **Reading/Writing/Vocabulary Concept Cards
Word Whacker
Unit Vocabulary review
Journaling
Exit Cards
Reasoning
The Answer Is…
Trade Books/Newspaper
Famous Mathematician Trading Cards

**45. **Math History Cross-curricular
Reaches all learners
Mathematicians were people too
Relevance
Interesting trivia

**46. **Children’s Literature Grandfather Tang’s 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

**47. **Tangram Geometry Vocabulary Discuss these terms during construction
Discuss these terms during construction

**48. **Integrating Technology Textbook Resources
Personal Tutors
Workbooks
BRAINPOP
Graphing Calculator
TI-84+
TI- Nspire

**49. **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!

**50. **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.

**51. ** 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.

**52. **

**53. **Let Me Nspire You…

**54. **Home Screen Calculator
Graphs and Geometry
Lists and Spreadsheets
Notes
Data and Statistics
New Document
My documents
System Info
Hints

**55. **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

**56. ** Rigor/Webb Levels/ Going Deeper/Extensions Your Age by Chocolate Math
NUMBER JUMBLERS

**57. **Other Organizations
NCTM
TMTA
(MT)˛
TI-User Group

**58. **Math Takes a Holiday Halloween
Thanksgiving
Christmas
Hanukah
Valentine’s Day
Pi Day

**59. **Reflections in the Coordinate Plane – A Performance Task

**60. ** 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.

**61. **What would the process be for finding the area of this heart?

**62. **App-p-tizing Pi Day Activities

**63. **Even the teacher had fun!

**64. **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
It’s Probably Pi: Buffon’s 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

**65. **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.

**66. **Happy Birthday

**67. **A-Mazing Mr. Einstein

**68. **p Pi Day Greeting Card Click here to send a Pi Day greeting card via email
http://www.123greetings.com/events/pi_day/

**69. **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/

**70. **Pi Karaoke Bob Garvey tapes [email protected]
“Pi equals 3141592
65358
979 323 846 264”

**71. **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")

**72. **Pi Poetry Simple Simon met a pi man Going to the fair. Said Simple Simon to the pi man, “You have unusual ware. The pie’s I’ve seen before were round But, gosh, your pi’s r2.”

**73. **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.

**74. **Pi Jokes Q: What do you get if you divide the circumference of a jack-o-lantern by its diameter?

**75. ** Q: What do you get when you take green cheese and divide its circumference by its diameter?

**76. **Q: What do you get when you take a native Alaskan and divide its circumference by its diameter?

**77. **Q: What do you get if you divide the circumference of a bowl of ice cream by its diameter?

**78. **What kind of pie are you ordering when you ask the waiter for
p z2 a

**79. **Pi Cartoons

**80. **Pi Cartoons

**81. **Pi Comics

**83. **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?

**84. **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.

**85. **Buffon’s Needle Experiment: It’s 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.

**87. **Pie Bake-Off Teachers serve as judges! Yummy!

**88. **Pi Aerobics

**89. **Sir Cumference and the Dragon of Pi

**90. **"Math's never a piece of cake, but sometimes it's just as easy as pi"

**92. **Ticket Out the Door