Cumberland County

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Cumberland County

• Thinking Maps Follow Up
• In Mathematics
• Holly Springs Middle School
• December 4, 2007
• Janie B. MacIntyre

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Agenda

• Getting Started
• Thinking Maps Review Game
• BBR Connections
• Viewing Curricular Samples
• Types of Knowledge in Math
• Seeing the Maps in the NCSCOS
• Curriculum Planning
• Maps Throughout a Lesson
• Map Making
• Literacy Strategies through vocabulary
  development
• NCSDPI Middle School Resources
• Additional Engagement Strategies

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Getting Started
What is your current level of comfort in using
Thinking Maps in your math classes?
Review of fundamentals about TMaps, student
learning and types of knowledge
TMaps used for instructional planning
Recognizing opportunities for TMaps in the SCOS
What do you hope to gain from our sessions?
Thinking Maps Follow-Up In Math
Curricular Samples
Observing how TMaps can be used throughout a
lesson
Using TMaps with other teaching strategies
What are your challenges in teaching
your students the math curriculum?
Opportunities to create instructional support
using Thinking Maps.
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Lets begin with a review of theThinking Maps.
With a partner

• complete the
• Concepts of Thinking Maps Card Game.

Map Name
Map Graphic
Type of Thinking
Key Questions
Key Words
Let me know when you and your partner have
finished!
7 minutes
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We already know in order for anyone to learn
anything.
there must be, either...
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an emotional connection or personal relevance,
in order for learning to occur.
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Viewing of Curricular Samples

• These slides will simply give you an opportunity
  to view a variety of ways Thinking Maps may be
  used
• within the mathematics curriculum.

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Getting Ready Take a sheet of colored,legal-
length paper

• Fold in halfhamburger bun-style
• Re-open the paper, revealing the 4 sections
  (front and back)
• Number in the top left hand corner of
• each section 1 3
• 2
  4
• 
  front back

On the top of section 1 write Fundamentals of
Thinking Maps in Math
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Section 1Fundamentals of Thinking Maps in Math
Create a Circle Map entitled..
Tally for each map you could use with your
curriculum.
Thoughts I had while observing curricular
samples in math.

• Be prepared to share.

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Curricular Samples for Mathematics
Janie MacIntyre
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Great for Assessment!
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Even
Composite
10²
placeholder
100
factor of 10,000
multiple of 10
divisible by 1,2,5,10,20, 25,50,100
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Algebra
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Definition
Visual Representation
A triangle with one right angle
Right Triangle
Triangle with a 90 degree angle
Personal Association or Characteristic
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Equivalent Fractions-name the same amount
Area/region model
Numerical model
2/4
5/10
1/2
Measurement /length model
Set model
Use to add, subtract, and compare fractions
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Robust Vocabulary Development
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The square root function
A parabola
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Roosevelt Elem Long Beach, CA
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Roosevelt Elem Long Beach, CA
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Roosevelt Elem Long Beach, CA
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Roosevelt Elem Long Beach, CA
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This is important so that I will understand the
value of money.
The Value of Money
________ ________ has more value than _________
__________.
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We could use 10.
We need to know how to convert to decimals.
We have to know that this is a two step problem.
We need some prior knowledge about what a tip
is.
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Break down numbers to simplify additions
To illustrate my strategy for adding
To show my thinking about groups of 10
Expanded notation helps with computation
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Time for Sharing

• Feel free to add to your own circle map.
• Of the 33 samples viewed, how many would you have
  been able to use with your students?

Were the curricular samples personally relevant
to you?
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Thinking Maps provides the support or SCAFFOLDING
for student learning, as teachers help them make
personal and meaningful connections to the
content.
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In much the same way scaffolding helps provide
support to build structures
Thinking Maps provide support as we
develop effective thinking in our students.
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BRAIN RESEARCH CONNECTION
It has been shown that explicitly engaging
students in the creation of nonlinguistic
representations stimulates and increases
activity in the brain. (see Gerlic Jausovec,
1999)
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DUAL CODING THEORY
Knowledge is stored in two forms
Linguistic Form
Nonlinguistic Form
Research proves that the more we use both
systems of representation, the better we are
able to think and recall knowledge.
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In addition to the information included in the
maps often being non-linguistic representations.

• the Thinking Maps themselves, are also
• non-linguistic representations of the content
  students are learning.

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Please include in your circle maps frame of
reference

• Students need linguistic
• and non-linguistic representations of
  information to be learned.

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In addition to the brains need for dual coding
of information

• there are two fundamental types of knowledge

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Section 2 Types of Knowledge Tree Map

• Types of Knowledge in Math
• Declarative Procedural

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Procedural
Declarative

• things that are always true
• absolutes
• givens
• George Washington was the first President of the
  United States
• A square has four congruent sides four 90
  degree angles.

• In order to achieve a desired result, a certain
  sequence or order must be followed.
• Procedure becomes automatic (mylenated).
• Reducing fractions
• Determining volume

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Procedural
Declarative

• How to use the Pythagorean Theorem to determine
  missing measurement of right triangle

Tell me something that you think would be an
example of this in mathematics

• How to use a protractor
• How to bisect an angle
• How to solve proportions
• How to reduce fractions
• How to construct a line plot
• How to determine the median of a set of data
• How to complete long division

Content Vocabulary, Laws, Rules,Theorems,
Postulates, Contributions of Mathematicians
Pythagorean Theorem a² b² c²
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Section 2 Underneath your examples of each
type of knowledge

• add the appropriate Thinking Maps for each
• type of knowledge.

Types of Knowledge in Math Declarative
Procedural
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Procedural
Declarative

• Flow Map

• Bubble Map
• Double Bubble Map
• Tree Map
• Circle Map
• Multi-flow Map
• Bridge Map
• Brace Map

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For the next activity, you shouldsit in grade
level groups.

• Please take your materials with you.
• You will be returning to your current locations
  when we are finished.

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Take out Cumberland Countys

• pacing guide
• order of instruction
• task analysis

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Section 3Seeing the Thinking Processes and
Thinking Maps in the NC Mathematics SCOS
Lets look at an example.
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When making connections to 8th SCOSremember
these key questions What type of
thinking could students use?
What type of knowledge does that require?
Which type of map could be appropriate?
Write these 3 questions in section 3.

• (2nd Quarter)
• 5.01 Develop an understanding of functions.
• (Defining Circle What is a function?)
• (Classifying Tree Types of
  functions.)
• (Seeing Relationships Bridge Function
  with its graph)
• a. Translate among verbal, tabular, graphic and
  algebraic representations of functions.
• (Classifying Tree Ways Functions can
  be Represented)
• (Sequencing Flow How to translate
  between representations of functions)

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• b. Identify relationships and functions as linear
  or non-linear.
• (Seeing Relationships Bridge
  Qualities of linear and non-linear functions)
• (Classifying Tree Types of
  functions)
• (Comparing Contrasting
  Double-Bubble linear non-linear functions)
• c. Find, identify, and interpret the slope (rate
  of change) and intercepts of a linear relation.
• (Sequencing Flow How to determine
  slope, or intercepts)
• (Classifying Tree Types of Slope)
• (Cause Effect Partial Multi-flow
  The given slope results in , one could
  predict)

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Let's examine a few Thinking Maps that could be
used with these objectives.
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The square root function
A parabola
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Your turn!

• Decide if you want to work in groups on the same
  goals or work independently on different goals
  and share the results for
• at least 1 quarter.
• Make connections between
• Cumberland Countys Order of Instruction and
  Task Analysis
• Thought processes
• Thinking Maps
• Underline or highlight textual indicators
• Write connections in the margins or on post-it
  notes.

Be prepared to share.
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KEY WORDS FOR THINKING handout may be helpful.
handouts 1A 1B
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After you have made connections to the thinking
to the Thinking Maps for at least 1 quarter

• Choose write 1 goal its
• thinking thinking map connections on
  plain paper to post share. (Identify the goal.)
• Create at least 2 Thinking Maps that
• could be used with that goal on plain paper
  to post share.

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Gallery Walk of Shared Goals Connections to
Thought Processes Thinking Maps

• Create a Tree Map on plain paper
• As you examine the goals and work of others, note
  additional Thinking Maps that could be used with
  that given goal.
• Gallery Walk of Goals
• 6th Grade 7th Grade
  8th Grade
• (additional ideas) (additional
  ideas) (additional ideas)

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Time to share

• What additional ideas did you have at each grade
  level
• What were you able to learn from this activity?
• How would that impact your use of Thinking Maps
  within your instruction?

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FOCUS ON
Maps throughout a lesson in MATH
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Once you make the connections between the
standards, the thought processes and the maps

• how could Thinking Maps be used with

Curriculum Planning?
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FOCUS ON
Maps throughout a lesson in MATH
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For Lesson or Unit Planning
Why do students need to learn this?
What thinking maps will students need, to do or
learn these new things?

• Use a Circle Map

What should students be able to do or know at
end of lesson or unit?
Lesson Or Unit
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Why and how is this important?
Brace Map
Identify the parts of the coordinate plane.
Bridge Map
Know content vocabulary.
See the connection between quadrant and the
members of an ordered pair of numbers.
Circle Map
Math Example
Real-life Uses of CP skills
Coordinate Plane
Locate any point from a given ordered pair.
Connect given points.
Determine the coordinates of any given point.
Flow Map
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Section 4Your Turn
Why do students need to learn this?
What thinking maps will students need, to do or
learn these new things?

• Overview of
• your lesson or
• unit

What should students be able to do or know at
end of lesson or unit?
Construct a circle map on the next unit or
lesson you will be teaching. Use the frame of
reference as indicated.
Lesson Or Unit
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Use a Flow Map to plan the components of
instruction to adhere to pacing demands.
Day 1 Introduction
Day 2
Day 3
Day 4
Day 5
Day 6
Day 7 Assessment
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Begin a unit of instruction with a Circle Map

• Establish prior knowledge
• through questioning.
• What do you remember
• about the Coordinate Plane?
• Shows misconceptions or areas
• of weakness.
• Allows immediate and thorough
• connection to relevant,
• real-life uses.
• Saves instructional time.

Use at the end for review to show student growth
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What content vocabulary is essential to student
understanding?
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Will analysis aid student understanding?What
constitutes a coordinate plane?
Horizontal axis or number line (x)
origin (0)
0
Coordinate Plane (grid)
Vertical axis or number line (Y)
I
II
Four quadrants I,II,III, IV
III
IV
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Your turn!

• Think about the overview of your next lesson or
  unit
• Using plain paper on your table
• construct the Thinking Maps you would need with
  your lesson or unit
• Be prepared to share
• (Concept being taught, type of map used, title of
  map
• the map itself.)

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Getting Ready Take a sheet of colored,legal-
length paper

• Fold in halfhamburger bun-style
• Re-open the paper, revealing the 4 sections
  (front and back)
• Number in the top left hand corner of
• each section 5 7
• 6
  8
• 
  front back

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Section 5What might a lesson or unit look like
with Thinking Maps?

• Create a Tree Map for notes about your coworkers
  Thinking Maps
• Thinking Maps used in Lessons Could Include
• Concept Type of Map Title of Map
  Special Notes
• Coordinate Plane Bridge
  Key Vocabulary Visual Cues
  for

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Lets talk about it!

• What ideas did you learn from your colleagues?
• What did you find interesting?
• What questions do you need to ask?

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Literacy Links to Vocabulary Development
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Section 5 Literacy Linksto Vocabulary
Development

• Marzanos Process
• Vocabulary Game

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Research Says

• Systematic vocabulary instruction is one of the
  most important instructional interventions that
  teachers can use, particularly with low-achieving
  students.

Marzano, 2004
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RESEARCH CONNECTIONS
Page 134

• Students need to be exposed to a word at least
  six times in context to learn the meaning of the
  word.
• Even superficial instruction of new words
  enhances learning those words in context.
• One of the best ways to learn a new word is to
  associate a mental image or symbolic
  representation with it.

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RESEARCH CONNECTIONS
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• Direct vocabulary instruction works.
• Direct instruction on words that are critical to
  new content produces the most powerful learning.

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When students read new information
andcomprehension is assessed
12ile gain

• If there is some regular vocabulary instruction
• If the direct instruction is for words that are
  critical to academic content

33ile gain
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A Six-Step Process for Teaching New Terms
Building Background Knowledge for Academic
Achievement Debra Pickering and Robert Marzano
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A Six-Step Process for Teaching New Terms
These two steps should be done orally with the
teacher leading the discussion. The activities
to be discussed in this follow-up should be
completed only after these first two steps.
Building Background Knowledge for Academic
Achievement Debra Pickering and Robert Marzano
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Create a Tree Map of Key Terms

• You may wish to arrange them by quarters of
  instruction, your pacing guide, order of
  instruction and task analysis.
• Use the Marzano word lists of academic vocabulary
  or the vocabulary lists from me to assist you as
  you prepare your vocabulary trees.

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Possibilities for what students may need to know
about a content area term or concept

• Association in another definition
  
• content area.
  
• Synonym
  attributes
• Characteristics
  properties
• Antonym
  functions
• Origin
• (word parts)
  examples
• Students
  
• Representation
  Real-life
• 
  applications

Teachers representation
Topic
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Use a Circle Map for Vocabulary Development

• What do I need
• to know about
• this word?

definition
associated words
context sentence
Unfamiliar vocabulary word
original sentence
illustration
synonym
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Definition
Visual Representation
A triangle with one right angle
Right Triangle
Triangle with a 90 degree angle
Personal Association or Characteristic
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What is it? (Category)
What is it like? (Properties)
closed
Plane figure
Mathematical shape
Straight sides
polygon
Geometric shape
Two- dimensional
pentagon
hexagon
rhombus
Illustrations (What are some examples?)
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NOW IT IS YOUR TURN

• Look over your vocabulary list.
• Create a Circle Map similar to one of the
  previous maps with one of your vocabulary words.

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Choose one word from your list.
Choose the 3 or 4 best ways to define your word
and write each in one area of the frame.
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What are some examples?
Essential Characteristics
What is it? (Category)
Non-essential Characteristics
What is it like? (Properties)
Definitions
Paraphrase or Define in your own words
Word parts
Personal Association or Characteristics
Visual Representations
Related words
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Polygon
poly (many)
polygon
gon (sides)
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Your turn

• From your academic vocabulary tree map or lists,
  choose 2 terms to analyze the word parts.
• Be prepared to share.

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Step 4 Engage students periodically in
activities that help them add to their knowledge
of the terms in their notebooks.
Comparing Terms Classifying Terms Solving
Analogy Problems
Marzano, 2004
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Comparing Enhances Meaning
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A pyramid and a prism are similar because they
both ________________. ________________.
A pyramid and a prism are different because
a pyramid___, but a prism____. a
pyramid___, but a prism____.
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NOW IT IS YOUR TURN

• Look over your vocabulary list.
• Do you have two words on your vocabulary list
  that are students could compare and contrast in
  order to better understand each word?
• Choose two words and create a Double Bubble Map.

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Step 4 Engage students periodically in
activities that help them add to their knowledge
of the terms in their notebooks.
Comparing Terms Classifying Terms Solving
Analogy Problems
Marzano, 2004
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Step 1 Select one or two academic vocabulary
words that have an identifiable
relationship. Create the beginning of a Bridge
Map and write the relating factor.
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Step 2 Identify two words that students would
know that have a similar relationship and
complete the Bridge Map. Challenge students to
continue to add related pairs of words.
This second relationship will anchor the first
pair of words.
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NOW IT IS YOUR TURN

• Look over your vocabulary list.
• Do you have one or two words on your list that
  students could use to create a Bridge Map?
• Create a Bridge Map with an anchor pair and one
  or two words from your vocabulary list.

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Vocabulary Demonstration!

• or . . .
• A Game

Stand with a partner. One should be facing the
screen, the other has his or her back to the
screen. The one facing the screen will give
clues about the words in the list without saying
the word or any part of it. The one facing away
from the screen will try to guess the correct
term. The category will be guessed LAST.
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Things associated with EDUCATION
Lets Practice
Schools Professional Development Administration St
ate Standards Assessment Students Success
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Switch Roles with your Partner

• Play the second round

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Things associated with Geometry
Lets Practice
Point Vertex Triangle Pythagorean
Theorem Plane Quadrilateral Congruence
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What is the point?

• Partner A
• What strategies did you use to get your partner
  to identify the words?
• Did your strategies change during the game?
• Partner B
• What strategies did you use to identify the words?

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Your turn!

• Develop at least 2 sets of content related
  vocabulary for what you are currently teaching.
  (Round 1 and Round 2)
• Have your students use this vocabulary building
  strategy in class tomorrow.

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Section 5 Literacy Linksto Vocabulary
Development

• Marzanos Process (handout p.6 word lists)
• 1 Grades K-2 2Grades 3-5
  3Grades 6-8 4Grades 9-12
• Circle Map Multiple associations
• Brace Word parts
• Double-Bubble comparing terms
• Bridge determining analogies
• Vocabulary Game

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Additional Engagement Strategies
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Play Fractions Card Games

• Divide participants into 2 groups
• Distribute cards and instructions. Play
• The instructions are stated in sequential order
  (flow map).
• Math stations can be set up throughout the class
  for multiple, simultaneous reinforcement
  activities.

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Computer Lab Time!
Bring your green notes sheets with you, please.
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Section 6 Connect Thinking Maps to NCSDPI
Math Strategies

• Week by Week essentials
• Key indicators
• Manipulative strategies that correlate to goals
  and objectives
• http//community.learnnc.org/dpi/math/archives/200
  5/06/grades_68_resou.php

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NC Middle School Math Resourceson-line and hard
copy for Holly Springs Middle School.
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Your Turn!

• Examine and select
• at least 1 strategy from DPIs Middle School
  Resources to support student learning of the
  concept you have been planning today.
• Examine the blackline masters and other materials
  needed.
• Embed this strategy within your lesson plan

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Section 7Free!!! Engaging Math Materials

• Short videos
• Lesson procedures, materials, goals connections
• Blackline masters
• www.thefutureschannel.com

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"Cheat Sheets" for Test Prep
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Section 8Cheat Sheets for Test Prep

• This bridge map can be used for test review
• or
• as an ongoing resource for students.
• RF When you encounter a problem
  involving_________,
• 
  
  (top of bridge)
• think about or use ____________.
• (bottom of
  bridge)
• (see
  handouts)

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Additional Thinking Maps Curricular Samples in
Mathematics "Fun Math"
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Contact Information

• Feel free to contact me with your questions or
  concerns
• Janie MacIntyre
• 812 Nichole Lane
• Rocky Mount, N.C. 27803
• 252-937-8418 home 252-903-7274
  cell
• jmacin0722_at_aol.com