S. O . S.
Student Owned Strategies for Reading
as Thinking in the Content Areas
Math Booster Pack
S.O.S.
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Owned
Reading Improvement Series
offered through an ODE/OAESD Collaborative
What is a Booster Pack,
and How Do I Use It?
This Booster Pack is a collection of “next step” resources you may find useful when providing
ongoing staff development in the S.O.S. reading series. As a facilitator, select items that you
feel would be most appropriate for the audience and length of time provided for each session.
Think about the teachers you will work with this year:
•
Perhaps they need a “refresher” on some of the key reading strategies you shared from
the first 5 modules – with content-specific examples.
•
Are they interested in learning a few new strategies to use with their students to boost
reading comprehension?
•
Teachers who have worked with the S.O.S. strategies in their classrooms for a year
should be ready to discuss lesson design and how to incorporate key strategies into their
instruction.
Resources to help you meet these objectives are included in this packet in four sections:
1.
Discussion starters: “What is math literacy?”
2.
A refresher of several S.O.S. reading strategies with content specific examples
3.
A sampling of new reading strategies and graphic organizers
4.
Ideas for lesson planning and sample lessons provided
Remember, the most effective staff development occurs when the strategies are
modeled, practiced and applied. So… have fun with the ideas in this Booster
Pack as you help teachers support successful reading in the content areas!
Math Booster Pack
Table of Contents
Page
Discussion Starters and Background Information............................................................. 1
Reading Strategy Refresher and Examples ....................................................................... 5
Pre Reading ...................................................................................................................... 6
- Anticipation Guide
- Think Aloud
- KWL
Vocabulary ...................................................................................................................... 12
- KAU
- Concept Definition Map
- Frayer Model
- Word Splash
- Multiple Meaning Words/Symbols & Prefix / Suffix
Reading for Information .................................................................................................. 24
- Graphic Organizers
Additional Reading Strategies and Graphic Organizers ................................................. 29
- Words Sorts
- KNWS
- Five-Step Problem Solving
- Verbal and Visual Word Association
- Three-Level Guides
- Semantic Mapping
- Notetaking Graphic Organizer
Putting it All Together – Creating a Lesson Using Reading Strategies ............................. 45
References........................................................................................................................... 53
Concept Definition Map
What is it? (category)
What is it like?
Comparisons
Math Literacy
Illustrations
What are some examples?
Things to Think About
1. What is math literacy?
2. What components of math instruction help students become science literate?
3. What are the potential obstacles to math literacy in 6-12 education, and what
can be done to address them?
Reading Mathematics is Challenging!
• Students must read from left to right, but also from right to left (integer
number line), from top to bottom or vice versa (tables), and even
diagonally (some graphs).
• Mathematics texts contain more concepts per word, per sentence, and
per paragraph than any other kind of text. The abstract concepts are often
difficult for readers to visualize.
• Students must be proficient at decoding not only words but also numeric
and nonnumeric symbols. The math reader must shift from words like
“plus” or “minus” to instantly recognizing their symbolic counterparts,
+ and – .
Adapted from: Barton, Mary Lee and Clare Heidema.Teaching Reading in Mathematics
A Supplement to Teaching Reading in the Content Areas, 2002
Mathematics Literacy
"The development of a student’s power to use mathematics involves
learning the signs, symbols, and terms of mathematics. This is best
accomplished in problem-solving situations in which students have an
opportunity to read, write and discuss ideas in which the use of the
language of mathematics becomes natural. As students communicate their
ideas, they learn to clarify, refine, and consolidate their thinking"
(National Council of Teachers of Mathematics)
"Reading mathematics means the ability to make sense of everything that
is on a page — whether the page is a worksheet, a spreadsheet, an
overhead transparency, a computer screen, or a page in a mathematics
textbook or journal — in other words, any resource that students might use
to learn and apply mathematics." (Teaching Reading in the Content Areas)
In addition to general reading skills needed to comprehend narrative
text, readers of math text must also be able to apply the following
knowledge and skills:
⇒ Understand specialized vocabulary and phrases unique to math
⇒ Understand vocabulary terms and phrases that have different meanings when
used in math
⇒ Interpret words, numeric and nonnumeric symbols
⇒ Recognize and understand organizational patterns common to math texts
⇒ Make sense of text using text structure and page lay-out that may not be user
friendly
⇒ Infer implied sequences and recognize cause-and-effect relationships
⇒ Use inductive and deductive reasoning skills
Comprehension Strategies
Organize
Knowledge
Activate Prior
Knowledge and
Set A Purpose
for Reading
Make
Inference
Respond
To the Ideas in the Text
Think While You Read
To Keep Track of Whether Things Make
SENSE!
Figure Out
What is
Important
Visualize
Use Fix-Up Strategies
When Things Don't Make Sense
?
Find out the
Meanings of
Unknown Words
Ask Questions
EFFECTIVE READING BEHAVIORS
INEFFECTIVE READING BEHAVIORS
Before Reading
 Preview text
 Build background information
 Think about key words or phrases
Before Reading
 Start reading without thinking about the topic
 Do not preview text for key vocabulary
 Do not know purpose for reading
 Mind often wanders
During Reading
During Reading
 Read different texts and for different tasks all the
same
 Do not monitor comprehension
 Seldom use any strategies for understanding
difficult parts
 Adjust reading for different purposes
 Monitor understanding of text and use
strategies to understand difficult parts.
 Integrate new information with existing
knowledge
After Reading
After Reading
 Decide if goal for reading has been met
 Do not know content or purpose of reading
 Evaluate comprehension
 Read passage only once and feels finished
from Irvin,
J.L.ideas
Reading
the Social Studies
Classroom
, Holt Rinehart
Winston,
2001
 Summarize
major
in Strategies
a graphicinorganizer
 Express
readiness
for aand
test
without
studying
or by retelling major points
 Apply information to a new situation
Adapted from: Irvin,J.L. Reading Strategies in the Social Studies Classroom, Holt, Rinehart and Winston, 2001
S.O.S. Reading Strategies
“Refresher”
with
Content Specific Examples
Anticipation Guide
(Pre-Reading Module p. 4)
Anticipation Guides can be used to activate and assess students' prior knowledge, to
focus reading, and to motivate reluctant readers by stimulating their interest in the topic.
Because the guide revolves around the text's most important concepts, students are
prepared to focus on and pay attention to read closely in order to search for evidence that
supports answers and predictions. Consequently, these guides promote active reading
and critical thinking. Anticipation Guides are especially useful in identifying any
misperceptions students have so that the teacher can correct these prior to reading.
How to use:
1. Identify the major concepts that you want students to learn from reading. Determine ways
these concepts might support or challenge the students' beliefs.
2. Create four to six statements that support or challenge the students' beliefs and
experiences about the topic under study. Do not write simple, literal statements that can be
easily answered.
3. Share the guide with students. Ask the students to react to each statement, formulate a
response to it, and be prepared to defend their opinions.
4. Discuss each statement with the class. Ask how many students agree or disagree with
each statement. Ask one student from each side of the issue to explain his/her response.
5. Have students read the selection with the purpose of finding evidence that supports or
disconfirms their responses on the guide.
6. After students finish reading the selection, have them confirm their original responses,
revise them, or decide what additional information is needed. Students may be
encouraged to rewrite any statement that is not true in a way that makes it true.
7. Lead a discussion on what students learned from their reading.
Anticipation Guide
Directions: In the column labeled Before, place a check next to any
statement with which you agree. After reading the text, compare
your opinions on those statements with information contained in the
text.
Before After
_____ _____
1. Multiples relate to multiplying and divisors relate
_____ _____
2. 0 is a multiple of any number.
_____ _____
3. 0 is a divisor of any number.
_____ _____
4. Multiples of 2 are called even numbers.
_____ _____
5. Multiples of 1 are called odd numbers.
Adapted from: Billmeyer, Rachel and Mary Lee Barton. Teaching Reading in the Content Areas: If Not Me, Then Who?
Aurora: McREL (Mid-continent Regional Education Laboratory), 1998
Examples
Anticipation Guide
Statistics
Directions: In the column labeled Before, place a check next to any statement
with which you tend to agree. After reading the text, compare your opinions about
those statements with information contained in the text.
Before
After
_______
_______
1. There are several kinds of averages for a set of data.
_______
_______
2. The mode is the middle number in a set of data.
_______
_______
3. Range tells how far apart numbers are in a set of data.
_______
_______
4. Outliers are always ignored.
_______
_______
5. Averages are always given as percents.
Anticipation Guide
Integers
Directions: In the column labeled Before, place a check next to any statement
with which you tend to agree. After reading the text, compare your opinions about
those statements with information contained in the text.
Before
After
_______
_______
1. The sum of two integers is always greater than both
of the numbers being added.
_______
_______
2. It is possible to add two integers and get a sum less
than zero.
_______
_______
3. The sum of zero and any other integer is always the
other integer.
_______
_______
4. The product of two integers is always greater than
both of the numbers being multiplied.
_______
_______
5. The product of two positive integers is always positive.
_______
_______
6. The product of two negative integers is always
negative.
Adapted from: Barton, Mary Lee and Clare Heidema. Teaching Reading in Mathematics:
A Supplement to Teaching Reading in the Content Areas, 2002
Think Aloud
(Intro Module p. 6)
∧
Consider using one or more of these questions as you model your own use of reading
strategies with students.
1.
Before you begin a reading assignment for math, do you leaf through the passage and
read the headings to see what the passage is about?
2.
Why might it be helpful to think about what you already know about a topic before reading
about it?
3.
When you have to read something for math, do you make sure you understand the
purpose for reading it? What difference would this make?
4.
If you thought a topic in your math text was going to be difficult to understand, what could
you do before you started reading to help you understand?
5.
How is reading in math class different from reading in English class?
6.
Should you stop and think about why you are reading? Why? When should you do this?
7.
How do you know if you've really understood a reading assignment for math class?
8.
What can you do if you are reading and don't understand what a sentence is about? How
would you decide what to do?
9.
What do you do when you come to a big word in your math text that you don't know?
10.
Are there times when it becomes difficult to understand what you're reading? What makes
you realize it is becoming more difficult? What strategies do you use to read difficult text?
Adapted from: M.T. Craig and L.D. Yore, "Middle School Students' Awareness of Strategies
for Resolving Comprehension Difficulties in Science Reading,", 1996
K-W-L
(Pre-Reading Module p. 13)
The basic K-W-L uses three columns in which to write down information that we Know
(background knowledge), Want to know (establishing purpose and asking questions), and
have Learned (main idea). In addition to teaching students to connect to background
knowledge, this activity also can develop habits of summarizing, questioning, predicting,
inferring, and figuring out word meanings.
K
W
L
What I know
What I want to
find out
What I learned
Example: Fiboriacci’s Sequence
K
W
L
What I know
What I want to
find out
What I learned
Fibonacci’s Sequence
1, 1, 2, 3, 5, 8, 13, 21 …
Fibonacci’s Rabbits
Multiplying populations
How do bees fit in the
Fibonacci pattern?
What is the connection
between the Fibonacci’s
sequence and the Golden
ratio?
Is there a formula for the
Fibonacci number
sequence?
What do pineapples and
pinecones have to do with
Fibonacci?
Adapted from: Billmeyer, Rachel and Mary Lee Barton. Teaching Reading in the Content Areas: If Not Me, Then Who?
Aurora: McREL (Mid-continent Regional Education Laboratory), 1998.
K-W-L Worksheet: Prime Numbers
K
W
L
What I know
What I want to
find out
What I learned
• A prime number has
exactly two divisors
(factors), 1 and itself.
• 2 is the only even
prime number.
• Successive odd
numbers that are both
primes are twin
primes:
- 3 and 5
- 5 and 7
- 11 and 13
• Why are prime
numbers so important?
• What is the sieve of
Eratosthenes, and how
do you use it to get
primes?
• Is there a connection
between prime
numbers and perfect
numbers?
• What is an emirp?
• What are some
patterns related to
prime numbers?
K-W-L Worksheet: Tessellations
K
W
L
What I know
What I want to
find out
What I learned
• What a tessellation is
• Squares, equilateral
triangles, regular
hexagons can be used
for a tessellation.
• You cannot use a
regular pentagon for a
tessellation.
• What combination of
shapes can be used in
a tessellation?
• What is meant by a
code for a
tessellation?
• What are some
irregular shapes that
tessellate?
Adapted from: Billmeyer, Rachel and Mary Lee Barton. Teaching Reading in the Content Areas: If Not Me, Then Who?
Aurora: McREL (Mid-continent Regional Education Laboratory), 1998.
K-W-L Worksheet: Estimation
K
W
L
What I know
What I want to
find out
What I learned
I know how to estimate
answers to math
problems in a rough way.
• What is front-end
estimation?
• What is the mental
math strategy of
trading off?
• Front-end estimation
is a way of
approximating an
answer to a math
problem.
• Trading off is an
addition strategy that
involves rounding the
numbers in a problem
to the nearest 10 to
made addition easier.
K-W-L Worksheet: Order of Operations
K
W
L
What I know
What I want to
find out
What I learned
I know how to add,
subtract, multiply, and
divide.
I know that these are all
performed from left to
right.
• What is an
expression?
• What is a numerical
expression?
• An expression is a
collection of numbers,
variables, and
symbols.
• What is a variable
expression?
• A numerical
expression has all
numbers and symbols.
• What are the rules for
ordering operations?
• A variable expression
includes variables.
• Multiply and divide
from left to right. Add
and subtract from left
to right.
Adapted from: Content Area Guide: Math, Readers Handbook: A Student Guide for Reading and Learning
Great Source, 2002.
Eight Principles of Vocabulary Instruction
1.
Be enthusiastic about content area language and the power it can offer to
students who understand how to use these words effectively.
2.
Remember that learning involves making connections between what we
already know and new information. Relate new vocabulary words to
experiences and concepts that students already know.
3.
Limit the number of words taught in each unit; concentrate on key
concepts.
4.
Teach concepts in semantically related clusters, so that students can
clearly see associations among related concepts.
5.
Model how to use graphic organizers.
6.
Allow students enough practice in working with strategies and graphic
organizers so that their use becomes habit.
7.
Use dictionaries and glossaries appropriately.
8. Repeatedly model how to determine a word's meaning in text materials.
Observing the process you use will help students know what to do when they
encounter unfamiliar words outside of the classroom.
Adapted from: Billmeyer, Rachel and Mary Lee Barton. Teaching Reading in the Content Areas: If Not Me, Then Who?
Aurora: McREL (Mid-continent Regional Educational Laboratory), 1998
K-A-U Vocabulary Strategy
K = Known ------- A = Acquainted -------U = Unknown
(Intro Module p. 1)
Before students read, the teacher presents a list of key words related to the topic of study. The
students analyze what they know about each word individually and the degree to which words
are known or unknown. It is easy to do this with the symbols of a +, , or — . This activity
leads naturally to the preteaching of key vocabulary to be used later in the reading.
Examples:
K
A
U
+

—
K
A
U
+

—
exponent
polygon
rectangle
pentagon
trapezoid
prism
polyhedron
cone
intersection
domain
intercept
slope
parabola
origin
Adapted from: Vacca, R.T. and Vacca, J.L.. Content Area Reading, 1996
base
power
variable
terms
equivalent
K
A
U
K
A
U
+

—
+

—
mean
median
mode
weighted average
line of best fit
correlation
range
Adapted from: Billmeyer, Rachel and Mary Lee Barton. Teaching Reading in the Content Areas: If Not Me, Then Who?
Aurora: McREL (Mid-continent Regional Educational Laboratory), 1998
Concept Definition Mapping
(Vocabulary Module p. 21)
What is it?
Concept Definition Mapping is a strategy for helping students learn the meaning of key
concepts, essential attributes, qualities, or characteristics of a word. Students must describe
what the concept is, as well as what it isn’t, and cite examples of it. Looking up the concept’s
definition in the dictionary is not nearly as effective as this process, which gives students a
more thorough understanding of what the concept means, includes, and implies. The mapping
process also aids recall.
How to use it:
1. Share an example of a Concept Definition Map with students with a key vocabulary word
or concept you are studying.
2. Discuss the questions that a definition should answer:
• What is it? What broader category or classification of things does it fit into?
• What is it like? What are its essential characteristics? What qualities does it possess
that make it different from other things in the same category?
• What are some examples of it?
3. Model how to use the map by selecting a familiar vocabulary term from a previous unit
and have students volunteer information for the map. For instance, a science teacher
might choose the concept migration. “What is it like?” responses might include
“seasonal,” “movement from one area to another,” “animals looking for food and
favorable climate to raise their young.” Examples could include Canadian geese,
whales, monarch butterflies, and elk.
4. Have students work in pairs to complete a map for a concept in their current unit of
study. They may choose to use a dictionary or glossary, but encourage them to use their
own experience and background knowledge as well.
5. After students complete their maps, instruct them to write a complete definition of the
concept, using the information from their maps.
What is it? (category)
What is it like?
Comparisons
Illustrations
What are some examples?
Adapted from: Billmeyer, Rachel and Mary Lee Barton. Teaching Reading in the Content Areas: If Not Me, Then Who?
Aurora: McREL (Mid-continent Regional Educational Laboratory), 1998
What is it? (category)
Properties
Classification of
numbers
multiple of 2 skip
count starting at 0
Even
2 is only even
number that
is a prime
Comparisons
Odd
ones digit is
0, 2, 4, 6, or 8
Prime
12
58
474
includes 0
but not 1
Examples
Properties
What is it? (category)
percents can be written in
fraction or decimal form
Number concept fraction
with denominator 100
(per hundred)
Comparisons
additive when base is
same: 70% of 130 = 50% of
130 + 20% of 130
Percent
Ratio
n% of A is the same
as A% of n
Fraction
interest rate
test scores
discounts
benchmark percents
10% 25% 50%
Examples
What is it? (category)
Properties
Geometric property
Shape classification
two sides of
equal length
(congruent)
Isosceles
pair of equal
angles
(congruent)
Comparisons
Equilateral
(regular)
has a line of
symmetry
Scalene
Triangles
Trapezoids
Illustrations
What are some examples?
Adapted from: Billmeyer, Rachel and Mary Lee Barton. Teaching Reading in the Content Areas: If Not Me, Then Who?
Aurora: McREL (Mid-continent Regional Educational Laboratory), 1998
What is it? (category)
Properties
What is it like?
Quadrilateral
4 sides
Rectangle
Square
2 side parallel
Trapezoid
2 scale divergent
or convergent
Comparisons
Some table tops
Chimney on house
with sloped roof
Funnel top
Illustrations
What are some examples?
Adapted from: Vacca, R.T. and Vacca, J.L.. Content Area Reading, 1996
What is it? (category)
Quadrilateral
Properties
What is it like?
All four sides are
congruent
rectangle
Square
Diagonals: congruent,
bisect each other,
& perpendicular
Comparisons
computer
disk
4 angles are congruent
and right (90 degrees)
different colors
on chess board
Illustrations
What are some examples?
Adapted from: Carol Santa. Project CRISS: Creating Independence Through Student-Owned Strategies
Frayer Model
(Vocabulary Module p. 24)
What is it?
The Frayer Model is a word categorization activity. Frayer believes learners develop their
understanding of concepts by studying them in a relational manner. Using the Frayer model,
students analyze a word’s essential and nonessential attributes and also refine their
understanding by choosing examples and non-examples of the concept. In order to understand
completely what a concept is, one must also know what it isn’t.
How to use it:
1. Assign the concept or word being studied.
2. Explain all of the attributes of the Frayer Model to be completed.
3. Using an easy word, complete the model with the class. (examples follow)
4. Have students work in pairs and complete their model diagram using the assigned
concept or word.
Example:
Essential Characteristics
Set of ordered pairs with no two
pairs having the same first
element
Nonessential Characteristics
May be one-to-one
May be linear
(has a straight line graph)
Has a domain and range
Inverse may be a function
Examples
Function
Nonexamples
f(x)= 2x + 1
y<x
y=_x_
perimeter of a rectangle with
given area
Area of a circle with given radius
Adapted from: Billmeyer, Rachel and Mary Lee Barton. Teaching Reading in the Content Areas: If Not Me, Then Who?
Aurora: McREL (Mid-continent Regional Educational Laboratory), 1998
Frayer Model
Definition (in own words)
Facts/Characteristics
WORD
Examples
Nonexamples
Example:
Definition (in own words)
A simple, closed, plane figure
made up of three or more line
segments
Facts/Characteristics
• Closed
• Simple (curve does not
intersect itself)
• Plane figure (2 dimensional)
• Made up of three or more line
segments
• No dangling parts
Polygon
Examples
Nonexamples
• Rectangle
• Circle
• Triangle
• Cone
• Pentagon
• Arrow (ray)
• Hexagon
• Cube
• Trapezoid
• Letter A
Adapted from: D.A. Frayer, W.C. Frederick, and H.G. Klausmeier, “A Schema for Testing the Level of Concept Mastery”,
University of Wisconsin
Frayer Model
Definition (in own words)
Facts/Characteristics
A whole number with exactly
two divisors (factors)
• 2 is the only even prime
number.
• 0 and 1 are not prime.
• Every whole number can be
written as a product of primes.
Prime
Examples
Nonexamples
1, 4, 6, 8, 9, 10, . . .
2, 3, 5, 11, 13, . . .
Definition (in own words)
Facts/Characteristics
A whole number that divides
exactly into a given whole
number
Every whole number has at
least two factors.
Every whole number can be
written as a product of prime
factors.
A polynomial by which a given
polynomial is divisible
Factor
Examples
Nonexamples
Factors of 12 are
1, 2, 3, 4, 6, and 12
• 5 is not a factor of 12.
• 0 is not a factor of any whole
(x + 1) and (x — 1) are
factors of x_ — 1
• (x + 1) is not a factor of
number.
x_ + 1
Adapted from: D.A. Frayer, W.C. Frederick, and H.G. Klausmeier, “A Schema for Testing the Level of Concept Mastery”,
University of Wisconsin
Word Splash
(As described in the ASCD video:
Prereading Strategies for the Content Areas)
(Pre-Reading Module p. 18)
Word Splash is designed to help students access prior knowledge of words, personally construct
meaning for the words related to the concept, and allows for a repetition of key ideas important to the
new unit of study.
This strategy is used at the beginning of a unit to activate prior knowledge and introduce students to
new words related to the topic.
Step One: Brainstorm, Predict and Write
• Introduce 6-7 words key to developing a conceptual understanding of the unit topic.
• Arrange the words on a board so that they can be rearranged later.
• Students write complete sentences using 3 of the words demonstrating their understanding of the
words.
• Large group share out of a few of the sentences.
Step Two: Explore Word Relationships
• Tell the class that one of the words is the “all-encompassing” word and the rest fit under it.
• Have students arrange the words in a graphic that makes sense to them or use word cards.
• A few students come up and rearrange the words on the board then explain their organization.
(Special education students and ELL students would benefit from having a sheet of words that they cut
out and manipulate on the desktop.)
Step Three: Read and Compare
• Students individually read the passage, paying attention to the words on the board.
• Their purpose is to see what new understandings of words develop through reading.
Step Four: Comparative Results
• Students revise three sentences to better portray the words as developed in the passage.
• In small groups, share sentences. Sentences continue to be revised based on group feedback.
• Each student stars strongest sentence then adds to the chart paper for their group.
Step Five: Share Revised Sentences with Class
• As a group, the students share the sentences they developed to represent the new concept.
(The group discussion and sharing help both ELL and Special Education students learn the words in
the context of the new unit.)
WORD SPLASH
Words from the text:
• sum
• product
• quotient
• order of operations
• commutative property
• zero
• integers
• data analysis
* Choose 3 of the words above.
On line A below, write a
complete sentence for each word - showing that you know
its meaning. After you read the text, write a sentence on
line B showing your new understanding of the word.
1. A)
B)
2. A)
B)
3. A)
B)
Key Strategies to Determine Word Meaning
(Vocabulary Module p. 7)
Multiple Meaning Words / Symbols
—
∪
add
addition
plus
positive
increased
make larger
more than
sum
older
higher
faster
subtract
take away
minus
negative
decrease
make smaller
less than
diminished
difference
younger
deeper
slower
lower
÷
x
multiply
times
product
double (x2)
triple (x3)
quadruple (x4)
divide
division
into
divided by
one half (_)
one third (_)
one forth (_)
Examples of Mathematic Prefixes, Suffixes, Roots
Morpheme
Math Usage
bi (two)
bisect, binomial, bimodal
cent (hundred)
centimeter, percent
circu (around)
circle, circumference
co, con (with)
coefficient, cosine, collinear, congruent
dec (ten)
decimal, decagon
dia (through)
diagonal, diameter
equi (equal)
equilateral, equiangular
hex (six)
hexagon
inter (between)
intersect, interpolate
kilo (thousand)
kilometer, kilogram
milli (thousand)
millimeter, milligram
octo (eight)
octogan
para (beside)
parallelogram
Using Graphic Organizers
Implementation Guide
(Reading for Info Module p. 15)
Overview
Graphic organizers are made up of lines, arrows, boxes, and circles that show the
relationships among ideas. These graphic organizers have the potential of helping students
organize their thinking and their knowledge. While textbooks contain many types of text, the
largest portion is or informational. Informational text has five major structures: (1) cause and
effect, (2) compare and contrast, (3) description, (4) problem and solution, and (5) sequence
or chronological order.
Strategy in Action
Students should complete the following steps to practice the strategy:
Step 1: Preview the Text. What did you notice while previewing this section (such as any
signal words, text structure, or graphic signals)?
Step 2: Read the Text. Now have the students read the passage.
Step 3: Determine Which Graphic Organizer Would Best Display the Information. Have
students decide which of the graphic organizers might organize the ideas in the text best,
depending on their purpose for reading. Be sure to remind students that the organizers can
be modified to suit their purposes. They can complete this part either individually or in small
groups.
Step 4: Create a Graphic Organizer. Working in small groups, have students create a
graphic organizer that displays the ideas in the text.
Step 5: Present the Graphic Organizer. Small groups then present their graphic organizers
to the class using an overhead transparency or chart. Remember there is no one best
answer. Students may display their work differently depending on their purpose for reading
and what they chose to emphasize.
Discussion
Once students have finished the activity, you may want to have a brief discussion with them
about the assignment. Encourage students to probe why they chose the graphic organizer
they did and how graphic organizers can help them organize ideas.
Adapted from: Modified from Judith Irvin, Reading and The Middle School Student.
Needham Heights: Allyn & Bacon, 1998
Sample Graphic Organizers
Concept Definition Webs
Hexagons
Acute
Pentagons
Obtuse
Right
Triangles
Polygons
Scalene
Isosceles
Equilateral
Quadrilaterals
Trapezoid
Parallelogram
Rectangle
Rhombus
Square
Statistical
Measures
Measures of
Location
Mean
Mode
Measures of
Dispersion
Median
Range
Adapted from: Barton, Mary Lee and Clare Heidema.Teaching Reading in Mathematics
A Supplement to Teaching Reading in the Content Areas, 2002
Quartiles
Sample Graphic Organizers
Generalization/Principle Diagrams
Generalization or Principle
Every composite number can be written as
a product of prime numbers.
Example
20 = 2 x 2 x 5
Example
39 = 3 x 13
Example
126 = 2 x 3 x 3 x 7
Example
154 = 2 x 7 x 11
Generalization or Principle
Every square number can be written as
the sum of two triangular numbers.
Example
16 = 6 + 10
Example
36 = 15 + 21
Example
100 = 45 + 55
Example
144 = 66 + 78
Adapted from: Barton, Mary Lee and Clare Heidema.Teaching Reading in Mathematics
A Supplement to Teaching Reading in the Content Areas, 2002
Sample Graphic Organizers
Compare/Contrast Venn Organizers
Triangular
Numbers
Square
Numbers
21
1
28
36
10
1225
4
9
3
25
6
Different
(Triangular but not square)
16
Alike
(Both triangular and square)
Different
(Square but not square)
Pyramids
Prisms
3-dimensional
solid
X
X
One base
X
Pair of parallel
bases
X
All triangular faces
except base
X
Polyhedron
X
cube
X
X
Adapted from: Barton, Mary Lee and Clare Heidema.Teaching Reading in Mathematics
A Supplement to Teaching Reading in the Content Areas, 2002
5. Doesn’t use radius or diameter
4. Uses length, width, and side
measurements
3. Use with all shapes but circles
2. Different formulas:
Quadrilateral—P = s_+ s_+ s_+ s_
Parallelogram—P =21 + 2w
Rectangle—P = 21 + 2w
Rhombus—P = 4s
Square—P = 4s
1. Doesn’t use pi (π)
Differences
5. Both are
measurements
4. Both have to
have labels
3. Both use
decimals or
fractions
2. Both have
formulas
1. Distance around
a shape
Similarities
Similarities
4. Uses pi (π), 3.14 or 22/7
3. Uses radius and diameter
2. Different formula: C = πd or C = 2πr
1. It’s only used for circles
Differences
Compare/Contrast Organizer
Adapted from: Reading Strategies for the Content Areas: During-Reading Strategies, ASCD, 2003
Additional
Reading Strategies
and
Graphic Organizers
Word Sorts
What is it?
Word sorts help students recognize the semantic relationships among key concepts. Students
are asked to sort vocabulary terms into different categories. The strategy can be used in two
different ways. In a “closed sort,” the teacher provides the categories into which students are to
assign the words. In an “open sort,” students group words into categories and identify their
own labels for each category. Word sorts help students develop a deeper understanding of key
concepts, and also are an excellent method of teaching the complex reasoning skills of
classification and deduction.
How to use it:
1. Students copy vocabulary terms onto 3” x 5” cards, one word per card - or the teacher
has words printed on a handout that students can tear into cards.
2. Individually or in groups, students then sort the words into categories. With younger
students or complex concepts, the teacher should provide students with the categories
and have students complete a “closed sort.”
3. As students become more proficient at classifying, teachers should ask them to
complete “open sorts”; that is, students sort words into labeled categories of their own
making. At this stage, students should be encouraged to find more than one way to
classify the vocabulary terms. Classifying and then reclassifying helps students extend
and refine their understanding of the concepts studied.
Word Sort
Words beginning
with a “P”
Dimensional
Figures
polyhedron
polygon
polygon
rectangle
perimeter
parallelogram
pentagon
trapezoid
Adapted from: Billmeyer, Rachel and Mary Lee Barton. Teaching Reading in the Content Areas: If Not Me, Then Who?
Aurora: McREL (Mid-continent Regional Educational Laboratory), 1998
Word Sorts
Geometry Word Sort
length
cubic
acute
similar
perimeter
linear
prime
reflection
volume
quadratic
scalene
rotation
radius
variable
equilateral
translation
right
width
Geometry Word Sort
Shapes
Measures
Relations
sphere
length
parallel
square
cube
perimeter
perpendicular
edges
circle
prism
volume
adjacent
lines
hexagon
cone
circumference
opposite
points
parallelogram
cylinder
radius
symmetry
rays
rhombus
pyramid
area
intersecting
Parts of
Shapes
Plane figures
Solid figures
diagonals
triangle
verticles
angles
congruent
bisector
similar
Adapted from: Billmeyer, Rachel and Mary Lee Barton. Teaching Reading in the Content Areas: If Not Me, Then Who?
Aurora: McREL (Mid-continent Regional Educational Laboratory), 1998
Number Sorts
(a variation of Word Sorts)
Provide students with a set of number cards. Ask them to place them in the
correct spot on this graphic organizer.
Multiples of 5
Prime
50
53
105
5
3
0
41
35
1
4
72
36
Less than 50
51
Adapted from: Billmeyer, Rachel and Mary Lee Barton. Teaching Reading in the Content Areas: If Not Me, Then Who?
Aurora: McREL (Mid-continent Regional Educational Laboratory), 1998
K-N-W-S
(K-W-L for Word Problems)
What Is It?
In this pre-reading strategy students use a process similar to K-W-L to analyze and plan how
to approach solving a word problem. Students answer what facts they KNOW, what
information is NOT relevant, WHAT the problem asks them to find, and what STRATEGY they
can use to solve the problem.
How to Use It?
1. Introduce students to the four-column K-N-W-S worksheet, or have them draw the
graphic organizer on their own paper.
2. Present students with a word problem, and model how to fill in information in each of the
columns. Explain how you knew what information should be included in each column.
3. Ask students to work in groups to complete a K-N-W-S for other word problems.
Students should discuss with their groups how they knew what to put in the columns.
4. Give students ongoing independent practice using this strategy to solve word problems.
K
N
What facts do I
KNOW from the
information in the
problem?
Which information
do I NOT need?
W
S
WHAT does the
What STRATEGY/
problem ask me to operation/tools will
find?
I use to solve the
problem?
Adapted from: Billmeyer, Rachel and Mary Lee Barton. Teaching Reading in the Content Areas: If Not Me, Then Who?
Aurora: McREL (Mid-continent Regional Education Laboratory), 1998.
Example:
Problem:
The ends of a rope are tied to two trees, 500 feet apart. Every 10 feet an
8-foot post is set 2 feet into the ground to support the rope. How many
support posts are needed?
K-N-W-S Worksheet: (K-W-L for word problems)
K
N
What facts do I
KNOW from the
information in the
problem?
Which information
do I NOT need?
WHAT does the
What STRATEGY/
problem ask me to operation/tools will
find?
I use to solve the
problem?
The posts are 8
feet tall.
How many
support posts are
needed?
Trees are 500 feet
apart.
Posts are placed
The posts are set
at 10-foot intervals 2 feet into the
between the trees. ground.
W
S
Draw a model to
understand how to
place posts.
Solve the problem
with the trees
closer and find a
pattern.
There are 50
(500 ÷ 10) 10-foot
intervals between
the trees.
Adapted from: Billmeyer, Rachel and Mary Lee Barton. Teaching Reading in the Content Areas: If Not Me, Then Who?
Aurora: McREL (Mid-continent Regional Education Laboratory), 1998.
Five-Step Problem Solving
What is it?
Students’ comprehension of word problems can be enhanced by teaching them to read word
problems as meaningful passages — as short stories from which students can construct
meaning based on their prior knowledge and experience. Teachers use this strategy by
presenting students with a graphic organizer that leads them through a five-step problemsolving process.
How could it be used in mathematics instruction?
This strategy gives students a graphic organizer to use in the problem-solving process. It can
help students understand the steps and explain their reasoning throughout the process.
How to use it:
1. Introduce students to the layout and design of the graphic organizer. Point out that the
diamond shape of the graphic reinforces the fact that all students begin with the same
information about a problem and should arrive at the same conclusion, if they are
successful at solving the problem. Explain each of the steps outlined in the graphic.
2. Present students with a word problem, reading it aloud and asking students about their
prior knowledge of the situation and elements included in the “story.”
3. Model for students how to complete the first step of the organizer, restating the question
in a number of ways. Ask students to identify which version is the clearest and to explain
the reasoning behind their choice. Once students know how to approach the problem,
they will feel more confident about solving it.
4. Model how to complete the remaining steps in the graphic organizer.
5. When students understand the steps in the graphic organizer, offer them opportunities
for guided practice. Select another word problem, and lead them through each step of
the process. Ask students to discuss their thinking as they read the problem and to
articulate the reasons for the responses they give.
6. Let students work in small groups to discuss and complete several more problems using
the five-step graphic organizer.
See Next Page ∨
Adapted from: Billmeyer, Rachel and Mary Lee Barton. Teaching Reading in the Content Areas: If Not Me, Then Who?
Aurora: McREL (Mid-continent Regional Educational Laboratory), 1998
Graphic Organizer for Five-Step Problem Solving
1. Restate the
problem/question:
2. Find the needed data:
3. Plan what to do:
4. Find the answer:
STEP 1
STEP 2
STEP 3
Answer:
5. Check. Is your answer reasonable?
Adapted from: Billmeyer, Rachel and Mary Lee Barton. Teaching Reading in the Content Areas: If Not Me, Then Who?
Aurora: McREL (Mid-continent Regional Educational Laboratory), 1998
Verbal and Visual Word Association (VVWA)
What is it?
The VVWA strategy puts together a vocabulary word and its definition with both a visual and a
personal association or characteristic of the term. This strategy helps students learn
vocabulary on their own and helps them retain the new vocabulary through visual
characteristic associations. This strategy has been shown to be especially effective for lowachieving students and for second language learners in content-area classes.
How could it be used in mathematics instruction?
Much of the vocabulary of mathematics can be represented visually. This strategy may be
used by students as they are introduced to new vocabulary to make immediate visual
associations. As students discover the critical characteristics of a concept or make personal
associations, they put these together with the definitions and visuals to deepen their
understanding of the concept.
How to use it:
1. Select vocabulary terms that would be appropriate for using VVWA.
2. Direct students to draw a rectangle divided into four sections for each term.
3. Instruct students to write the vocabulary word in the upper-left box of the rectangle.
Instruct them to write the text definition of the term or give them a definition to write in
the lower-left box.
4. Direct students to draw a visual representation of the vocabulary word (perhaps found in
a graphic in the text) in the upper-right box of the rectangle. Then suggest that they
make their own personal association, an example of characteristic, to put in the fourth
box at the lower right.
Vocabulary
Term
Visual
Representation
Definition
Personal
Association
or
Characteristic
Adapted from: Billmeyer, Rachel and Mary Lee Barton. Teaching Reading in the Content Areas: If Not Me, Then Who?
Aurora: McREL (Mid-continent Regional Educational Laboratory), 1998
Verbal and Visual Word Association (VVWA)
Examples:
Right
Triangle
ramp or slide
A triangle with one
right angle (90_ )
(square corner)
Normal
Distribution
Distribution of
statistical measures
(data) that has a
symmetrical graph
Bell shaped
Think of Liberty Bell
Measures are close
to middle like
people’s heights
Adapted from: Billmeyer, Rachel and Mary Lee Barton. Teaching Reading in the Content Areas: If Not Me, Then Who?
Aurora: McREL (Mid-continent Regional Educational Laboratory), 1998
Three-Level Guides
What is it?
The Three-Level Guide helps students analyze and solve word problems. Using a teacherconstructed graphic organizer, students must evaluate facts, concepts, rules, mathematics,
ideas, and approaches to solving particular word problems.
How to use it:
1. Construct a guide for a given problem similar to the one shown on the next page. The
first level (Part I) should include a set of facts suggested by the data given in the
problem. The students’ goal will be to analyze each fact to determine if it is true and if it
will help them to solve the problem.
2. The second level (Part II) of your guide should contain mathematics ideas, rules, or
concepts that students can examine to discover which might apply to the problemsolving task.
3. The third level (Part III) should include a list of possible ways to get the answer.
Students will analyze these to see which ones might help them solve the problem.
4. Introduce students to the strategy by showing them the problem and the completed
three-level guide. Explain what kind of information is included at each level.
5. Model for students how you would use the guide in solving the problem.
6. Present students with another problem and guide. Have them analyze the information
you have included to determine its validity and usefulness in solving the problem.
7. With advanced students, ask them to select a word problem from the text and complete
a three-level guide to be shared with the class.
Adapted from: Billmeyer, Rachel and Mary Lee Barton. Teaching Reading in the Content Areas: If Not Me, Then Who?
Aurora: McREL (Mid-continent Regional Educational Laboratory), 1998
Example: Three-Level Guides
A Three-level guide to a math problem
Read the problem and then answer each set of questions, following the directions given
for the set questions.
Problem: Sam’s Sporting Goods has a markup rate of 40% on Pro tennis
rackets. Sam, the store owner, bought 12 Pro tennis rackets for $75 each.
Calculate the selling price of a Pro tennis racket at Sam’s Sporting Goods.
Part I
Directions: Read the statements. Check Column A if the statement is true according to the
problem. Check Column B if the information will help you solve the problem.
A (true?)
B (help?)
Sam’s markup rate is 40%.
Sam bought 12 Pro Tennis rackets.
Pro tennis rackets are a good buy.
Sam paid $75 for a Pro tennis racket.
The selling price of a Pro tennis racket is
more than 75%
Part II
Directions: Read the statements. Check the ones that contain math ideas useful for this
problem. Look at Part I, Column B to check your answer.
Markup equals cost times rate.
Selling price is greater than cost.
Selling price equals cost plus markup rate.
Markup divided by cost equals markup rate.
A percent of a number is less than the
number when the percent is less than
100%.
Part II
Directions: Check the calculations that will help or work in this problem. Look at Parts I
and II to check your answers.
0.4 x $75
12 x $75
$75 x 40
1.4 x $75
40% x $75
$75 + ( _ x $75)
Adapted from: Billmeyer, Rachel and Mary Lee Barton. Teaching Reading in the Content Areas: If Not Me, Then Who?
Aurora: McREL (Mid-continent Regional Educational Laboratory), 1998
Semantic Mapping
What is it?
A semantic map is a visual tool that helps readers activate and draw on prior knowledge,
recognize important components of different concepts, and see the relationships among
these components.
How Could It Be Used In Mathematics Instruction?
This strategy can be incorporated into the introduction of a topic to activate students’ prior
knowledge and then used throughout a unit or series of lessons on the topic. Students will be
able to visualize how terms are connected and/or related. This strategy can be used to build
connections between hands-on activities and reading activities.
How to use it:
1. Write the major topic of the lesson or unit on chart paper. Let students brainstorm a list of
terms that relate in some way to this major topic.
2. Write the major topic in the center of another sheet of chart paper and circle it.
3. Ask students to review the brainstormed list and begin to categorize the terms. The
categories and terms should be discussed and then displayed in the form of a map or
web.
4. Leave the chart up throughout the series of lessons or unit so that new chapters and
terms can be added as needed.
Category
Category
Term
Term
Term
Term
Term
Term
Major
Concept
Category
Category
Term
Term
Term
Term
Term
Term
Adapted from: Billmeyer, Rachel and Mary Lee Barton. Teaching Reading in the Content Areas: If Not Me, Then Who?
Aurora: McREL (Mid-continent Regional Educational Laboratory), 1998
Examples:
Formulas
Unknowns/Variables
A = lw
C = 2πr
P = 2(l + w)
numerical
degree
dependent
Equations
Number Relations
2x3=3x2
2 x (5 + 3) = 10 + 6
72 – 58 = 74 – 60
Systems
Degree
(Graphing)
linear
quadratic
cubic
simultaneous equations
consistent/inconsistent
dependent/independent
Operations
Parts
addition
subtraction
multiplication
division
square root
absolute value
ones place
tens place
tenths place
etc.
numerator
denominator
place value
Numbers
Uses
counting
comparing
ordering
Types
prices
scores
measures
labels
sizes
dates
positive
negative
fraction
decimal
percent
prime
composite
odd
even
Adapted from: Barton, Mary Lee and Clare Heidema, Teaching Reading in Mathematics:
A Supplement to Teaching Reading in the Content Areas, 2002
triangular
square
perfect
abundant
Example:
Units
Tools
ruler, tape measure
scale
cup
clock
thermometer
protractor
Metric Customary Nonstandard
meter
foot
pencil
cm
inch
paper clip
km
mile
glass
liter
quart
gram
ounce
kg
pound
Celsius
Fahrenheit
Measurement
Formulas
Types
Length
Cover
(1-dim)
(2-dim)
width
area
height
surface
perimeter
area
circumference
Volume
(3-dim)
volume
Other
capacity
weight
mass
time
temperature
angle measure
rectangle: A = Iw
P = 2(I + w)
circle:
A = πr_
C = 2πr
sphere:
V = 4/3πr_
cylinder: V =πr_h
Adapted from: Barton, Mary Lee and Clare Heidema, Teaching Reading in Mathematics:
A Supplement to Teaching Reading in the Content Areas, 2002
NOTES
(Reading for Info Module p. 11)
Information Worth Noting
Questions?
(I wonder….)
Summary of Key Ideas
Graphic Representation of
Key Ideas
↵
↵
↵
↵
↵
Created by: MaryBeth Munroe, Southern Oregon S.D.
Putting it All Together
~ Lesson Planning ~
The Strategic Teacher Shares Reading Strategies
Belief in
Ability to
Affect
Learning
A Strategic
Learner
Repertoire of
Effective
Teaching
Methods
Personal
Characteristics
Content
Knowledge
Knowledge and
Understanding of
Students
The
Strategic
Teacher
Strategic
Knowledge and
Expertise of Reading
Strategy
Explicit
Instruction
Practice and
Feedback
Modeling
How and
When to
Use a
Strategy
Benefits of a
Strategy
Thinking
Aloud
Adapted from: McEwan, E.K. Raising Reading Achievement in Middle and High School: 5 Simple-to-Follow
Strategies for Principals. 2001 by Corwin Press, Inc. International Reading Association
S.O.S. Reading Strategies
Session
Pre-Reading
During Reading
After Reading
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Introduction Session
K.A.U.
Think Aloud
Think-Pair-Share
Pre-Reading Session
Give One, Get One
Anticipation Guide
K.W.L.
D.R.T.A.
Word Splash
Predicting Nonfiction
THIEVES
P.A.C.A.
X
X
X
X
X
X
X
X
Vocabulary Session
Modified K.A.U.
Vocab Alert!
Context Clues
Prefix – Suffix
Concept Definition Map
Frayer Model
3+3
Reading for Info Session
Determine Text Features
Determine Text Structures
Graphic Organizers
Read, Cover, Remember, Retell
I.N.S.E.R.T.
S.C.A.N. & R.U.N.
P.R.I.M.E.
Questioning Session
Visualizing Information
Question Answer Relationship
Question Around
Thick and Thin Questions
Reciprocal Teaching
Re Quest
Cubing
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
The Lesson
Research Suggests a New Format
Traditional Format
New Format
Prereading activities
Discussion
Predictions
Questioning
Brainstorming
Setting purpose
Reading
assignment
given
Independent
reading
Guided ACTIVE
reading
• silent
• pairs
• group
Activities
to clarify,
reinforce,
extend
knowledge
Discussion to see if
students learned main
concepts, what they
"should have" learned
Adapted from: Billmeyer, Rachel and Mary Lee Barton, Teaching in the Content Areas: If Not Me, Then Who?
Aurora: McREL (Mid-continent Regional Education Laboratory), 1998.
Putting it all Together
Lesson Planning
1.
Determine your objectives for the lesson. What do you want students to know or to be
able to do at the end of the lesson?
2.
Select a strategy for accessing students’ prior knowledge of the general topic.
Examples: KWL, Anticipation Guide, etc.
3.
Preview the text material for vocabulary.
4.
a.
Identify critical vocabulary students will need to know prior to reading.
b.
Select vocabulary strategies appropriate for the text and lesson.
Examples: Frayer Model, Word Splash, Concept Definition Map, etc.
Preview the text material for organization.
a. Determine the organizational pattern(s) used in the text.
1. Note text features to point out to students prior to their reading.
2. Note signal words to which students should pay attention.
3. Select a graphic organizer that aligns with the pattern.
b. To provide students with strong guidance in organizing the text information, devise
prereading questions that
1. Align with or emphasize the organizational pattern
2. Will aid comprehension by focusing students’ attention to their purpose for
reading (Quiz? Performance task? Discussion?)
3. Will help students meet your original objectives for the lesson.
5.
Select “during reading” questions (process questions that focus on metacomprehension
strategies such as making predictions, confirming or revising those predictions, and
noting graphic aids that signal important ideas). If students are prompted to focus on their
reading process, their metacomprehension will improve.
6.
Select post-reading questions and activities that help students meet your objectives,
reflect on and apply what they have learned, and revise existing schema (e.g., writing-tolearn; performance activity; discussion).
Adapted from: Billmeyer, Rachel and Mary Lee Barton, Teaching in the Content Areas: If Not Me, Then Who?
Aurora: McREL (Mid-continent Regional Education Laboratory), 2000.
Teacher's Checklist
YES
NO
•
Have I identified my objectives for this lesson – what I want
students to know and be able to do?


•
Have I previewed the text and determined key
concepts/vocabulary students need to know?


•
Have I included activities and strategies that will help students
develop a clear understanding of these key concepts?


•
Have I selected activities to assess, activate, and build
students' background knowledge?


•
Have I identified the text's organizational pattern(s) and
whether it highlights information I consider most important?


•
If the organizational pattern does not highlight key
information, have I determined the frame of mind or pattern I
will tell students to use while reading?


•
Have I selected a suitable graphic organizer students can use
to organize key concepts?


•
Have I decided the purposes students should keep in mind
while reading (e.g., whether they will be using the information
in a discussion, performance activity, on a quiz)?


•
Have I developed "during reading" questions that will prompt
students to employ metacognitive skills?


•
Have I selected post-reading questions and activities that
require students to make meaningful connections, and to
deepen their understanding by applying what they have
learned?


Adapted from: Strategic Teaching, McREL (Mid-Continent Regional Education Laboratory)
Example Lesson #1
Using M.C. Escher to Teach Geometry Concepts
Pre-Reading
Reading Purpose: To give the student the opportunity to become familiar with the
artist/mathematician M.C. Escher and to gain an awareness of how he uses concepts in
geometry, such as tesselations, polygons and tilings, to create imaginative works of art which
include surprising puzzles and paradoxes.
KWL: To provide students with background information and to prepare them to participate in a
discussion about what they already know, they first view a film on the life of M.C. Escher
and look at examples of works of art that he created.
After seeing the video students discuss what they know about Escher and record this
information either visually, in a list, or by using sentences in the column K-Know.
Students continue to reflect on what they want to know and record their ideas and
questions in the W-Want to Know column.
Know
Want to know
What I Learned
During Reading: INSERT Notes
Students read the article independently, and use the INSERT strategy to take notes in the
margin, highlighting important or interesting information.
⇑ = I already knew this
+ = New information
! = Wow
?? = I don’t understand
After-Reading
Students reconvene and share what they have learned. They record new information on the
L-Learned section of the KWL organizer.
Video and Reading Selections
• The Fantastic World of M.C. Escher (video)
• Agnesi to Zeno: Over 100 Vignettes from the History of Math, by Sanderson Smith, (1996)
• M.C. Escher, Artist and Geometer, Key Curriculum Press, (1996)
Adapted from: Pam Mathews, Corvallis School District
Sample Lesson #2
Full Circle: A Geometry Lesson
Purpose: To teach students how to read mathematical text, interact with examples, learn new
vocabulary, concepts and techniques involved with attributes of circles.
Pre-Reading
1. Each student will record 5 terms that they associate with circles.
2. Each student will compare their list with a partner and add new ideas to their list.
3. The whole class will help generate a class list of terms.
During Reading
In small groups, students read the assigned article. Each group has a different article on
circles.
After Reading
1. Students who read the same article will meet to create a presentation for the class.
2. One student will be selected to present the material to the class and other students will
be available to field questions from the audience.
Reading Selections
• Circles: Definition of a circle, chords, tangent and secant lines
http://www.math.psu.edu/geom/koltsova/section7.html
• Circles and Angles
http://www.math.psu.edu/geom/koltsova/section8.html
• Circle Formulas
http:forum.swarthmore.edu/dr.math/faq/formulas/faq.circle.html
Adapted from: Pam Mathews, Corvallis School District
Special thanks to the following educators
for contributing samples of classroom reading strategies:
•
•
•
Reynolds High School teachers
Centennial High School teachers
Pam Mathews, Corvallis School District
References
Classroom Strategies for Interactive Learning (1995), by Doug Buehl
Guiding Reading and Writing in the Content Areas (1998), by M. Carrol Tama and
Anita Bell McClain
Invitations: Changing as Teachers and Learners K-12 (1994), by Regie Routman
Raising Reading Achievement in Middle and High School (2001), by Elaine McEwan
Real Reading, Real Writing: Content-Area Strategies (2002), by Donna Topping and
Roberta McManus
Teaching Reading in Mathematics: A Supplement to Teaching Reading in the Content Areas
(2002), by Mary Lee Barton and Clare Heidema
Teaching Reading in the Content Areas: If Not Me, Then Who? (1998), by Rachel Billmeyer
and Mary Lee Barton
Tools for Thought: Graphic Organizers for Your Classroom (2002), by Jim Burke
Yellow Brick Roads: Shared and Guided Paths to Independent Reading 4-12 (2000),
by Janet Allen
Math