Power Strategies
I’m ready for the
power…..
strategy, that is!
Informal assessments
continually check
for understanding
Let’s
make &
take our
own!
Identifying similarities
and differences might be the
“core” of all learning.
It enhances students’ understanding
of and ability to use knowledge.
-Marzano, 2001
3 highly effective “forms” to
identify similarities and differences
Comparing
 Classifying
 Creating
analogies
Graphic Organizers for Comparing
Characteristics
Items to be compared
#1
#2
#3
Similarities
Differences
Similarities
Differences
Similarities
Differences
Similarities
Differences
Comparison Matrix
-more useful to provide a greater number of details
Venn Diagrams
when comparing two items
What it looks like
Examples
Problem Situations
Attributes:
What am I comparing?
After completing the
Venn Diagram,
students will write a
summary statement.
Two things are
DIFFERENT from
the others in some
way. Circle them
and explain why
they are different.
ds:
ok
Triangle
uch
Cube
Rectangle
Square
Hexagon
Pyramid
Trapezoid
ds:
ok
Two things are
DIFFERENT from the
others in some way.
Circle them and
explain why they are
different.
Rhombus
Rhombus
uch
Isosceles
Triangle
Rectangle
Square
Equilateral
Triangle
Card
Sorts
in
Mathematics
Matching
Card
Activity
Teaching Reading
in Mathematics by
Mary Lee Barton
Write the number 1 in each box that represents a one-dimensional (1-D) concept
Write the number 2 in each box that represents a two-dimensional (2-D) concept
Write the number 3 in each box that represents a three-dimensional (3-D) concept
3
cm
Side of a
square
(m)
Area of a
square
(m2)
1
1
2
4
3
9
4
16
5
25
C=d
Perimeter is
to Polygon
as
Circumferenc
e is to
_______
Volume of a
cylinder
A  w(6  w)
Analogy
Distance
around the
bases on a
baseball field
2
in
Number of
cubic yards of
concrete needed
to pave a
driveway
Place a  in each box that represents a linear concept
Place a  in each box that represents a quadratic concept
Place a  in each box that does not represent a linear or quadratic concept
1
ft  yd
3
Density
(g/cm3)
Mass
(grams)
5
15
10
30
15
45
20
60
25
75
Time in
Seconds
Height of a
ball thrown
upward (feet)
0
0
1
48
2
64
3
48
4
0
Force  ma
Wages are found by
multiplying $12 times
# of hours worked
h(t )  24t  16t 2
Amount of canvas
needed to make a
tarpaulin to cover a
swimming pool
Place a  in each box that represents a positive trend.
Place a  in each box that represents a negative trend.
Place a  in each box that represent no trend.
As one set of values
increases, the other
set tends to increase.
Mosquito
population and the
sale of insect
repellent.
Gas
(gal)
Miles
5
150
4
112
7
217
6
192
3
87
Person’s age and shoe
size
As one set of values
increases, the other set
tends to decrease.
Outdoor temperature
and layers of clothing
The points show no
relationship.
3 highly effective “forms” to
identify similarities and differences
 Comparing
Classifying
 Creating
analogies
Graphic Organizers for Classification
Place Categories in column headings
-most useful when all categories are equal in
generality
-more useful when all categories are not equal in
generality
Semantic Feature Analysis…
Equation
yx
y  4x  2
y 7x
y4
x  8
has a
positive
slope
has a
negative
slope
has a
slope of
zero
has an
undefined
slope
has a
non-zero
xintercept
has a
nonzero y-
intercept
passes
through
the
origin
Self-Assess Prior Knowledge
Yes
or
No
I can I can give I can find on the
define an example graph or I can
graph it
Coordinate
pairs
x intercept
y intercept
Linear
equation
I can find on a table
using my graphing
calculator
Which one is NOT related to the other four?
Identify it and explain your reasoning.
Coordinate
Plane
Axis
Origin
Ordered
Pair
Order of
Operations
Which one is NOT related to the other three?
Identify it and explain your reasoning.
Frayer Model… example
Definition
Facts
• Parallel lines lie in the same plane
Parallel lines are
• Parallel lines have the same slope
• Parallel lines NEVER meet.
lines that lie in the
• The symbol for parallel lines is
same plane but do
not intersect.
parallel lines
Examples
Nonexamples
Sorting things into categories
Use big picture ideas
 Use to assess prior knowledge
 Use after learning to assess new
knowledge

Grouping
a.k.a sorting, categorizing, matching…
How would you group these
items?
What’s your rationale?
Can you group these
items in several
ways?
All In OR Odd Man Out?
An activity where you roll,
you decide, you explain…
Directions
1.
2.
3.
4.
5.
Roll the number
cube.
Group the words.
Describe the
rationale for each
group using
complete
sentences.
Create a graphic
organizer.
Turn in your work.
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Use ALL the
vocabulary words
given.
The groups do
NOT need to be
equally divided.
You have the
option of having
one (1) Odd Man
Out if you roll 2,
3, 4, 5 or several
Odd Men Out if
you roll a 6.
daisy
soil
seed
sun
rose
stem
yellow
water
Group
(3)
daisy
rose
sun
soil
water
seed
stem
Rationale
Daisies and roses are
types of flowers.
The sun, soil, and
water are essentials
elements that for
growing plants.
A stem grows from a
seed. Both are parts
of a plant.
Odd Man Out
YELLOW is a
color and/or
an adjective.
Though
yellow can
describe a
daisy and a
rose, it does
not fit into
the rationale
given.
water
Most plants
need water
and soil to
grow.
soil
stem
Stems grow from
seeds. They are
parts of a plant.
seed
yellow
daisy
Yellow is a
color that
describes
daisies,
roses, and
the sun.
rose
sun
Let’s Practice
number
line
negative
number
coordinate
integer
positive
number
inequality
negative
opposites
absolute
value
positive
Making generalizations
Look at the examples of polygons above. Write down as
many properties as you can that are COMMON TO ALL of
these polygons.
ALL POLYGONS ________________________________________________________
______________________________________________________________________
______________________________________________________________________
3 highly effective “forms” to
identify similarities and differences
 Comparing
 Classifying
Creating Analogies
Examples,
Carpenter is to
hammer as painter
is to brush.
Hot is to cold as
night is to day.
Oxygen is to
humans as carbon
dioxide is to plants.
Core is to earth as
nucleus is to atom.
Creating
Analogies
Analogies help us to see
how seemingly dissimilar
things are similar.
They increase our
understanding of new
information.

-Marzano,2001
Teacher vs. Student Directed
Analogy
Student-directed
analogy task
Teacher-directed
analogy task

Eighty is to eight
As
Dime is to ______.
Sphere is to circle
As
_____ is to ______.
Vocabulary & Notation
“There is no more
single important
factor that effects
student achievement
than vocabulary &
notation.”
Leading the Way to Accelerating Math Achievement by Bill
Hanlon
Symbol

Meaning
Sentence with symbols
/ Complete Sentence
AB  CD
Perpendicular
Line AB is perpendicular
to line CD
Floor  Wall
The classroom floor is
perpendicular to the wall.

║

Picture
Foldables… example
SLOPE
What are you talking about?!?! 
1.
Draw an isosceles right
triangle. Include all
markings to indicate both
that it is isosceles and right.
3.
Draw MN . k passes
through B and is a
perpendicular bisector of MN
5.
Draw and label a pair of
parallel lines (a & b) with the
transversal (c ) cutting
through them. Label the
angles created with the
numbers 1-8. List all 4 pairs
of corresponding angles.
Define: Solution of a system of linear equations.
Word Bank “helper words”
Ordered
pair
1. Write a system of linear equations whose solution is (6, 2).
2. Fill in the table below
(include the solution)
x y1 y2
3. Sketch a graph &
label the solution
Use
Mental
Model
s
Square Numbers
X X X
X X X
X X X
AVID
Obj 6: The student will demonstrate an understanding of geometric relationships and spatial reasoning.
G04A: The student is expected to select an appropriate representation
(concrete, pictorial, graphical, verbal, or symbolic) in order to solve problems.
Alana claims that the
exterior angle for any
regular polygon is either
an acute angle or an
obtuse angle.
Consider each of the following regular polygons:
Triangle
Quadrilateral
Pentagon
Hexagon
Which one could disprove Alana’s theory?
Draw pictures to support your solution choice.
Probes Informal
Assessments
Used to informally assess before and
throughout instruction.
 Analyze misconceptions
 Make better instructional decisions

Circle the letter of each line segment that is approximately 2¼ units long.
Explain Choices:
How can we use them?
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Differentiated Instruction
Assessing Point of Entry
Analyzing trends in student thinking
Giving student interviews
Promoting student-to-student dialogue
Allowing for individual think time
Developing Vocabulary
Improving students’ process skills
Assessing effectiveness of instructional activities
Moving beyond the individual classroom
Types of Probes
 Selected
Response
 Multiple Selections Response
 Opposing Views/Answers
(Concept Cartoons)
 Examples and Non-Examples
List
 Justified List
 Strategy Elicitation
Before creating a Probe consider
the following questions
What knowledge will students need to
complete this probe?
 What mistakes might students make
that will lead to incorrect answers?
 How will this probe assist in diagnosing
student learning?
 What percentage of students could
respond correctly to the initial problem
if the misconceptions addressed in this
probe were corrected?

Other Formative Assessment
Strategies…
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Sticky Bars
Ring of Truth
Chain Note and Pass the Question
Justified list
P-E-O
Paint the Picture
Concept Cartoons
Exit Tickets
Friendly Talk
Traffic Light Dots
I Used to Think…but Now I Know