Good core instruction
Keeping it front and center
• Formative Feedback System
• Teaching Thinking Skills
Day 2
Debra Pickering
Senior Scholar
Marzano Research Laboratory
Teachers often observe that students
cannot or will not
engage in higher order thinking.
To what extent do you observe this?
When you see higher order thinking, what do you
believe stimulates that type of thinking?
If you do not see higher order thinking, what are some
reasons for this deficiency?
Thinking Skills as standards
Why?
• 21st century…
• Common core…
• Life skills…
• Cognitive Challenge
Standard
Measurement Topic
Measurement Topic
Measurement Topic
Scale
4
In addition to 3, demonstrates in-depth understanding or
skill that is beyond what was targeted in the teaching
3
Complex, Targeted understanding/skill
2
Simpler, Foundational understanding/skill
1
With help, partial understanding/skill
0
Even with help, no understanding or skill demonstrated.
Scale
4
3
In addition to 3, demonstrates in-depth understanding or
skill that is beyond what was targeted in the teaching
3.5
The Complex, Targeted understanding/skill
1
2.5
Simpler, Foundational understanding/skill
1.5
With help, partial understanding/skill
0
.5
Even with help, no understanding or skill demonstrated.
2
From:
Cris Tovani’s
What Do They Really
Know?
64%
72%
…
Student
%
correct
Stan./
Target
Stan./
Target
Stan./
Target
Stan./
Target
Jane..
John…
100%
90%
100%
85%
100%
95%
100%
100%
100%
80%
Jen…
Jamal…
Jackson…
47%
100%
60%
40%
100%
60%
60%
100%
80%
85%
100%
40%
20%
100%
60%
Scale
4
3
In addition to 3, demonstrates in-depth understanding or
skill that is beyond what was targeted in the teaching
3.5
The Complex, Targeted understanding/skill
1
2.5
Simpler, Foundational understanding/skill
1.5
With help, partial understanding/skill
0
.5
Even with help, no understanding or skill demonstrated.
2
2
From:
Cris Tovani’s
What Do They Really
Know?
Student’s
score?
3
2
Student’s Score?
Conventions- 3
Claims/Support- 2
Assessment:
Samples/Bank
Knowledge:
Understanding
Ability
3
3
2
2
Level of COGNITIVE
CHALLENGE
Focus on
knowledge
complexity
Focus on
Thinking Skills
Level of COGNITIVE
CHALLENGE
Assessment:
Samples/Bank
Knowledge:
Understanding
Ability
4
3
3
2
2
Level of COGNITIVE
CHALLENGE
Assessment:
Samples/Bank
Knowledge:
Understanding
Ability
3
This is already at
higher level of
complexity
Complex
2
Simpler
3
Explain
Execute
2
Explain
Execute
Level of COGNITIVE
CHALLENGE
Assessment:
Samples/Bank
Knowledge:
Understanding
Ability
3
2
Solve real-world
problems that require
identifying and
performing addition and
subtraction of whole
numbers up to two
places
Complex
Add and subtract whole
numbers up to two
places
Simpler
3
Execute
2
Execute
Level of COGNITIVE
CHALLENGE
Assessment:
Samples/Bank
Knowledge:
Understanding
Ability
3
2
Understanding of how
topography and natural
resources influence
culture, and vice versa
Understand terms:
Topography
Natural Resources
Culture
3
Explain
2
Explain
Complex
Simpler
Knowledge:
Understanding
Ability
Higher Level
Thinking
Assessment:
Samples/Bank
4
3
3
2
2
Higher Level
Thinking
Knowledge
Utilization
Knowledge
Analysis
Knowledge
Comprehension
Knowledge
Retrieval
Knowledge:
Understanding
Ability
Assessment:
Higher Level
Thinking
Samples/Bank
4
3
Represent?
Comprehend
Integrate?
Symbolize?
3
2
Retrieve
Recall?
Recognize?
2
Knowledge:
Understanding
Ability
Assessment:
Higher Level
Thinking
Samples/Bank
4
3
2
Errors?
Analyze
Infer?
Compare?
Infer?
Comprehend
Integrate?
Symbolize?
3
2
Knowledge:
Understanding
Ability
Assessment:
Higher Level
Thinking
Samples/Bank
4
3
2
Analyze and Use
Compare?
Induce?
Make decision?
Comprehend
Execute
Represent
3
2
What about Level 4?
Knowledge:
Understanding
Ability
Higher Level
Thinking
Assessment:
Samples/Bank
4
3
3
2
2
Task for Level 3
Knowledge but with
higher cognitive
challenge or new
context, twist
Knowledge:
Understanding
Ability
Assessment:
Higher Level
Thinking
Analysis
3
Samples/Bank
4
3
Comprehension
2
Retrieval
2
Task for Level 3
Knowledge but with
higher cognitive
challenge or new
context, twist
Knowledge:
Understanding
Ability
Assessment:
Higher Level
Thinking
Use
3
Samples/Bank
4
3
Analysis
2
Comprehension
2
Task for Level 3
Knowledge but with
higher cognitive
challenge or new
context, twist
Thinking Skills as standards
Why?
• 21st century…
• Common core…
• Life skills…
• Cognitive challenge
Thinking Skills as standards
Issues (“Yeah, but thinking skills... ”)
• …should just be “embedded…”
• …can’t be taught in isolation…
• …just require higher level questions …
• …aren’t tested on standardized tests…
• …--who and when and how…
Thinking Skills as standards:
Which thinking skills?
Cognitive
challenge
Knowledge
Utilization
Knowledge
Analysis
Knowledge
Comprehension
Knowledge
Retrieval
Using Knowledge
Engaging in Tasks requiring
Cognitively Complex Processes
• Decision Making
• Problem Solving
• Experimental Inquiry
• Investigation
• Invention
Analyzing Knowledge
Examining and Generating
Similarities and Differences
• Comparing
• Classifying
• Abstracting/Metaphorical Thinking
Examining and Generating
Arguments and Assertions
• Analyzing Perspectives
• Constructing Support
• Analyzing Errors in Reasoning
Examining and Generating
Logical Inferences
• Inductive Reasoning
• Deductive Reasoning
Comprehending Knowledge
• Integrating
• Symbolizing
Retrieving Knowledge
• Recalling
• Recognizing
Prompting
the thinking that
higher level questions and tasks
demand
A and B are similar because they both
________________.
________________.
________________.
A and B are different because
A is __________, but B is ___________.
A is __________, but B is ___________.
A is __________, but B is ___________.
Fun and Enjoyment are similar because they both
________________.
________________.
________________.
Fun and Enjoyment are different because
Fun is ___, but Enjoyment is ___________.
Fun is____, but Enjoyment is ___________.
Fun is ____,but Enjoyment is ___________.
A win and a victory are similar because they both
________________.
________________.
________________.
A win and a victory are different because
Win is ___, but Victory is __________.
Win is ___,but Victory is ________.
Win is ___,but Victory is ________.
Fractions and Decimals are similar because they
both ________________.
________________.
________________.
Fractions and Decimals are different because
Fractions __, but Decimals __.
Fractions __, but Decimals __.
Fractions __, but Decimals __.
A monarchy and a dictatorship are similar because
they both ________________.
________________.
________________.
A monarchy and a dictatorship are different
because
a monarchy___, but a dictatorship____.
a monarchy___, but a dictatorship____.
a monarchy___, but a dictatorship____.
Power and a authority are similar because they
both ________________.
________________.
________________.
Power and authority are different because
power is___,but authority is____.
power is___, but authority is____.
power is___, but authority is____.
Teaching
the thinking that
higher level questions and tasks
demand
Teaching
the thinking that
higher level questions and tasks demand
Provide structure—process guidelines,organizers
Teaching
the thinking that
higher level questions and tasks demand
Provide structure—process guidelines,organizers
Teach!
• Model, Model, Model
• Use Teacher-Structured and Student-structured
Tasks
• Monitor and Provide feedback
Analyzing and Generating
Similarities and Differences
•Comparing
•Classifying
• Abstracting/Metaphorical Thinking
Comparing
Classifying
Abstracting/
Metaphorical
Thinking
=
=
=/
=/
Comparing
• Would it be useful to show how things are similar and/or different?
• Would it be useful for students to focus on identifying how similar things
are different and how different things are similar?
• Would it be helpful to have students describe how comparing things affects
their knowledge or opinions related to those things?
Classifying
• Would it be helpful to have students group things?
• Would it be beneficial for students to generate a number of ways to group
the same list of things?
Abstracting
• Is there an abstract pattern that could be applied?
• Could something complex or unfamiliar be understood better by generating
an abstract pattern and applying it to something simple or more familiar?
• Are there seemingly different things that could be connected through the
generation of an abstract pattern?
Comparing
=
=
=/
=/
Understanding Comparing.
• Comparing is a process of identifying similarities and
differences among items. (Often called comparing
and contrasting.)
• We compare every day—automatically. In the
classroom, we can compare methodically.
• When you compare ideas, you can gain knowledge,
insights, and new perspectives related to what is
being compared.
Comparing
Process Guidelines
•Select the items you want to compare and a method of
organizing your ideas , e.g., Venn, matrix, bubble graphic.
•Identify the characteristics on which you want to base your
comparison of the items.
•Gather and record the relevant information for each characteristic
for the items.
•Identify how the items are similar and different with respect to
each characteristic.
Comparing
Process Guidelines
•Reflect on your work and articulate what you learned, e.g.,
what you notice that hadn’t occurred to you before,
what surprises and troubles you, or
what is confusing and clear.
Comparing
Thoughtful Applications
•Decide if it would be valuable to add, delete, combine, or change
any of the characteristics, or to include other items.
•Consider whether you need more information before deciding
that you have identified the important similarities and differences
for each characteristic.
Item 1
Item 2
Item 3
Characteristic
1
Similarities and
Differences
Characteristic
2
Similarities and
Differences
Characteristic
3
Similarities and
Differences
Characteristic
4
Similarities and
Differences
Characteristic 1:Similarities and Differences.
For characteristic 1, Item 1 and Item 2 are mainly similar.
They both……
Characteristic 2:Similarities and Differences.
Characteristic 3:Similarities and Differences.
Characteristic 4:Similarities and Differences.
Item 1
Item 2
Item 3
Characteristic
1
Similarities and
Differences
Characteristic
2
Similarities and
Differences
Characteristic
3
Similarities and
Differences
Characteristic
4
Similarities and
Differences
Food
eaten
Frontier
Days
Food
eaten
today
Item 3
Characteristic
1
Similarities and
Differences
Characteristic
2
Similarities and
Differences
Characteristic
3
Similarities and
Differences
Characteristic
4
Similarities and
Differences
Comparing
Process Guidelines
•Select the items you want to compare and a method of
organizing your ideas , e.g., Venn, matrix, bubble graphic.
•Identify the characteristics on which you want to base your
comparison of the items.
•Gather and record the relevant information for each characteristic
for the items.
•Identify how the items are similar and different with respect to
each characteristic.
Example from Dimensions of Learning, ASCD, 1999
Example from Dimensions of Learning, ASCD, 1999
Monarchy
How the
leaders come to
power
The reaction
from the
people
The role of the
people
Dictatorship
Democracy
How the
leaders come to
power
The reaction
from the
people
The role of the
people
Monarchy
Dictatorship
Democracy
King or queen gain
throne because of
heritage; sometimes a
monarch takes over
another country by
force. Often leader for
life.
Usually the dictator takes
power through coercion
or force. Often is leader
for life.
The leaders are elected by the
people; sometimes people are
accused of “coercing” or
forcing people to vote in for
certain people. The leader does
not have total power and can
be voted out of office.
Through history there
are examples of
monarchs loved by
people—but some were
hated by certain groups
who were persecuted.
Often in history the
dictator is hated or
feared by most people.
People are often split on their
reactions but accept the leader
if the leader was elected. They
know they can try to elect
someone new before too long.
People are generally
expected to obey the
rule of the monarch.
Monarch holds power
and can change laws.
Can become like
dictators
People must obey the
dictator. Often there are
serious consequences for
not being loyal.
Generally the people are seen
to have power through their
votes. If they don’t like what is
happening, they can elect new
leaders.
Belle in
“Beauty &
the Beast”
Family
Background
Personality
Traits
How she
ended up
Her enemy
Jasmine in
“Aladdin”
Poor; daughter
of inventor; no
mother in story
Rich, daughter of
ruler; no mother
in story
Loved to read & Loved to have
stay home; strong adventures;
opinions. Obeyed strong opinions;
disobeyed father
father
Marries prince;
father lives with
her
Garcon—man
who wanted to
marry her
Marries prince;
lives in palace
with father
Ariel in
“Little
Mermaid”
Rich, daughter of
king; no mother
in story
Loved to have
adventures; strong
opinions;
disobeyed father
Marries prince;
leaves father to
live with prince
Evil sorcerer— Sea witch—
man who wanted woman who
wanted to destroy
to marry her.
her father
Characteristic 1:Similarities and Differences.
All similar in that no mother in story; Jasmine and Ariel were similar
because they were rich with father as ruler; Belle was different from
them -- was poor and father was inventor
Characteristic 2:Similarities and Differences.
Characteristic 3:Similarities and Differences.
Characteristic 4:Similarities and Differences.
Attack on Pearl
Harbor
Attack on World
Trade Center
Food eaten
during frontier
days
Food eaten
today
What did you learn?
Characteristic 1________________
Easy to see that
items are very
different for this
characteristic…
Characteristic 2________________
…and
very
similar for this
characteristic.
Attack on Pearl
Harbor
Attack on World
Trade Center
Characteristic _______________
Effect on Americans
Characteristic _______________
Motivation of attackers
Food eaten
during frontier
days
Food eaten
today
Characteristic _______________
Variety
Preparation
Preservatives
Food eaten during
frontier days
Food eaten today
Characteristic ________________
Variety
The variety of food today and in past is very different. In the past, the available
food was limited to what was grown and what was hunted in the region where a
person lived. Today we have food from all over the world. In addition, unlike the
past, the number of recipes available to us and the prepared foods we can now buy
contributes to the vast variety of food we enjoy today.
Comparing Terms
David Hyerle---Double Bubble
different
different
different
similar
Item
similar
Item
different
similar
different
different
similar
Comparing Terms
David Hyerle---Double Bubble
different
1
different
2
different
1
similar
Item
similar
Item
different
2
similar
different
3
different
3
similar
Comparing Terms
David Hyerle---Double Bubble
different
1
different
2
different
3
different
1
Item
Rural
Item
Urban
different
2
different
3
Item 1
Item 2
Item 3
Characteristic 1
Similarities and
Differences
Characteristic 2
Similarities and
Differences
Characteristic 3
Similarities and
Differences
Characteristic 4
Similarities and
Differences
Topic sentence
1
Sim & Diff
2
Sim & Diff
3
Sim & Diff
Detail/Expand
Detail/Expand
Detail/Expand
Conclusion
Thesis
1
Sim & Diff
2
Sim & Diff
3
Sim & Diff
Develop/Support
Develop/Support
Develop/Support
Conclusion
Item 1
Item 2
Item 3
Characteristic 1
Similarities and
Differences
Characteristic 2
Similarities and
Differences
Characteristic 3
Similarities and
Differences
Characteristic 4
Similarities and
Differences
Huck inn
Huck inn
MAKE‐OVERS
Refocusing on Reasoning
Unit: Earth’s atmosphere
Original
Learning Goal: Know/Understand the make‐up of the earth’s atmosphere.
Know the characteristics of the ocean
Be ready to label and describe the earth’s atmosphere and the characteristics
of the ocean
Make‐over
Reasoning Process. Comparing
Task: Using what we learned during the ocean unit,
compare two journeys. One starts on the earth’s
surface and goes down deeper and deeper into the
ocean. The other starts on the earth’s surface and goes
higher and higher into space. Include in the
comparison how the temperature, pressure, light, and
even emotions, would change during the two journeys.
Irene
Sandy
Item 1
Item 2
Item 3
Characteristic 1
Similarities and
Differences
Characteristic 2
Similarities and
Differences
Characteristic 3
Similarities and
Differences
Characteristic 4
Similarities and
Differences
Set up and begin to complete a comparison matrix on
• bookstores
• reality TV shows
• computers
• pizzas
• your choice
Make a list of insects
Classify them into at least three
categories…..
…..as if you were a frog
Insects: as if you were a frog.
Characteristic: How they move.
Categories:
Fly:
Crawl:
Swim:
Other characteristics that could be used:
Availability:
Ease of catching:
Taste:
Make a list of insects
Classify them into at least three
categories…..
…..as. if you were a frog
…..as if you were an exterminator
Classifying
Classifying
Classifying
Process Guidelines
•Identify the items that are to be classified and the characteristic
that will be the focus of the classification,
e.g., size, theme, material, uses, genre, causes, origins, etc.
•Based on the selected characteristic, create the categories by
specifying the attribute(s) that the items must have for
membership in the category.
Example characteristic: classifying wars according
to the causes; categories might include causes that were
predominantly economic, political, or cultural.
•As you place items in categories, determine if you need to
combine categories or split them into smaller categories; and
specify the attribute(s) for any new categories
Classifying
Process Guidelines
•Reflect on your work and articulate what you learned, e.g.,
what you notice that hadn’t occurred to you before,
what surprises and troubles you, or
what is confusing and clear.
Classifying
Thoughtful Applications
•Decide if it would be valuable to reclassify the items using a
different characteristic or set of categories, or to add more
items to classify.
•Consider whether this classification is leading to any insights
or extended learning.
Understanding Classifying.
• Classifying is a process of grouping items according
to similar attributes.
• We classify every day—often unconsciously.
However, in the classroom, we can classify
methodically to increase our understanding of what
we are studying.
• When you classify—and reclassify—items, it forces
you to look at different attributes of the items and can
lead to your seeing an item quite differently when it is
in a new category.
Classifying and Stereotyping
Would you classify the following as living, dead, or ??
Living?
1. Mummies
2. Fossils
3. Lightning
4.
5.
6.
7.
Seaweed
The Loch Ness Monster
Thoughts
Coral Reefs
8. Ghosts
9. Fingernails
10. Pearls
Once
Dead?
living,
now dead
Dead, never
??
living
Major system affected
Respiratory Digestive
System
System
Diabetes
Hypoglycemia
Emphysema
Heart attack
Circulatory Muscle/
System
Skeletal
System
Multiple Sclerosis
Osteoporosis
Shingles
Crohn’s Disease
Nervous
System
Ulcer
Stroke
Anorexia
Alzheimer's
Major Cause:
Life Style
Diabetes
Hypoglycemia
Emphysema
Heart attack
Genetic
Environment
Multiple Sclerosis
Osteoporosis
Shingles
Crohn’s Disease
Unknown
Ulcer
Stroke
Anorexia
Alzheimer's
“Life Sports”
Not “Life Sports”
Tennis
Basketball
Weightlifting
Baseball
Track
Gymnastics
Hockey
Swimming
Volleyball
Car Racing
Golf
Archery
Bowling
Ping Pong
Hoseback Riding
Billiards
Boxing
Geography Terms
Basin
Harbor
Plateau
Bay
Highland
Port
Canal
Hill
Prairie
Canyon
Isthmus
Rain Forest
Cape
Lowland
Reservoir
Channel
Marsh
Strait
Delta
Mountain
Stream
Divide
Range
Swamp
Fjord
Peak
Tundra
Classify the following:
Cinderella
Hansel and Gretel
Dr. Jekyll and Mr. Hyde
Shrek
George Washington, Boy
Surveyor
A Tale of Two Cities
Rapunzel
Harry Potter and the
Sorcerer’s Stone
Little Red Riding Hood
Zorro
Romeo and Juliet
Peter Rabbit
The Hobbit
Christmas Carol
The Tortoise and the Hare
The Color Purple
Organize the following wars/conflicts into three or more groups.
• For each category, clearly the identify attributes that
must be present for membership
• Explain how all of the conflicts within a category have the
defining attributes of that category.
The Civil War
The War of 1812
The Vietnam War
The French Revolution
World War I
World War II
The French & Indian War
The American Revolution
The Spanish American War
The War in the Persian Gulf
Original:
Observing Olympics (6th grade PE)
This assignment must be six typed pages (maximum font=16).
For the next three weeks, watch some of the Olympics, read
newspaper and magazine articles, and listen to the news.
Write about what you hear and see.
(If you do not have access to television or newspapers, see me)
Make-over
We have been learning what some sports require in order to
excel. Some require a healthy cardiovascular system, others
require muscle strength, and still others have major
requirements for the right equipment.
We are going to create some categories for sports, based on
what is required to excel. You will then use these categories
to classify some of the sports in the Olympics….
uneven
bars
floor
exercise
javelin
marathon
badminton
basketball
cycling
diving
shotput
speed skating
archery
tennis
acrobatic
skiing
equestrian
boxing
canoeing
fencing
figure skating handball
hockey
judo
downhill
skiing
pentathlon
pole vault
sailing
luge
swimming
beach
volleyball
balance
beam
triathlon
rowing
synchronized table
swimming
tennis
volleyball
long
jump
water polo weightlifting wrestling skateboarding
When C.L. Sholes was inventing a typewriting machine in the
early 1870’s, he found that the machine jammed if he typed
too fast. So he deliberately arranged the position of the letters
in a way that forced typists to work slowly. Nevertheless,
Sholes’ typewriter design was a great improvement over
earlier models, and it was soon in use all over the world.
Today, although typewriters have been improved in many
ways, nearly all of them have keyboards like the one Sholes
devised in 1872. The letter arrangement is called QWERT,
after the five left-hand keys in the top letter row. You can see
QWERT keyboards on computer consoles as well as on
typewriters.
Unfortunately, the QWERT arrangement slows typing,
encourages, errors, and causes greater fatigue than another
arrangement devised by August Dvorak in 1930, which has
proved in several tests to be much faster and more accurate
than QWERT.
Millions of people have learned the QWERT keyboard,
however, and it is being taught to students in schools right
now. So, it seems that we will continue to live this 19th century
mistake.
Abstracting/
Metaphorical
Thinking
Understanding
Abstracting–Metaphorical Thinking
• Abstracting is the process of finding and explaining
general patterns that can be applied to seemingly different
ideas of scenarios.
• We see this in the arts, e.g., My Fair Lady is abstracted
from Pygmalion; West Side Story is abstracted from
Romeo and Juliet.
• Abstracting can help us see unfamiliar things through the
lens of something that is familiar; and can help us see
familiar things from a new perspective.
• Abstracting is the foundation of metaphorical thinking.
Abstracting/Metaphorical Thinking
•Identify what is important or basic to the information (ideas,
concepts, situations) with which you are working.
•Write that basic information in a more general form by:
replacing terms referring to specific things with terms referring
to more general things, and
summarizing information whenever possible.
•Keep experimenting with terms that are even more general or
specific than the ones chosen initially.
•Identify different information, ideas, or situations to which the
general version could be applied and determine the significant
similarities and differences between the two.
Specific/Literal
Step 1
General
Pattern
Step 2
General Pattern
in new Specific
Step 3
Step 1—Specific/Literal
Step 2—General/Abstract
C.L. Sholes invented a
keyboard, QWERT, that would
slow down typists, thus solving
the problem of key sticking.
Someone invented/created
something to address an
issue/problem.
Typewriter keys stopped sticking
The issue/problem went away.
Another keyboard was invented
that was shown to be better than
QWERT.
Something else was invented
that was shown to be better than
the original.
QWERT is still used despite the
fact that keys no longer stick
and another keyboard
configuration was shown to be
better.
The original invention is still
used/accepted even though the
issue/problem is no longer
present, and something new has
been shown to be better.
Life
Life is just a bowl of cherries.
General version
Bowl of
cherries
Life is just a bowl of cherries.
The world is your oyster.
Life is a box of chocolates.
http://passinginlitandfilm3.wordpress.com/2010/11/04/pocahontas
-avatar/
The Odyssey
Star Wars
Unit: Structures and Functions of the Cell
Original:
Learning Goal: Know/understand the major structures and
functions of the cell
Task: Construct a model of a plant and an animal cell
Make‐over
Reasoning Process: Creating Metaphors
Think of another system other than the cell. Then show how the
structures and the functions of that system—at a general level‐‐
are similar to, an different from, that of the cell.
Found online: desperate cry from student
Cell analogy???
I am in dire need of an analogy comparing a cell to some
sort of system. For example, my teacher came up with a
factory. If it does not fit into a certain system where things
work together, then I cannot use it.
**INCLUDE EACH ORGANELLE WITH IT'S SPECIFIC
ANALOGY IN THE SYSTEM PLEASE**
Cell
General version
Nucleus– controls
metabolism, growth
and reproduction
Selectively permeable
membrane--will allow
certain materials to
cross over and will
keep others from
doing so
Cell
General version
Nucleus– controls
metabolism, growth
and reproduction
Selectively permeable
membrane--will allow
certain materials to
cross over and will
keep others from
doing so
The place
systems are
controlled
Starship
Enterprise
Bridge...
Transporter room...
Regulates what
gets in and what
gets out
Apple
General pattern
The best part is under the
Have to get through surface
skin of the apple so
to get to good stuff
people often peel it
Sometimes it looks fine
until you peel it and start
to eat.
The surface makes it hard
to know what is really inside
Different types have
different flavors
There are different types
with different characteristics
People use the apple to
make tons of things like
pie, sauce, bread, etc.
The parts can be used for
many different purposes
If you cut it just right, the
middle looks kind of like a
star
There are interesting
surprises inside if you look
at it in certain ways
Adapted from Wormeli, Metaphors and Analogies
Someone with
bold new ideas
Someone with
great wealth
Someone has a
valuable asset
It is used for doing
much good for people
It is also exploited to
do great harm
Abstracting/Metaphorical Thinking
•Keep experimenting to determine how general or specific the
general pattern should be.
Step 1—Specific/Literal
Step 2—General/Abstract
Cinderella lives with her
wicked stepmother and spoiled
stepsisters, all of whom were
jealous of her.
A person lived with some
other people.
The king announced that there
would be a ball to find his son a
wife; Cinderella was not allowed
to go.
A fairy godmother arrived and
provided Cinderella with
everything she needed to attend
the ball—but only until
midnight.
Cinderella met the prince then
lost her slipper at the ball. The
prince searched for the maiden
who would fit into the slipper.
It fit Cinderella and she married
the prince.
There was a party.
Things didn’t work out.
Things finally worked out.
Abstracting/Metaphorical Thinking
•Keep experimenting to determine how general or specific the
general pattern should be.
•Continue to apply the new general pattern to increasingly
diverse specific information, ideas, ideas or situations
Abstracting/Metaphorical Thinking
•Identify what is important or basic to the information (ideas,
concepts, situations) with which you are working.
•Write that basic information in a more general form by:
replacing terms referring to specific things with terms referring
to more general things, and
summarizing information whenever possible.
•Keep experimenting with terms that are even more general or
specific than the ones chosen initially.
•Identify different information, ideas, or situations to which the
general version could be applied and determine the significant
similarities and differences between the two.
In the 1820’s, U.S. settlers began moving into the
Mexican territory of Texas. At first, the settlers were content
to live under the new Mexican republic. But when Santa
Anna came to power, he laid down oppressive new laws,
making the settlers so resentful of his government that
finally, in 1836, they declared Texas to be independent of
Mexico.
Santa Anna led an army into Texas to punish the
rebels. At a fortress call the Alamo, his troops defeated a
vastly outnumbered force of Texans. All of the Texas rebels
were killed, but their courage in the face of great odds
inspired a rebel battle cry: “Remember the Alamo.” A few
months later, the Texans got their revenge. One day, when
Santa Anna’s troops were resting in their camp, the Texans
launched a surprise attack and defeated Santa Anna. After
this defeat, Santa Anna agreed to grant Texas its
independence.
Step 1—Specific/Literal
Step 2—General/Abstract
In 1820, U.S. citizens settled in
the Mexican Territory of Texas.
People from outside entered
and settled into a part of an
established place.
Santa Anna, ruler of this
territory, passed oppressive laws
and eventually drove the new
settlers to declare Texas as
independent.
Santa Anna fought back and began
to defeat the rebels in military
battles—e.g., The Alamo
The leader of the established place
was oppressive to newcomers.
Newcomers declared their part
now belonged to them.
The rebels would not give up
and finally defeated Santa Anna
in a sneak attack. Santa Anna
granted Texas its independence.
The newcomers would not give up
and finally won with a sneak
attack. The leader yielded and
gave the newcomers the part they
wanted.
The leader fought back and
began to win—some very
highly publicized victories.
The Odyssey
Specific/Literal
General/Abstract
A young man with special
talents is destined for
possible greatness.
He must work through a
series of tests and trials of
body and will.
He is aided by wise,
esoteric advisors in a
battle of good vs. evil.
He comes close to death
and destruction.
He overcomes his
limitations and is
triumphant
Star Wars
Specific/Literal
The American
Specific/Literal
Revolution
General/Abstract
People unhappy with their
present situation seek to
find/establish a new way of life.
They start a new community
with new traditions.
Influences from their old
life still try to control them
They reach a point that they
must take a stand and defend
their new ideas.
Gradually the new life established
itself as a new culture with
traditions and identity.
????
Specific/Literal
Unit: Structures and Functions of the Cell
Original:
Learning Goal: Know/understand the major structures and
functions of the cell
Task: Construct a model of a plant and an animal cell
Make‐over
Reasoning Process: Creating Metaphors
Think of another system other than the cell. Then show how the
structures and the functions of that system—at a general level‐‐
are similar to, an different from, that of the cell.
Comparing
Classifying
Abstracting/
Metaphorical
Thinking
=
=
=/
=/
Analyzing and Generating
Arguments and Assertions
• Analyzing Perspectives
• Constructing Support
• Analyzing Errors in Reasoning
Analyzing
Perspectives
Constructing
Support
Analyzing
Errors in
Reasoning
Constructing Support
• Are there important claims to be refuted or supported?
• Would it be important to examine existing arguments that support
or refute a claim?
Analyzing Errors
• Are there situations in which it would be beneficial to identify
errors in reasoning?
Analyzing Perspectives
• Would it be useful to identify and understand the reasoning or logic
behind a perspective on a topic or issue?
• Would it be useful to analyze opposing perspectives on a topic or
issue?
These thinking skills are a major area of focus for the
Common Core. Although they are sometimes
“assigned”, they are often not TAUGHT to all students
in a way that develops their expertise.
Analyzing
Perspectives
Analyzing perspectives
?????????
?????????
Issue or
situation
?????????
• Emphasis is on “analyzing”
• The initial goal is to understand,
not to change or even accept other perspectives
Analyzing Perspectives
For a targeted issue or situation about which people
react differently,
•Identify multiple perspectives, yours and/or the
perspectives of a range of others.
•Explain the reasons or reasoning underlying each
perspective.
•Avoiding judgment or rebuttal, continue to analyze in
order to accurately represent each perspective.
(Note: The same general perspective might have
multiple sets of reasons.)
Analyzing Perspectives
•Examine your work and determine if it would be
valuable to explore more perspectives or analyze more
deeply any of the perspectives identified.
Analyzing perspectives
Be careful that you offer reasons underlying the
perspective and not just a restatement of the
perspective.
Examples:
Analyzing perspectives
Be careful that you offer reasons underlying the perspective and not just
a restatement of the perspective.
Examples:
We should not require students to wear uniforms to school
because it is just wrong.(restatement)
We should not require students to wear uniforms to school
because it denies students the ability to express their unique
identity. (reason)
Analyzing perspectives
Be careful that you offer reasons underlying the perspective and not just
a restatement of the perspective.
Examples:
We should require students to wear uniforms to school
because it is a good idea. (restatement)
We should require students to wear uniforms to school to
prevent students from wearing inappropriate clothes that
distract others from their studies. (reason)
Analyzing perspectives
Issue:
Required school uniforms
Perspective: Yes. School uniforms should be required
Reasons: They help to avoid the situations where clothes distract
students from their studying in class.
Perspective:
No, School uniforms are a bad idea.
Reasons: Students should have the right to wear what they want--to help them
establish their identity. We want them to be individuals, not lemmings.
Students should have the right to privacy and freedom of choice.
Perspective:
Reasons:
Yes. Uniforms are a good idea.
There are schools that have increased their achievement after
uniforms were required. It establishes a serious feeling tone.
It also helps students from poverty to not feel embarrassed
about not having the "cool" clothes.
Public Option Health Care
Issue:
Perspective:
Reasons:
In total support.
Health care is a right for all, not just for the rich. As long as
insurance companies decide, many will be denied that right.
The public option is the only fix.
Perspective: Totally against
Reasons: The government will put all other insurance out of business then bureaucrats will
decide on how and when we get our care.
This is a step toward socialism. People who want health care have it now through
Medicaid so there is no need.
Perspective:
Yes and no.
Reasons:
Just expand medicaid and we can provide care without changing the
private sector insurance.
Issue:
Perspective:
Reasons:
Perspective:
Reasons:
Perspective:
Reasons:
Increasing taxes on those making more than...
Analyzing Perspectives
For a targeted issue or situation about which people
react differently,
•Identify multiple perspectives, yours and/or the
perspectives of a range of others.
•Explain the reasons or reasoning underlying each
perspective.
•Avoiding judgment or rebuttal, continue to analyze in
order to accurately represent each perspective.
(Note: The same general perspective might have
multiple sets of reasons.)
Proposed rule--Limit soft-drink cup and bottle sizes at food service
establishments to no larger than 16 ounces. People could buy as
many as they want.
Issue:
Including state test scores in teacher evaluations
Perspective:
Reasons:
Perspective:
Reasons:
Perspective:
Reasons:
Unit: The novel The Grapes of Wrath
Original
Learning Goal: Know the plot, settings, themes in the novel.
Task: As you read this novel, keep a learning log that summarizes the major events,
settings, and themes of the novel
Make‐over
Learning Goal: Understand that authors use literature to
communicate beliefs and perspectives that can both influence and
reflect a society.
Reasoning Processes: Analyzing Perspectives
Task: This novel created controversy. There is a perspective that
Steinbeck wanted simply to expose the conditions of migrant
workers. However, others believed that he was trying to push
socialism, even communism, as preferable to capitalist evils.
Examine these two perspectives to identify the reasoning or logic
of each. Then identify and explain a completely different
perspective.
Issue:
Perspective:
Reasons:
Perspective:
Reasons:
Perspective:
Reasons:
Analyzing perspectives
Thesis
Develop/Support
Develop/Support
Develop/Support
Conclusion
Constructing
Support
Constructing Support
…is the process of developing a network of support for
assertions.
Constructing Support
Process Guidelines
•Identify whether you are stating facts that need to be
verified, or opinions that need to be supported.
•If you are stating an opinion, determine whether the
situation warrants supporting that opinion.
•When the situation warrants it, clearly state the point of
view you are supporting
•Use a variety of devices, such as facts, evidence,
examples, or appeals, to support the reasons for your
point of view.
Constructing Support
Process Guidelines
• Reflect on your work and articulate what you learned, e.g.,
what you notice that hadn’t occurred to you before,
what surprises and troubles you, or
what is confusing and clear.
Understanding Constructing Support
• Constructing Support is the process of developing a network
of support for assertions.
•This is used when supporting an assertion that is an
opinion.
•
The total national budget for Year A was $200B. Year
B, it was $275B.
Create a set of data that could be used to provide
multiple calculations to construct support for the
following:
 Military spending increased from Year A to Year B
 Military spending decreased from Year A to Year B
Fact or Opinion?
Fact or Opinion
1. I am the best, most qualified, candidate for the job.
2. I have been serving in the legislature for six years.
3. My opponent has not served in a public office before this.
4. My opponent is too inexperienced to be ready to do the job
on day one.
5. President Bush was wrong to go to war in Iraq.
6. My opponent voted for the war.
7. The wealthy should pay higher taxes than they do now.
8. 10% of the people pay 65% of the income taxes in this
country.
9. Global warming is being caused by human activity.
Fact or Opinion
or SPIN?
Fact or Opinion
or SPIN?
Boys got into a fight after playing the video
game Grand Theft Auto.
Fact or Opinion
or SPIN?
Indiana may soon be Rust Belts’ first “rightto-work” state.
Indiana senate passes anti-union “right-towork” bill.
A newspaper, under the Freedom of Information Act,
requested that several tech companies tell them how
many minorities they have working there.
A few companies (including giants like Apple, Google and
Yahoo!) refused the request. Headline?
Steve Jobs Tries to Cover Up
Apple’s Racial Profile
Fact, Opinion, or Spin
Fact, Opinion, or Spin
Fact, Opinion, or Spin
Fact or Opinion
or SPIN
Constructing Support
Process Guidelines
•Identify whether you are stating facts that need to be
verified, or opinions that need to be supported.
•If you are stating an opinion, determine whether the
situation warrants supporting that opinion.
•When the situation warrants it, clearly state the point of
view you are supporting
•Use a variety of devices, such as facts, evidence,
examples, or appeals, to support the reasons for your
point of view.
Constructing Support•Monitor the quality of the persuasive techniques to avoid
including fallacies or invalid reasoning (see Errors in
Reasoning).
•Assess and, when necessary, amend or modify your
arguments until you are confident about the strength of your
support .
Understanding Constructing Support
• Constructing Support is the process of developing a network
of support for assertions.
•This is used when supporting an assertion that is an
opinion.
• There can be logical, reasoned support or support that
includes devices and techniques used to manipulate.
The focus here is on “reasoned” support.
Persuasion or Manipulation?
What distinguishes persuasive
“reasoned support” from
“manipulation”?
• Asking a “teen idol” to try write a song to convince
young people not to smoke?
• Using a slogan (“just say no”) to prevent drug use.
• Scare tactics?
Constructing Support
Process Guidelines
•Identify whether you are stating facts that need to be
verified, or opinions that need to be supported.
•If you are stating an opinion, determine whether the
situation warrants supporting that opinion.
•When the situation warrants it, clearly state the point of
view you are supporting
•Use a variety of devices, such as facts, evidence,
examples, or appeals, to support the reasons for your
point of view.
Appeals
Persuasion or Manipulation?
Personality
Be persuaded because you like me…
Friendly, humble, funny,…
Rhetoric
Be persuaded because I SOUND good…”
Word choice, parallel construction, poetic
Tradition
Be persuaded because it is right…
Patriotic, Christian, American
Logic and Reason
Be persuaded because I offer sound arguments…
Reasoned ArgumentIrene
Evidence:
Last night five crimes were committed
within two blocks.
Claim:
Something must be done about the
escalating crime rates.
Elaboration:
That dramatic increase can be seen by
examining the documents….
Other cities have been able to reduce
crime rate, such as…
Qualifier:
Any of our actions must not infringe on
personal freedoms.
Reasoned Argument
Evidence:
Last night five crimes were committed
within two blocks.
Claim:
Something must be done about the
escalating crime rates.
Elaboration:
That dramatic increase can be seen by
examining the documents….
Other cities have been able to reduce
crime rate, such as…
Qualifier:
Any of our actions must not infringe on
personal freedoms.
Try one.
Proposed rule--Limit soft-drink cup and bottle sizes at food service
establishments to no larger than 16 ounces. People could buy as
many as they want.
•More than half of New York City adults (58%) are overweight or obese.
•The proportion of New York City adults who are obese increased from
18% to 23% between 2002 and 2010.
•Nearly 40% of New York City's public school students (K-8) are obese
or overweight.
•The percentage of New York City adults who have diagnosed diabetes
increased 16% between 2002 and 2010; nearly 10% of adult New
Yorkers now have diagnosed diabetes.
•The calorie-packed beverages consumers now down with abandon
increase the risk of diabetes, and are responsible for a big share of the
"massive suffering and premature death" linked to obesity.
•20 ounce bottle of Coca Cola has roughly the same calorie count as a
McDonald's hamburger
•Drinks that are more than half milk or 70 percent juice would be
exempt, and it wouldn't apply to lower-calorie drinks like water or diet
soda, or to alcoholic beverages.
Generate ideas for assigned the require “reasoned support” for these subject areas.
Subject areas
Reasoned arguments-- Examples
Music
...classical music is more complex than popular music
Visual arts
...the stained glass designs used in medieval
churches were the literary history of that time for an
illiterate society
PE/Health
Language arts
Math
Social Studies
Science
Colorado DOE Website
Analyzing
Errors in
Reasoning
Analyzing Errors in Reasoning
…is recognizing rhetorical strategies and fallacies.
Examining Errors in Reasoning
Process Guidelines
•Determine if the information being presented is important or is
intended to influence your beliefs or actions.
•If the information is important or intended to influence you,
identify statements or claims that are unusual, violate what you
know to be true, or seem wrong.
•Look for errors in the reasoning underlying the statements or
claims you have identified. (Faulty logic? Attacks? Weak
References? Misinformation?)
•If you find errors, seek clarification or more accurate information
before deciding to accept or reject the statement or claim.
Examining Errors in Reasoning
Process Guidelines
• Reflect on your work and articulate what you learned,
e.g.,
what you notice that hadn’t occurred to you before,
what surprises and troubles you, or
what is confusing and clear.
Examining Errors in Reasoning
Thoughtful Applications
•Monitor your own objectivity by insuring that the errors
you detect are actually errors in reasoning, not simply
claims or statements you disagree with.
•Continue to seek clarification or accurate information so
you are confident about accepting or rejecting the claim
or statement.
Examining Errors in Reasoning
Process Guidelines
•Determine if the information being presented is important or is
intended to influence your beliefs or actions.
•If the information is important or intended to influence you,
identify statements or claims that are unusual, violate what you
know to be true, or seem wrong.
•Look for errors in the reasoning underlying the statements or
claims you have identified. (Faulty logic? Attacks? Weak
References? Misinformation?)
•If you find errors, seek clarification or more accurate information
before deciding to accept or reject the statement or claim.
Girl Scalped by Berserk Tortilla-Making Machine
Fountain of Youth Found In NYC Subway Toilet
Elvis Is Dead, Alive, Dead, Alive and Alive Again.
Aliens Passing Gas are the Cause of the Hole in the Ozone Layer!
Hubby Sues Ex-Wife: Give Me Back My Kidney Now!
Man Marries Pet Goldfish and Takes It to Baltimore Aquarium For
Honeymoon.
Divorced Couple In Court Battle For Custody of Pet Cockroach
________________ want to push granny over the cliff.
________________ want country to go broke.
________________ want socialism in the USA.
________________ is launching a war on all women.
________________ want to kill babies.
________________ only care about their buddies.
________________ refuse to compromise.
Examining Errors in Reasoning
Process Guidelines
•Determine if the information being presented is important or is
intended to influence your beliefs or actions.
•If the information is important or intended to influence you,
identify statements or claims that are unusual, violate what you
know to be true, or seem wrong.
•Look for errors in the reasoning underlying the statements or
claims you have identified. (Faulty logic? Attacks? Weak
References? Misinformation?)
•If you find errors, seek clarification or more accurate information
before deciding to accept or reject the statement or claim.
• Get into groups of four and assign an A,B,C,D
• A- Faulty Logic
• B- Attacks
• C- Weak References
• D- Misinformation
Fallacies:
“You can’t prove the moon is not made of cheese, so it must be.”
Arguing from ignorance (can’t prove opposite)
“You are wrong because you are stupid and unethical.”
Arguing against the person (ad hominen)
“Agree with me because of a woman I met the other day with this
tragic story..”
Playing on emotion (sob stories)
“Pass this bill or this country is doomed.”
Using force and fear (you will be sorry)
“This is not very useful because you can’t do anything with it.”
Begging the question (circularity; assumes what it
must prove)
There is a perspective that doing a better job of
teaching these thinking skills should be considered by
educators as a “moral imperative.”
Others would argue that it is just not wise to
encourage teachers to teach these.
Analyze perspectives on both sides.
• Identify something you teach.
• Consider whether applying one of these processes
would help students to deepen their understanding.
• Describe the task and begin to do it according to the
processes we have learned.
• To what extent do you think that applying the
process would have the desired effect?
Analyzing and Generating
Logical Hypotheses
•Inductive Reasoning
•Deductive Reasoning
1. Taking a person’s life is always wrong. Capital punishment involves
taking a person’s life. Therefore, capital punishment is always wrong.
a. Inductive
b. Deductive
***
2. Six in ten children who are allowed to drink at home with their
parents become alcoholics later in life. Therefore, attitudes towards
drinking are formed by others near to us.
a. Inductive
b. Deductive
***
3. I noticed that when Mr. Jones teachers Contract Law, students have
achieved good results on the exam. This semester, Mr Jones is teaching
Contract Law. Therefore, students will do well in the exam.
a. Inductive
b. Deductive
***
Cats are
black and
have yellow
eyes.
Inductive
Reasoning
Cats are
black and
have yellow
eyes.
Inductive
Reasoning
Deductive
Reasoning
This is
gonna
hurt..
Inductive Reasoning
• Each time a kick a ball up in the air, it comes down. If I kick
this ball up in the air, it will come down.
Deductive Reasoning
• According to Newton’s Laws, what goes up must come down.
If I kick this ball up in the air, it will come down.
Inductive Reasoning
• Are there important unstated conclusions that could be
generated from observations or facts?
• Are there situations for which probable or likely conclusions
could be generated?
• Are there issues or situations for which students could
examine the inductive reasoning used?
Deductive Reasoning
• Are there generalizations (or rules or principles) that could be
applied to reach conclusions and make predictions?
• Are there topics or issues for which students could examine
the validity of the deductive reasoning used?
Cats are
black and
have yellow
eyes.
Inductive
Reasoning
Inductive Reasoning
Process Guidelines
• For a particular topic, focus on multiple pieces of
information or observations. Try not to assume
anything.
• Look for patterns or connections in the information you
have identified.
• Make a general statement that explains the patterns or
connections you have observed.
• Make more observations to see if you generalization
holds up; if it does not, change it as necessary.
Observation
Information
___________
___________
___________
___________
Observation
Information
___________
___________
___________
___________
Observation
Information
___________
___________
___________
___________
Observation
Information
___________
___________
___________
___________
General statement:__________________________________
__________________________________________________
__________________________________________________
__________________________________________________
More
Observations
Information
_____________
_____________
____________
Inductive Reasoning
Process Guidelines
•
Reflect on your work and articulate what you learned,
e.g.,
what you notice that hadn’t occurred to you before,
what surprises and troubles you, or
what is confusing and clear.
Inductive Reasoning
Thoughtful Application
• Assess the extent to which you are confident about the
general statement. Ask:
 Are there enough specifics to warrant a
conclusion?
 Is there anything I am missing or overlooking?
• Even if the statement holds up, consider generating
alternative general statements for the information or
observations
Deductive
Reasoning
This is
gonna
hurt..
Deductive Reasoning
Process Guidelines
•Identify a specific situation or item that is being studied.
•Consider generalizations or principles that might apply to the
specific situation or item.
•Determine whether the specific situation or item meets the
conditions that have to be in place for those generalizations
or principles to apply.
•If the conditions are met, identify what is known about the
specific situation, that is, what meaningful conclusions can
be drawn that would contribute to understanding the
specific situation or item.
Deductive Reasoning
Process Guidelines
• Reflect on your work and articulate what you learned, e.g.,
what you notice that hadn’t occurred to you before,
what surprises and troubles you, or
what is confusing and clear.
Deductive Reasoning
Most questions in the classroom ask for
Deductive Reasoning.
Classroom Examples, Page 153
Read explanation of Euler DiagramsPage 156-157
Draw a Euler for this relationship
He is a politician so he must be lying.
HE
Politicians
People
who
always lie
Draw a Euler for this relationship
He is a politician so he must be lying.
People who always lie
Politicians
HE
Draw a Euler for this relationship
All triangles have three sides that add to 180 degrees.
This is a triangle.
What do you know about “this”?
this
Things with three sides that add to 180 degrees
Triangles
this
Draw a Euler for this relationship
Some triangles have one 90 degree angle.
This is a triangle.
This
What do you know about “this”?
Things with one 90 degree angle
Triangles
This
This
This
Lewis Carroll
Puzzle 2— Raking in the Bucks
A. If I am paid $10.00, then I will buy the book.
B. If the leaves are falling, then I will rake them.
C. If I rake them, I will be paid $10.
Build your syllogism.
Final Conclusion:
If _____________________, then ___________________.
Lewis Carroll
Puzzle 3— Popcorn Friends
A. If you eat popcorn, then you will sneeze.
B. If you donʼt go to the dance, you wonʼt have any friends.
C. If you are sick, you wonʼt be able to go to the dance.
D. If you sneeze, then you are sick.
Final Conclusion:
If _____________________, then ____________________
Lewis Carroll
Puzzle 5— For Want of a Nail2
A. If the horseshoe is lost, then the horse will be lost.
B. If the horse is lost, then the knight will be lost.
C. If the horseshoe nail is lost, then the horseshoe will be lost.
D. If the battle is lost, then the kingdom will be lost.
E. If the knight is lost, then the battle will be lost.
Final Conclusion:
If ________________________, then _______________.
He is a politician so he must be lying.
People who always lie
Politicians
HE
Valid reasoning from untrue premises
SOMEONE at your school should develop expertise in
teaching Inductive and deductive reasoning...
Perhaps that “someone” is not YOU.
Deductive Reasoning
Thoughtful Application
• Assess carefully the extent to which you are confident
that the generalization or principle applies to the specific
situation. Ask:
Is there anything about the specific situation or item
that would preclude applying the generalization or
principle?
• Even if the generalization or principle seems to apply,
consider whether applying alternative generalizations or
principles would be useful.
“SCOPES”
(Progressions)
for
MEASUREMENT TOPICS
STRAND: Number Sense
MEASUREMENT TOPIC:
LEVEL 3
Place Value
LEVEL 1
LEVEL 2
LEVEL 4
Understands the
concept of place
value for numbers 119
Understand that the two
digits of a two-digit
number represent
amounts of tens and
ones
Understands that the
three digits of a threedigit number represent
amounts of hundreds,
tens, and ones
Understands the
concept of rounding
whole numbers to the
nearest 10 or 100
Knows 10 can be thought
of as a bundle of ten
ones - called a "ten"
Knows the numbers from
11-19 are composed of a
ten and one, two, three,
four, five, six, seven,
eight, or nine ones
Knows the numbers 10,
20, 30, 40, 60, 70, 80, 90
refer to one.....nine tens
and zero ones
Knows that 100 can be
thought of as a bundle of
ten tens - called a
"hundred"
Knows the numbers
100....900 refer to one,
two.....nine hundreds
and zero tens and zero
ones
Knows the symbols of
and meanings of the
following: >, =, <
Knows the term:
rounding
Knows from memory
multiplication of a
number by multiples of
10
4
In addition to the 3.
0 knowledge, infers
or applies BEYOND
WHAT WAS
TAUGHT
3
No major errors
or gaps in the
TARGETED,
COMPLEX
KNOWLEDGE
2
Knows the terms:
No major errors tens place, ones
or gaps in the place
SIMPLER,
FOUNDATIONAL
KNOWLEDGE
249
STRAND: Number Sense
MEASUREMENT TOPIC:
LEVEL 5
LEVEL 6
3
No major errors
or gaps in the
TARGETED,
COMPLEX
KNOWLEDGE
Understands place
value for multi-digit
whole numbers
Understands the
relationship between
place value and the
properties of
operations
Understand the place
value system: that a digit
in one place represents
10 times as much as it
represents in the place to
its right and 1/10 of what
it represents in the place
to its left
2
No major errors
or gaps in the
SIMPLER,
FOUNDATIONAL
KNOWLEDGE
Knows the rules for
rounding multi-digit
whole numbers to
any place
Knows the patterns in
the number of zeroes in
the product when
multiplying a number by
powers of 10.
Place Value
4
In addition to the 3.
0 knowledge, infers
or applies BEYOND
WHAT WAS
TAUGHT
250
Homework:
Become an overnight expert. 
For your assign reasoning process, read through
the DOL Manual and the Scales plus Process
Guidelines.
Be ready to facilitate your group’s conversation
about the reasoning process.
A= Problem Solving Pages 205-213
B= Experimental Inquiry Pages 224-233
C= Investigation Pages 234-245