Math1ubd

Situation 1
A housewife goes to a supermarket to buy grocery
items. At the dairy section she took the can of the milk that
is being advertised in the TV commercials to be creamy in
taste. Way back home, she found that the milk she bought
has less nutritional value than the other brands.
Situation 2
Rina learned that calcium is good for the bones and
can be derived from milk. She heard about the daily
calcium requirement that the body needs from a TV
commercial. With this information, she scout for the most
economical, creamy and rich in calcium milk at the grocery
store.
next

Training of Trainers ffoorr tthhee MMaassss TTrraaiinniinngg
ooff FFiirrsstt YYeeaarr TTeeaacchheerrss oonn tthhee 22001100 SSEECC
Bureau of Secondary Education
CURRICULUM DEVELOPMENT DIVISION
Session 1
Session 2
Session 3
Session 4
quit

Session 1: Understanding the Math
Curriculum Framework
• Explain the math framework as you
understand it.
• Any misconceptions?
• Share your thoughts on what you can do
and how you will deliver the desired
results.
• Fill up the matrix
“Something New, Something Better”.
• Answer this open-ended question:
The 2010 curriculum in math should
_______________________________
menu

CONCEPTUAL FRAMEWORK OF SECONDARY
MATHEMATICS PROGRAM
Functional Literacy for All
Problem Solving Communicating
Mathematically
Reasoning
Mathematically
Making Math
Connections and
Representations
Computational
skills and
Comprehension
Application to
Real Life
Creative and
Critical
Thinking
Visual Imagery
Math
VALUING
Integration with
Other Disciplines ICT Integration
Investigations/
Games & Puzzles
Practical Work/
Outdoor Activities
Experiential
Learning Constructivism Cooperative
Learning
Session 1

All students will...
Use multiple approaches to investigate and
understand mathematical content.
Formulate problems from everyday and
mathematical situations.
Develop and apply strategies to solve a
wide variety of problems, including multi-step
and non-routine problems.
Verify and interpret results with respect to
the original problem.
Generalize solutions and strategies to new
problem situations.
Acquire confidence in using mathematics
meaningfully.
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Recognize and formulate problems from
situations within and outside mathematics.
Apply the process of mathematical
modeling to real-world problem situations.
Explore and use multiple strategies for
solving problems.
Determine, collect, and analyze appropriate
data with respect to the original problem or
in new problem-solving situations.
Access and use appropriate problem-solving
tools, including calculators,
computers, and measurement devices.
Generalize problem-solving strategies to a
wide range of adult oriented, real-world
situations. framework

COMMUNICATING MATHEMATICALLY
Communication of mathematical ideas will help
students clarify and solidify their understanding
of mathematics. By sharing their mathematical
understandings in written and oral form with
their classmates, teachers, and parents,
students develop confidence in themselves as
mathematics learners and enable teachers to
better monitor their progress.
next

Relate physical materials, pictures, and diagrams
to mathematical ideas.
Reflect on and clarify thinking about mathematical
ideas and situations.
Relate everyday language to mathematical
language and symbols.
Use the skills of reading, listening, and viewing to
interpret and evaluate mathematical ideas.
Model situations by using oral, written, concrete,
pictorial, graphical, and algebraic methods.
next

Ask clarifying and extending questions related to
mathematics students have read or heard about.
Develop mathematical ideas, formulate mathematical
definitions, and express generalizations discovered
through investigations.
Appreciate the economy, power, and elegance of
mathematical notation and its role in the development
of mathematical ideas.
Develop the appropriate reading, writing, listening, and
speaking skills necessary for communicating
mathematically in a variety of settings.
next

Discuss mathematics with others, reflecting and
clarifying individual thinking about mathematical
outcomes.
Make convincing arguments and informed decisions.
Define everyday, work-related, or test-related
mathematical situations by using concrete, pictorial,
graphic, or algebraic methods.
Appreciate the value of mathematical language and
notation in relation to mathematical ideas.
framework

R e a s o n i n g M a t h e m a t i c a l l y
M a t h e m a t i c a l r e a s o n i n g i s t h e c r i t i c a l s k i l l t h a t e n a b l e s
a s t u d e n t t o m a k e u s e o f a l l o t h e r m a t h e m a t i c a l s k i l l s .
W i t h t h e d e v e l o p m e n t o f m a t h e m a t i c a l r e a s o n i n g ,
s t u d e n t s r e c o g n i z e t h a t m a t h e m a t i c s m a k e s s e n s e
a n d c a n b e u n d e r s t o o d . T h e y l e a r n h o w t o e v a l u a t e
s i t u a t i o n s , s e l e c t p r o b l e m - s o l v i n g s t r a t e g i e s ,
d r a w l o g i c a l c o n c l u s i o n s , d e v e l o p a n d d e s c r i b e
s o l u t i o n s , a n d r e c o g n i z e h o w t h o s e s o l u t i o n s c a n
b e a p p l i e d . M a t h e m a t i c a l r e a s o n e r s a r e a b l e t o r e f l e c t
o n s o lu t i o n s t o p r o b l e m s a n d d e t e r m i n e w h e t h e r
o r n o t t h e y m a k e s e n s e . T h e y a p p r e c i a t e t h e p e r v a s i v e
u s e a n d p o w e r o f r e a s o n i n g a s a p a r t o f m a t h e m a t i c s .
next

A l l s t u d e n t s w i l l . . .
D r a w l o g i c a l c o n c l u s i o n s a b o u t m a t h e m a t i c s .
U s e m o d e l s , k n o w n f a c t s , p r o p e r t i e s , a n d r e l a t i o n s h i p s t o
e x p l a i n m a t h e m a t i c a l t h i n k i n g .
J u s t i f y s o l u t i o n s a n d e x p l a i n s o l u t i o n p r o c e s s e s .
U s e p a t t e r n s a n d r e l a t i o n s h i p s t o a n a l y z e m a t h e m a t i c a l
s i t u a t i o n s .
B e l i e v e t h a t m a t h e m a t i c s m a k e s s e n s e .
next

R e c o g n i z e a n d a p p l y d e d u c t i v e a n d i n d u c t i v e r e a s o n i n g .
M a k e a n d e v a l u a t e m a t h e m a t i c a l c o n j e c t u r e s a n d
a r g u m e n t s .
F o l l o w l o g i c a l a r g u m e n t s .
J u d g e t h e v a l i d i t y o f a r g u m e n t s .
A p p r e c i a t e t h e p e r v a s i v e u s e a n d p o w e r o f r e a s o n i n g
a s a p a r t o f m a t h e m a t i c s .
next

D r a w l o g i c a l c o n c l u s i o n s f r o m m a t h e m a t i c a l s i t u a t i o n s ,
u s i n g c o n c r e t e m o d e l s a n d v e r b a l s k i l l s .
U n d e r s t a n d a n d a p p l y d e d u c t i v e , i n d u c t i v e a n d p r o p o r t i o n a l
r e a s o n i n g , w i t h s p e c i a l a t t e n t i o n t o s p a t i a l a n d v i s u a l
r e a s o n i n g w i t h p r o p o r t i o n s a n d g r a p h s .
P o s e m a t h e m a t i c a l q u e s t i o n s a n d e v a l u a t e a r g u m e n t s .
V a l i d a t e i n d i v i d u a l t h i n k i n g a n d i n t u i t i o n .
S e e h o w m a t h e m a t i c s m a k e s s e n s e .
framework

Mathematical Connections
and Representations
Making connections enables students to see
relationships between different topics and to
draw on those relationships in future study.
This applies within mathematics, so that
students can translate readily between fractions
and decimals, or between algebra and
geometry; to other content areas, so that
students understand how mathematics is used
in the sciences, the social sciences, and the
arts; and to the everyday world, so that
students can connect school mathematics to
daily life.
next

Representations are necessary to students'
understanding of mathematical concepts and
relationships. Representations allow students to
communicate mathematical approaches,
arguments, and understanding to themselves
and to others. They allow students to recognize
connections among related concepts and apply
mathematics to realistic problems.
next

Link conceptual and procedural knowledge.
Relate various representations of concepts or
procedures to one another.
Recognize and value the relationships among
different topics in mathematics.
Use mathematics in other curriculum areas and in
daily living.
Explore problems and describe results by using
graphical, numerical, physical, algebraic, and verbal
mathematical models or representations. next

Apply mathematical thinking and modeling to solve
problems that arise in other disciplines.
Recognize equivalent representations of the same
concept.
Relate procedures in one representation to
procedures in an equivalent representation.
View mathematics as an integrated whole, which is
connected to past learning, the real world, adult life
skills, and work-related settings.
next

Explore problems by using appropriate technology,
and describe results by using a variety of
mathematical models and representations.
create and use representations to organize, record,
and communicate mathematical ideas;
select, apply, and translate among mathematical
representations to solve problems;
use representations to model and interpret physical,
social, and mathematical phenomena.
framework

Experiential learning is the process of making
meaning from direct experience. It is learning
through reflection on doing.
framework

Constructivism is a theory of knowledge which
argues that humans generate knowledge and
meaning from their experiences.
framework

Cooperative learning is an approach to
organizing classroom activities into academic and
social learning experiences. Students must work in
groups to complete the two sets of tasks
collectively. Everyone succeeds when the group
succeeds.
framework

Write in the “Something New” column the new thrusts in your teaching
that you commit to implement in light of the requirements of the Math
curriculum. In the “Something Better” column, you will write the
improvements in your teaching you commit to make.
Something New Something Better
Session 1

Session 2: Understanding Stage 1
• What are the common elements of Stage 1
across quarters?
• Analyze across quarters the relationship
between the elements and the purpose each of
them serves.
• Share your observations.
• How is the Content Standard formulated?
• Examine the Performance Standard and specify
the performance expected of learners.
• In unpacking the Content Standards, write in
meta strips what students are expected to know
(knowledge) and do (skills).
menu

• CCoonntteenntt ssttaannddaarrddss
What learners should know,
understand and be able to do?
• PPeerrffoorrmmaannccee ssttaannddaarrddss
What learners should create/
add value to/transfer?
Demonstrate
understanding
EEsssseennttiiaall
UUnnddeerrssttaannddiinngg
((EEUU))
Perform
understanding
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Quarter I: Topic: Time Frame:
Stage 1
Content Standard: Performance Standard:
Essential Understanding(s):
Essential Question(s):
The learner will know: The learner will be able to:
Stage 2
Product or Performance Task: Evidence at the level
of understanding
Learner should be able to
demonstrate
understanding of
_________________ using
the six (6) facets of
understanding:
Evidence at the level of
performance
Stage 3
Teaching/Learning Sequence
Resources (websites, courseware, etc.)
Materials/Equipment Needed
Session 2

Stage 1 – Desired Results
Established Goals:
• What relevant goals (e.g., content standards, course or program objectives, learning
outcomes) will this design address?
Content Standards:
· What should students know and be able
to do?
Performance Standards:
·How well must students do their work?
·At what level of performance would the student
be appropriately qualified or certified?
Essential Understandings (EU):
Students will understand that . . .
• What are the big ideas?
• What specific understandings about them
are desired?
• What misunderstandings are predictable?
Essential Questions (EQ):
• What provocative questions will foster inquiry,
understanding, and transfer of learning?
· Provocative questions
-have no one obvious right answer
-raise other important questions
-address the philosophical or conceptual
foundations of a discipline
-recur naturally
-are framed to provoke and sustain learner
interest
Students will know. . .
• What key knowledge and skills will
students acquire as a result of this unit?
• What should they eventually be able to
do as a result of such knowledge and skills?
Students will be able to . . .
Session 2

MATHEMATICS I
General Standard: The learner demonstrates understanding of key concepts and principles of number and number sense as applied to
measuring, estimating, graphing, solving equations and inequalities, communicating mathematically and solving problems in real life.
QUARTER I (Real Number System, Measurement and Scientific Notation)
Stage 1: Results/Outcomes Stage 2: Assessment
STANDARDS ESSENTIAL
Product/
Performance
At the
Level of
Content Performance Understanding Question Understanding Performance
The learner
The learner
Daily tasks involving
demonstrates
formulates real-life
measurement,
understanding
problems involving
conversion,
of the key
real numbers,
estimation and
concepts of real
measurements and
scientific notation
number
scientific notation
make use of real
systems,
and solves these
numbers.
measurements
using a variety of
and scientific
strategies.
notation.
How useful are
Problems
Assessment of problems
real numbers?
formulated
formulated based on the
1.are real life
following suggested
2.involve real
criteria:
numbers,
·real-life problems
measurement and
·problems involve real
scientific notation
numbers, measurement
and
and scientific notation
3.are solved using a
·problems are solved
variety of strategies.
using a variety of
strategies
Tools: Rubrics for
assessment of problems
Physical quantities formulated and solved
are measured using
different measuring
devices. The
precision of the
measurement is
dependent on the
measuring device
used.
Explanation
Express numbers
in different ways
and explain.
Criteria:
Thorough
Coherent
Explain how to
use the calibration
model and find
its degree of
precision
Criteria:
Accurate
Justified
Express big and
small quantities in
scientific notation
Criteria:
Accurate
Justified
Interpretation
“Tell a Story” of
situations where
numbers are used
or how measuring
devices are used.
How are
different
measuring
devices useful?
How does one
know when a
measurement is
precise?
accurate?
Session 2

Which define what students should be able to know and
do at the end of the program, course, or unit of study;
generally expressed in terms of overall goals, and
specifically defined in terms of content and
performance standards.
template

Which specify the essential knowledge (includes the
most important and enduring ideas, issues, principles
and concepts from the disciplines), skills and habits
of mind that should be taught and learned. They
answer the question, “What should students know
and be able to do?”.
template

Which express the degree or quality of proficiency that
students are expected to demonstrate in relation to the
content standards. They answer the question, “How well
must students do their work?” or “At what level of
performance would the student be appropriately
qualified or certified?”
template

Which are the big and enduring ideas at
the heart of the discipline and which we
want the children to remember even long
after they leave school.
template

Which are open-ended, provocative questions
that spark thinking and further inquiry into the
essential meanings and understandings.
template

Which are expressed in terms of knowledge
and skills that teachers can use as guide in
formulating their own classroom objectives.
template

Session 3: Understanding Stage 2
• What is the relationship between the EU and assessment?
• Analyze the following:
 the relationship between the Performance Standards and
the Products and Performances across quarters;
 what Products and Performances are for; and
 How Products and Performances may be differentiated.
• How would you link the Facets of Understanding to the
assessment of the attainment of the Content Standard?
• Formulate questions using the FUs.
• Formulate assessment tools for Products and Performances.
• Express orally or in writing your understanding of Stage 2.
menu

MATHEMATICS I
General Standard: The learner demonstrates understanding of key concepts and principles of number and number sense as applied to
measuring, estimating, graphing, solving equations and inequalities, communicating mathematically and solving problems in real life.
QUARTER I (Real Number System, Measurement and Scientific Notation)
Stage 1: Results/Outcomes Stage 2: Assessment
STANDARDS ESSENTIAL
Product/
Performance
At the
Level of
Content Performance Understanding Question Understanding Performance
The learner
The learner
Daily tasks involving
demonstrates
formulates real-life
measurement,
understanding
problems involving
conversion,
of the key
real numbers,
estimation and
concepts of real
measurements and
scientific notation
number
scientific notation
make use of real
systems,
and solves these
numbers.
measurements
using a variety of
and scientific
strategies.
notation.
How useful are
Problems
Assessment of problems
real numbers?
formulated
formulated based on the
1.are real life
following suggested
2.involve real
criteria:
numbers,
·real-life problems
measurement and
·problems involve real
scientific notation
numbers, measurement
and
and scientific notation
3.are solved using a
·problems are solved
variety of strategies.
using a variety of
strategies
Tools: Rubrics for
assessment of problems
Physical quantities formulated and solved
are measured using
different measuring
devices. The
precision of the
measurement is
dependent on the
measuring device
used.
Explanation
Express numbers
in different ways
and explain.
Criteria:
Thorough
Coherent
Explain how to
use the calibration
model and find
its degree of
precision
Criteria:
Accurate
Justified
Express big and
small quantities in
scientific notation
Criteria:
Accurate
Justified
Interpretation
“Tell a Story” of
situations where
numbers are used
or how measuring
devices are used.
How are
different
measuring
devices useful?
How does one
know when a
measurement is
precise?
accurate?
Session 3

What is evidence of understanding?
Learners truly understand when they:
• can explain
• can interpret
• can apply
• have perspective
• can emphatize
• have self-knowledge
Session 3

Provides thorough, supported, and
justifiable accounts of phenomena,
facts and data.
(Describe – Express – Justify – Predict
- Synthesize)
Facets

Tells meaningful stories, provides a
revealing historical or personal
dimension to ideas and events; makes
it personal or accessible through
images, anecdotes, analogies, and
models.
(Be aware of – Realize – Recognize –
Reflect -- Self-assess)
Facets

Effectively uses and adapts what is
known in diverse context.
(Build –Create – Design – Perform –
Solve)
Facets

Can see and hear points of view
through critical eyes and ears, sees
the big picture.
(Analyze – Argue – Compare –
Contrast – Infer)
Facets

Finds value in what others might find
odd, alien, or implausible; perceives
sensitively on the bases of prior direct
experience.
The ability to get inside another
person’s feelings and worldview.
(Assume role of – Consider – Imagine –
Relate – Role play)
Facets

Perceives the personal style, prejudices,
projections, and habits of mind that both
shape and impede their own understanding.
The wisdom to know one’s ignorance and
how one’s patterns of thought and action
inform as well as prejudice understanding.
(Be aware of – Realize – Recognize – Reflect
-Self-assess)
Facets

Interpretation
Explanation
Application

Perspective
Self-Knowledge
Empathy

Session 44:: UUnnddeerrssttaannddiinngg SSttaaggee 33
• IInntteerrpprreett yyoouurr iiddeeaass aabboouutt tthhee ffoolllloowwiinngg;;
 WWHHEERREETTOO ddeessiiggnn pprriinncciipplleess;; aanndd
 44--pphhaassee tteeaacchhiinngg//lleeaarrnniinngg sseeqquueennccee..
• DDoo aa mmiiccrroo tteeaacchhiinngg ooff eeaacchh pphhaassee ooff tthhee lleessssoonn
iinn QQuuaarrtteerr 11 ((44 tteeaacchheerrss,, ii..ee..,, 11 tteeaacchheerr ffoorr eeaacchh
pphhaassee))..
• GGiivvee yyoouurr ccoommmmeennttss aanndd oobbsseerrvvaattiioonnss aabboouutt
tthhee mmiiccrroo tteeaacchhiinngg..
• WWhhaatt aarree yyoouurr eennrriicchhmmeenntt((ss))// mmooddiiffiiccaattiioonn((ss))
yyoouu wwoouulldd pprrooppoossee ttoo mmaakkee oonn tthhee lleessssoonn??
menu

• EExxpplloorree
• FFiirrmm UUpp
• DDeeeeppeenn
(Create, add
• TTrraannssffeerr
value)
UU nn dd ee rr ss tt aa nn dd ii nn gg
C o n t e n t S t a n d a r d Performance Standard
AA ss ss ee ss ss mm ee nn tt
W H E R E T O
Session 4

WW HH EE RR EE TT OO
WW - How shall we help learners know wwhheerree they are
headed (the learning goals) and why they are
going there (reason for learning the content)?
WWhhaatt is expected (unit goal and performance
requirements)?
In wwhhaatt ways will learners be evaluated
(evaluation criteria)?
next

Questions to consider for W
Goals:
• Where are we going in this unit or course?
• What are the goals or standards toward which we
are going?
• What will students be learning?
• What resources and learning experiences will help
us get there?
Relevance & Value:
• Why is this worth learning?
• In what ways will this knowledge or these skills
benefit students in school? In the future?
next

Examples for W
Goals:
• Directly state the desired results at the beginning of the unit.
• Present unit & course goals, syllabus, & schedule on first day.
• Post and discuss EQs at the start of the unit.
• Invite students to generate questions.
• Ask students to identify personal goals.
Relevance & Value:
• Present the rationale for the unit & course goals.
• Discuss the benefits to students.
• Identify people & place beyond the classroom where this
knowledge & these skills are applied.
• Use K-W-L to have students identify things they want to learn.
next

Questions to consider for W
Expectations:
• What is expected of students?
• What are key assignments and assessments?
• In what ways will students be expected to
demonstrate learning? Understanding?
• What criteria and performance standards will be
used for assessment?
Diagnosis:
• From where are students coming?
• What prior knowledge, interests, learning styles,
talents do they bring?
• What misconceptions may exist?
next

Examples for W
Expectations:
• Present the culminating performance task requirements.
• Review scoring rubrics.
• Show models and exemplars for expected products &
performances.
• Involve students in identifying preliminary evaluation
criteria.
Diagnosis:
• Give a pretest on content knowledge.
• Give a diagnostic skills test.
• Use K-W-L to see what students already know (or think they
know).
• Have students create a visual organizer to reveal their initial
knowledge & understandings.
• Check for possible & probable misconceptions.
WHERETO

HH - How shall we help hhooookk and engage
learners’ interest through thought-provoking
experiences at the
beginning of instructional episode
(digging into the EUs thru inquiry,
research, problem-solving,
experimentation)?
next

Hooking aanndd HHoollddiinngg SSttuuddeennttss
BBrraaiinnssttoorrmm oonn hhooww wwiillll yyoouu hhooookk && hhoolldd
ssttuuddeenntt iinntteerreesstt??
• OOdddd ffaacctt,, aannoommaallyy,, ccoouunntteerriinnttuuiittiivvee eexxaammppllee
• PPrroovvooccaattiivvee eennttrryy qquueessttiioonn
• MMyysstteerryy
• CChhaalllleennggee
• PPrroobblleemm oorr iissssuuee
• EExxppeerriimmeenntt –– pprreeddiicctt oouuttccoommee
• RRoollee ppllaayy oorr ssiimmuullaattiioonn
• PPeerrssoonnaall eexxppeerriieennccee
• AAllllooww ssttuuddeenntt cchhooiiccee ffoorr
• EEmmoottiioonnaall ccoonnnneeccttiioonn
• HHuummoorr
WHERETO

EE - What eexxppeerriieenncceess shall we provide
to help learners make their
understandings real?
How shall we eeqquuiipp them for success
throughout the unit or course?
next

EEqquuiippppiinngg SSttuuddeennttss
EExxppeerriieenncciinngg && IInndduuccttiivvee LLeeaarrnniinngg
• What experiential or inductive learning will
help students to explore the EUs and EQs?
Direct Instruction
• What information or skills need to be taught
explicitly to equip students?
Homework & Other Out-of-Class
Experiences
• What homework & other out-of-class
experiences are needed to equip students?
next

Examples ooff EEqquuiippppiinngg SSttuuddeennttss
EExxppeerriieenncciinngg && IInndduuccttiivvee LLeeaarrnniinngg
• Concept attainment
• Research/I-Search project
• Historical investigation
• Scientific experimentation
• Problem-based learning
• Creative expression
• Artistic or production
• Exploration of issues
• Construction project
• Socratic seminar
• Simulation
next

DDiirreecctt IInnssttrruuccttiioonn
To help students:
• Compare ideas & information
• Find information (e.g. research)
• Evaluate information & ideas
• Generate & test hypothesis
• Communicate ideas
• Manage their time
• Monitor their understanding
• Organize information
• Persuade
• Review each other’s work
• Revise their own work
• Use problem-solving strategies
• Self-evaluate
• Summarize key ideas
next

HHoommeewwoorrkk && OOtthheerr OOuutt--ooff--CCllaassss EExxppeerriieenncceess
• Practicing Skills
• Reading with a purpose
• Working on project or performance task
• Studying & synthesizing information (e.g.
create a concept map)
• Reflecting on ideas, process, or product
(e.g. journal entry)
• Revising work
next

Equipping SSttuuddeennttss ffoorr PPeerrffoorrmmaannccee
HHiissttoorriiccaall RRoollee--PPllaayy
PPeerrffoorrmmaannccee TTaasskk oorr OOtthheerr EEvviiddeennccee::
AAssssuummee tthhee rroollee ooff aa hhiissttoorriiccaall cchhaarraacctteerr & rroollee--ppllaayy hheerr ppaarrttiicciippaattiioonn
iinn aa ddeebbaattee oonn aa ccuurrrreenntt iissssuuee..
To successfully perform, the
student will have to know:
Rules of devate
Debate procedure
and be able to:
Succinctly state a position
Use rebuttal techniques
THEN, what teaching &
learning experiences will be
needed to equip him/her for a
successful performance?
• Review the rule of debate
• Show videotape excerpts of
debates to illustrate the
procedure & effective debating
strategies
• Teach rebuttal techniques
next

Equipping SSttuuddeennttss ffoorr PPeerrffoorrmmaannccee
PPeerrffoorrmmaannccee TTaasskk oorr OOtthheerr EEvviiddeennccee::
To successfully perform, the
student will have to know:
__________________________
__________________________
and be able to:
__________________________
__________________________
THEN, what teaching &
learning experiences will be
needed to equip him/her for a
successful performance?
• _______________________
• _______________________
• _______________________
• _______________________
WHERETO

RR - How shall we cause learners to
rehearse, rreefflleecctt, rreevviissiitt, rreevviissee,
refine, and rreetthhiinnkk bbaasseedd uuppoonn
ttiimmeellyy ffeeeeddbbaacckk?
next

QQuueessttiioonnss ttoo CCoonnssiiddeerr ffoorr RR
RReetthhiinnkk
• WWhhaatt EEUUss ddoo wwee wwaanntt ssttuuddeennttss ttoo rreetthhiinnkk??
• HHooww wwiillll yyoouurr ddeessiiggnn cchhaalllleennggee ssttuuddeennttss ttoo rreevviissiitt iimmppoorrttaanntt
iiddeeaass??
RReevviissee oorr RReeffiinnee
• WWhhaatt sskkiillllss nneeeedd ttoo bbee pprraaccttiicceedd && rreehheeaarrsseedd??
• HHooww mmiigghhtt ssttuuddeenntt pprroodduuccttss && ppeerrffoorrmmaanncceess bbee iimmpprroovveedd??
RReefflleecctt
• HHooww wwiillll yyoouu eennccoouurraaggee ssttuuddeennttss ttoo rreefflleecctt uuppoonn
 tthheeiirr lleeaarrnniinngg && tthhiinnkkiinngg??
 TThhee eevvoolluuttiioonn ooff tthheeiirr uunnddeerrssttaannddiinngg??
 TThheeiirr uussee ooff ssttrraatteeggiieess??
• HHooww wwiillll yyoouurr ddeessiiggnn hheellpp ssttuuddeennttss ttoo bbeeccoommee mmoorree
mmeettaaccooggnniittiivvee??
next

EExxaammpplleess ooff RR
RReetthhiinnkk
HHeellpp ssttuuddeennttss rreetthhiinnkk bbyy hhaavviinngg tthheemm::
• SShhiifftt ppeerrssppeeccttiivvee
• RReeccoonnssiiddeerr kkeeyy aassssuummppttiioonnss
• CCoonnffrroonntt aalltteerrnnaattiivvee vveerrssiioonnss
• TTaakkee tthhee rroolleess ooff ……
• PPllaayy ddeevviill’’ss aaddvvooccaattee
• RReeeexxaammiinnee tthhee aarrgguummeenntt aanndd eevviiddeennccee
• CCoonndduuccttss rreesseeaarrcchh
• CCoonnssiiddeerr nneeww iinnffoorrmmaattiioonn
• RReetthhiinnkk tthhee nnaaïïvvee iiddeeaa tthhaatt ……
• AArrgguuee && ddeebbaattee
• CCoonnffrroonntt ssuurrpprriisseess && aannoommaalliieess
next

RReevviissee oorr RReeffiinnee
PPrroovviiddee ooppppoorrttuunniittiieess ffoorr ssttuuddeennttss ttoo rreevviissee &&
rreeffiinnee tthheeiirr wwoorrkk tthhrroouugghh::
• DDrraaffttiinngg && eeddiittiinngg sseessssiioonnss
• PPeeeerr ccrriittiiqquueess
• RReehheeaarrssaallss
• PPeeeerr rreessppoonnssee ggrroouuppss
• PPrraaccttiiccee sseessssiioonnss
• SSeellff--aasssseessssmmeenntt
next

RReefflleecctt
EEnnccoouurraaggee ssttuuddeennttss ttoo rreefflleecctt tthhrroouugghh tthhee uussee ooff::
• RReefflleeccttiivvee jjoouurrnnaallss && tthhiinnkk llooggss
• RReegguullaarr sseellff--aasssseessssmmeennttss
• MMeettaaccooggnniittiivvee pprroommppttss
• TThhiinnkk aalloouuddss
• II –– SSeeaarrcchh ppaappeerrss
WHERETO

EE - How shall learners eexxpprreessss their
understandings and eennggaaggee in
meaningful self-eevvaalluuaattiioonn ooff tthheeiirr
wwoorrkk?
next

Encouraging SSeellff--EEvvaalluuaattiioonn –– EE
• What do you really understand about _____________________?
• What questions & uncertainties do you still have about _________?
• What was most effective in _________________________________?
• What was least effective in _________________________________?
• How could you improve ___________________________________?
• What are your strengths in _________________________________?
• What are your deficiencies in _______________________________?
• How difficult was _________________________________________?
• How does your preferred learning style influence ______________?
• What would you do differently next time ______________________?
• What are you most proud of? Why?___________________________
• What are you most disappointed in? Why? ___________________?
• What grade or score do you deserve? Why? __________________?
• How does what you’ve learned connect to other learnings?______?
• How has what you’ve learned relate to the present & future?_____?
• What follow-up work is needed? ____________________________?
• Other: __________________________________________
WHERETO

TT - How shall we ttaaiilloorr (differentiate)
our instruction to address the unique
strengths and needs of every learner
(flexible to interests & learning styles)?
next

Tailoring the Design ffoorr DDiivveerrssee LLeeaarrnneerrss
CCoonntteenntt
• At the beginning of a unit, assess prior
knowledge & skills, & develop differentiated
activities to accommodate different knowledge
& skill levels.
• Provide students with open-ended questions,
activities, assignments that enable students to
give different but equally valid responses.
• Appeal to various modalities (e.g. present information
orally, visually, & in writing).
• Use a variety of resource materials (e.g. multiple reading
materials at different levels) to help students understand
a difficult concept.
next

Tailoring tthhee DDeessiiggnn ffoorr DDiivveerrssee LLeeaarrnneerrss
PPrroocceessss
• Accommodate students with different
learning styles by providing
opportunities for them to work alone and
in groups.
• Encourage students to develop their own
research questions for in-depth
exploration of a key idea or question.

Tailoring tthhee DDeessiiggnn ffoorr DDiivveerrssee LLeeaarrnneerrss
PPrroodduucctt
• Allow students choices of products (e.g.
visual, written, oral) for activities &
assignments.
• Provide students with options for
demonstrating understanding through
various products and performances
without compromising the goals or
standards.
WHERETO

OO - How shall we oorrggaanniizzee learning
experiences so that learners move
from teacher-guided and concrete
activities to independent applications
that emphasize growing conceptual
understandings (sequenced to
maximize engagement & effectiveness)?
next

OOrrggaanniizziinngg tthhee LLeeaarrnniinngg
TThhee LLooggiicc ooff ““CCoovveerraaggee””
What is most appropriately and effectively
covered in a linear & didactic fashion?
• Present information in a logical, step-by=step fashion
(Teacher as tour guide).
• Follow the sequence of the textbook.
• Move from the facts & basic skills to the more advanced
concepts & processes.
• Expose students to a breadth of material dictated by
established goals.
• Use hands-on & other experiential activities selectively
because these can make considerable time.
• Teach & test the discrete pieces before having students
apply what they are learning.
next

OOrrggaanniizziinngg tthhee LLeeaarrnniinngg
TThhee LLooggiicc ooff ““UUnnccoovveerraaggee””
What is most appropriately and effectively
“uncovered” in an inductive, inquiry-oriented
experiential manner?
• Begin with a hook and teach on an as-needed basis. Don’t
front load all of the information before application.
• Make the sequence more surprising & less predictable.
• Ensure that there are ongoing cycles of model, practice,
feedback & adjustment built into the unit.
• Focus on transferable, EUs
• Move back & forth between the whole & the parts rather
than teaching all the little bits first, out of context (Think of
sports, the arts, and vocational/technical projects.
Session 4

LLeeaarrnniinngg//IInnssttrruuccttiioonnaall PPllaann
I. EExxpplloorree
• Diagnose.
• Activate prior knowledge.
• Clarify expectations and how learning shall be assessed:
standards; products/performances; criteria; tools.
• Hook and engage learner interest.
• Ask EQ; encourage learner questions; welcome tentative
responses as guide to further exploration.
WHERETO

II. FFiirrmm UUpp
• Provide variety of learning resources (books, videos,
readings/documents, web-based resources, etc) and
differentiated activities to validate responses to EQ;
process learners’ meanings and check these against
the EU.
• Encourage learners to reflect, revise, or rethink their
understanding.
• Check for understanding; provide feedback; check
against content standard.
WHERETO

III. DDeeeeppeenn
• Provide variety of learning resources and
differentiated activities/learning experiences in similar
contexts to further validate learner understanding.
• Encourage learners to reflect, rethink, revise their
understanding.
• Have learners express their understanding.
• Check for mastery of EU; provide feedback; check
against content standard.
WHERETO

IV. TTrraannssffeerr
• Provide for transfer of learning to a new or
different context.
• Evaluate product/performance; check
against performance standard.
WHERETO

Quarter I: Topic: Time Frame:
Stage 1
Content Standard: Performance Standard:
Essential Understanding(s):
Essential Question(s):
The learner will know: The learner will be able to:
Stage 2
Product or Performance Task: Evidence at the level
of understanding
Learner should be able to
demonstrate
understanding of
_________________ using
the six (6) facets of
understanding:
Evidence at the level of
performance
Stage 3
Teaching/Learning Sequence
Resources (websites, courseware, etc.)
Materials/Equipment Needed
Session 4

TThhaannkk yyoouu aanndd MMAABBUUHHAAYY!!
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