1. Warm Up
   
 
In the above addition, all the s represent distinct digits. How small can you make the 2-digit sum?
Can A Frist Grader Do This?
It is not hard; according to our standards—a first grade problem (1.NBT.4).  But you still need to use many SMPs to get to the bottom of it.
Way bottom, pun not intended, scroll down there if you wish to check your work or desperately need the answers.
39 98

2. Can A Frist Grader Do This?
1.NBT.C.4 Add within 100…
1.OA.A.1 … by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.

3. Minimum Sum
A B
+ C D
E F
In the above addition, all the letters represent distinct digits. How small can you make the 2-digit sum EF?
It is not hard; according to our standards—a first grade problem (1.NBT.4).  But you still need to use many SMPs to get to the bottom of it.
Way bottom, pun not intended, scroll down there if you wish to check your work or desperately need the answers.
39 98

4. Seeing the Whole Elephant!
Day 4!
Jennings;
the second of Gödel’s incompleteness theorems states that no consistent system can prove its own consistency, meaning that no sane mind can prove its own sanity
“I would never die for my beliefs because I might be wrong.” ― Bertrand Russell
Who is this short Asian?
NISL asked me to come here to point you to the moon, so do not just look at my finger.
Be humble, not American bashing...
Mirror helps you straighten your tie, don’t break the mirror or shoot the messenger.
Chekov’s gun?
Elephant
Peter Jennings “More than one truth.”
[ Poll audience for grade levels; Elephant! ]
serious reality + serious reflection
pointing you to the moon
zoom out and look at the sandbox of Ed
Andrew Chen
Seeing the Whole Elephant! Leadership for Excellence in Mathematics
NISL Course 2, UNIT 6
EduTron

5. "The Music Is Not in the Guitar" and Other Lessons from Yoda and Morpheus
Permission to speak my mind in plain English.
Gesture.
Longview; issues kept me up at night. Analytical!! Humble.
Andrew Chen
Standards Institute
UnboundEd
June 29, 2017
Orlando FL, U.S.A.
EduTron

6. Later today: Grade Level
Now: see how topics progress across grades & zoom in to some critical ones.
Not an insult when… AJ, Chuck, Catelin

7. Free App: Photo Math
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8. Computational Fluency
Balance (“Rigor”)
K-12 Mathematics
Conceptual Understanding
Problem Solving
A random collection of rules to get to the right answer…
Coach baseball team?
risk of teaching only procedures and not the other two legs if teachers hold on to feelings that kids are not motivated or they don’t have time.
Computational Fluency
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9. Which Leg Is Missing? 8 x 24 =? 24  8 =? 8  24 =?
One inch is 2.54 cm (centimeters). How many inches are in 8 cm?
One pound of apple is $2.54. How many pounds can $8 buy?
One pound of apple is $2. How many pounds can $8 buy?
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10. Prep “Classroom”

11. Piling Cubes Ms. Gerson has 48 identical cubes, each with 3-cm edges.
She glues them all together to form a rectangular solid.
If the perimeter of the base is 42 cm,
find the surface area of the rectangular solid (in square centimeters).

12. Standards for Mathematical Practice in Common Core Standards
Make sense of problems & persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Use appropriate tools strategically.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated reasoning.
We learned not to dictate pedagogy. CCS has theses nice practice standards.
K-12 Habits of Mind.
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13. Core Action Reflections
Have I observed Focus, Coherence, and Rigor in the interaction?
What does it feel like as a student in this simulated classroom? What worked?
What would I like our teachers to be able to learn from this classroom? What worked?

14. Designer Numbers II
A, B, C, D, E, and F are numbers as indicated on the following number line:
How can one construct the largest number using one operation (+ - x ) of two of these numbers ? 
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15. Solve for a b c d e f
Solve for the variables a through f in the system of equations below, using the digits from 0 through 5. Every digit should be used only once. A variable has the same value everywhere it occurs, and no other variable will have that value.
a + a + a = a2
b + c = b
d × e = d
a – e = b
b2 = d
d + e = f
A = 0 or 3, must be 3
C = 0
B = 2
D = 4
E = 1
F = 5

16. Mathematical Problems
Solving
Real World
and
Mathematical Problems

17. Quizzes: What is SMP and Rigor in CCSSM?
How do I pull them off in my classroom?
Do this after a demanding rich problem with rigor
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18. Fractions What’s the Big Deal? EduTron Do map
what you do in grade 1 impacts what a grade 9 teacher is able to do with his/her students.  
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19. Conceptual?
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20. 2011 TIMSS 8th Grade Mathematics Item ID M052228
Which Leg Is Missing?
Conceptual, not computational. 3-legs.
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21. What Does It Take to _____?
EduTron

22. What Does it take to add 1/3 to 1/4
Visualize size of #
Visualize size of F
𝟏 𝟑  𝟏 𝟒 =?
C.D.
C.D.
C.M.
C.M.
Eq. F 𝟏 𝟑 = 𝟐 𝟔 = 𝟑 𝟗 =…
Eq. F 𝟏 𝟑 = 𝟐 𝟔 = 𝟑 𝟗 =…
𝑭= 𝑵 𝑫 𝟏 𝟖 =? 𝟑 𝟖 =?
𝑭= 𝑵 𝑫 𝟏 𝟖 =? 𝟑 𝟖 =?
𝟑 𝟖 = 𝟏 𝟖 + 𝟏 𝟖 + 𝟏 𝟖 ÷𝑾 ÷𝑾 𝑾 𝑾 𝑾 𝑾 +𝑾 +𝑾
Estimate
Estimate
Number Line
Number Line
Counting
Counting
Multiples
Multiples
Skip Counting
Skip Counting
𝟑 𝟖 + 𝟕 𝟖 =?
𝟑 𝟖 + 𝟕 𝟖 =?

23. Butterfly Method

25. Mathematics is ruthlessly cumulative.
Do map
what you do in grade 1 impacts what a grade 9 teacher is able to do with his/her students.  
EduTron

26. Theorems A Math Teacher at Grade N is actually Teaching Grades K to N
A Math Teacher at Grade N should know the math in Grades K to N+2 and beyond
A happy teacher = a teacher who knows the coherent progression from grade to grade—how concepts connect and build up.
Could there be an example of this somewhere in the presentation?
Show What does it take to add 2 fractions?
Laying foundations for future grades
Remediating missing foundations from earlier grades
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27. Visualizing the Backbone of Common Core State Standards Grades K-8 Mathematics
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28. The Coherence Map CCSSM-Graph Coherence Map EduTron
This will be covered in today’s session.
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29. From Whole Numbers to Fractions
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30. 𝟏 𝟑 𝟐 𝟏 𝟐 𝟑 3rd Length Location Length Location Length Location  1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5
 
 
 
Number of “Wholes”
Number of “Wholes”
Number of “Wholes”
Ratio 3:1
Ratio 1:3
Ratio 5:2

31. Down side of teaching fractions initially as part of a whole with pizzas
“All fractions are smaller than 1?”
“Fractions are not numbers—they are certain ‘part of a whole’?”
“How do I multiply 2/3 of a pizza by ¾ of another pizza?”

32. 4.NF.3 and 4.NF.4
Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
Understand … 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/ /8 ; 2 1/8 = /8 = 8/8 + 8/8 + 1/8, etc.
Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.
a. Understand 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4).
b. …express 3 × (2/5) as 6 × (1/5), …
Extend used 34 times K-8, 10x in HS.34x
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33. From Fractions to Ratios
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34. Encapsulation: Maturing of Representations
Dogs
Discrete diagrams
based on counts
Cats
Concrete
Dogs
based on lengths
Double number lines
Cats
Dogs 4
Tape diagrams
based on lengths*
Cats 3 3
Encapsulation: Maturing of Representations
for Ratio Relationship
Dogs
abstract
Ratio tables
Abstract
Cats
Cats 12
abstract
Equations
& Graphs
Cats = 𝟑 𝟒 Dogs ( y = k x )
Dogs 16

35. From Equivalent Ratios to Proportional Relationships?
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36. From Proportional Relationships to Linear Functions
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37. EduTron

38. Significant Milestones
123 = 1  
(x2 + 3x – 4) = 1x2 + 3  x1 – 4
= 164
(x2 + 3x – 4) + (x – 1)
(x2 + 3x – 4) + (x – 1)
123  41 = 5043
(x2 + 3x – 4)  (x – 1)
(x2 + 3x – 4)  (x – 1)
123  41 = 3
(x2 + 3x – 4)  (x – 1)
123 = 3  41
(x2 + 3x – 4) = (x – 1)  (x + 4)
17   5 = (17+3) x 5
(3x – 4)a + (3x – 4)b = (3x – 4)(a + b)
(x2 + 3x – 4) (x2 + 2x – 5)
(x2 – 1) (x – 1) +
1/8 + 1/6 = 7/24
Place value  Polynomials
Factors and factoring
Fractions
Generic ones:
Signed number operations
Variables EE  Functions
Geometrical Footprint
Number Line  Coordinate Plane (Where does y come from? We wanted to see the footprint of f(x).)
=  -2 = 6
a = x = -3
f(x) = x2 + 3x – 4 g(x) = (x – 1)
f(x) on Coordinate Plane y = f(x)
Roots, Asymptotes
Numbers on Number Line
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39. Quizzes: What is Coherence in CCSSM? How do I take advantage of it?
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40. Dissecting “Units” in CCSSM
Andrew Chen
The Short Asian

41. Story of Units Adding quantities only when they have the same unit
2 quarters + 3 dimes
2 coins + 3 coins = 5 coins
10 nickels + 6 nickels = 16 nickels
50 cents + 30 cents = 80 cents
0.5 dollars dollars = 0.8 dollars
½ hour + 20 minutes
30 minutes + 20 minutes = 50 minutes
1/2 hours + 1/3 hours = 5/6 hours
1/6 + 3/8 (1 sixth + 3 eighths)
8 forty-eighths + 18 forty-eighths = 26/48
4 twenty-fourths + 9 twenty-fourths = 13/24
1/8
1/6
1/8
1/8

42. 3 Numerator 8 Denominator Enumerate (count units) with this number1 8
Enumerate (count units)
with this number 1 8 1 8 3
Numerator 8
Denominator 1 8
Show size of denomination (unit)
with this number

43. Story of Units Adding quantities only when they have the same unit
1 hundred + 2 tens + 3 ones
tens + 4 ones
1 hundred + 9 tens + 7 ones
1 ten + 2 ones + 3 tenths
ones + 6 tenths + 4 hundredths
1 ten + 2 ones + 9 tenths + 4 hundredths

44. Story of Units When quantities are multiplied their units are also multiplied
2 ft x 3 pounds = 6 ft x pounds [Torque]
11 inches x 8.5 inches = 93.5 in2 [Area]
2 inches x 3 inches x 4 inches = 24 in3 [Volume]
3 acres x 0.5 ft = 1.5 acre.ft [Volume]
60 miles/hour x 2 hours [Speed x time = distance] = 120 (miles/hour) x hour = 120 miles
2 kilowatt x 3 hours = 6 kW.h [Power x time = energy]
1/6 x 3/8 [UF1 x UF2 = UF3]
= 1 sixths x 3 eighths = 3 sixths x eighths = 3/48

45. Story of Units When quantities are multiplied their units are also multiplied
23 x 45
= (2 tens + 3 ones) x (4 tens + 5 ones)
= (2 tens x 4 tens) + (2 tens x 5 ones) (3 ones x 4 tens) + (3 ones x 5 ones)
= tens x tens tens x ones ones x tens ones x ones
= hundreds tens tens ones
= …
= 1035

46. = (2 ones + 3 tenths) x (4 tens + 5 ones)
Story of Units When quantities are multiplied their units are also multiplied
2.3 x 45
= (2 ones + 3 tenths) x (4 tens + 5 ones)
= (2 ones x 4 tens) + (2 ones x 5 ones) (3 tenths x 4 tens) + (3 tenths x 5 ones)
= ones x tens ones x ones tenths x tens tenths x ones
= tens ones ones tenths
= …
= 103.5

47. S = distance/time = 2/5 miles ÷ 3/7 minutes
Story of Units When quantities are divided their units are also divided
A car traveling at constant speed travels 2/5 of a mile in 3/7 of a minute.  What is the speed S of the car in miles per hour?
S = distance/time = 2/5 miles ÷ 3/7 minutes
2 miles x x 60 minutes x 3 minutes x hour
2 x 7 x 60 miles minutes 5 x 3 x 1 minutes hour
56 miles/hour

48. All Those Units Decoded and Unified
Measurement Units (feet, inches, pounds, etc.)
Base 10 Units (10, 100, 1000, 0.01, etc.)
Fractional Units (Unit Fractions) ( 1 8 , , , etc.)
Polynomial Units ( 𝑥 2 , 𝑥 3 , 𝑥 7 , etc.)
+ 
 
Adding (or subtracting) quantities only when they have the same unit
When quantities are multiplied (or divided) their units are also multiplied (or divided)

49. Progression of “Units” in CCSSM K-8
MD length unit
ft in m cm $ ¢ hour min
m cm mm kg g mg area in2
unit conversion 3.5 ft = ? inches
RP unit rate, 3.5 ft = ? cm
RP problem solving
NBT & OA EE
…. Slope
NF unit fraction 𝟑 𝟖 = 𝟏 𝟖 + 𝟏 𝟖 + 𝟏 𝟖
equivalent fractions 𝟑 𝟖 = 𝟔 𝟏𝟔 =…
whole: single unit or set of objects 1 8

50. Future Intensive Immersion Work
How do I
increase my own content knowledge (CK)?
increase my own PCK?
teach ____? (fractions, etc.)
increase rigor in what I do?
instill SMP in my student?
create/use/find rigorous resources to engage my students effectively?

51. Lessons
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52. “Stop trying to hit me and hit me."
Morpheus Yelled…
“Stop trying to hit me and hit me."
In "The Matrix", when Morpheus says to Neo "stop trying to hit me and hit me"
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53. Empire Strikes Back - Raising the X- Wing Video 0:40 to 1:27
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54. Alright, I’ll give it a try.
No. Try not. Do, or do not!! There is no try.
In "The Matrix", when Morpheus says to Neo "stop trying to hit me and hit me"
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55. I can't promise I'll try, but I'll try to try.
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56. Adywans Empire Strikes Back - Raising the X-Wing Video 3:40 to 5:13
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57. I can’t… I don’t believe it.
That is why you fail.
In "The Matrix", when Morpheus says to Neo "stop trying to hit me and hit me"
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58. Yoda: Train yourself to be self-contained you must.
You: Alright, I’ll give it a try.
Yoda: No. Try not. Do, or do not!! There is no try.
[Translation: One must genuinely believe that the more you know, the more flexible and effective you will be in helping every student. So, you must actively grow yourself across grades.]
I am directly challenging your belief system and will.
0:50 to 1:27
Luke: Alright, I’ll give it a try.
Yoda: No. Try not. Do, or do not!! There is no try.
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59. How Do I Train Myself to be Self-Contained?
Use the Force (CCSSM-Graph, CSSM Progressions, etc.)
Familiarize myself with the coherent progression of materials so that I can use them for patching up gaps and enrichment
Learn with and through others
Duh! COHERENCE!
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60. Yoda: Make time to “torture” every student you must.
You: But my students… I can’t believe you’re asking me to … no time…
Yoda: That is why you fail.
[Translation: High expectation works. Make every student taste the productive struggle and success you are inducing.]
actively grow yourself across grades.]
I am directly challenging your belief system and will.
0:50 to 1:27
Luke: Alright, I’ll give it a try.
Yoda: No. Try not. Do, or do not!! There is no try.
EduTron

61. How Do I Make Time and use material to “Torture” Every Student?
Build 3-Legged Stools (Common Core Rigor)
Dare to Demand (Practices)
Use the Force, e.g., Illustrative Mathematics, EngageNY, etc.
“Listen” CAREFULLY to Students
Take Zen Master Approach
Do NOT Rob Students of Their Productive Struggle
Duh! RIGOR!
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62. "The Music Is Not in the Guitar" and Other Lessons from Yoda and Morpheus
Permission to speak my mind in plain English.
Gesture.
Longview; issues kept me up at night. Analytical!! Humble.
Andrew Chen
Standards Institute
UnbounEd
June 29, 2017
Orlando FL, U.S.A.
EduTron

63. The Music is NOT in the Guitar

66. The Music Is Not in the Guitar
“It's like saying 'Give a man a Les Paul guitar and he becomes Eric Clapton,' ….”
“It's not true.”
Roger Waters, 1972
Giving every teacher a perfect set of standards and the perfect textbook, then all of them become master teachers?

67. Learn from Santana
"The key... is discipline. Teens don't want to hear that. They think they can just snap their fingers, and Voila! But with discipline comes knowledge, coordination, balance, muscle memory, confidence-- things that make it possible to hit the bull's-eye three times in a row. But you must practice."
-Carlos Santana
2003, Parade Interview
Genius? Talent? Effort? Which is more important? Poll. Nail it! Mozart next.

68. Learn From …
"It is a mistake to think that the practice of my art has become easy to me. I assure you no one has given so much care to the study of composition as I. There is scarcely a famous master in music whose works I have not frequently and diligently studied."
- Wolfgang Amadeus Mozart

69. The “Physics” of K-12 Math Education
Instruction
Perfect
Standards
Perfect
Perfect
Instructional Materials
Perfect
Tests
PARCC
SBAC
Educator Evaluation
PD & Coaching on Content Knowledge, Formative Assessments, etc.
Barking up the wrong tree

70. Can I Teach Good Math with ONLY Stick and Sand?
High expectations for teachers and students
Stay connected:
EduTron

71. Top 3 Forms of Assessment
Ongoing Assessment (minute-by-minute)

72. Recipe for Effective Teaching
Know the Subjects Well (K to N++)
Capitalize on Student Mistakes, Get Analytical
Watch: “I Taught My Cat Latin!?”
Watch: “Training Wheels that Won’t Come Off”
Balance: Skills, Concepts, and Problem Solving
Balance: Inquiry + Active Engagement + Lecture
Believe: Effort-based, not Just Talent-based
“Every Student, Every Period, …”
Open Classroom Door
Stay Humble, keep learning. Make connections. There is a whole elephant out there.
Know the subjects well, so well that you can see the whole elephant
Believe in Effort-based, not talent-based, DATA from abroad
Training Wheels that won‘t come off; know what your students will be heading into
crutches, short cuts and tricks are short term solution - can be hard to undo in the future
I taught my cat Latin!? Teaching is mostly about listening, assessing along the way.
Open your (classroom) door
Do not just enjoy teaching to the top – common rookie mistakes
Walk a mile in their shoes
Stay Humble

73. EduTron

74. Dharamsala, HP, India - April 22-24, 2015
“It is when without thinking about it you help someone who is less well off, when you are kind to someone else and do those things that raise others up, you end up being joyful.” Tutu
“If we think we want to get joy for ourselves, we realize that it’s very shortsighted, short-lived. Joy is the reward, really, of seeking to give joy to others. When you show compassion, when you show caring, when you show love to others, do things for others, in a wonderful way you have a deep joy that you can get in no other way. You can’t buy it with money. You can be the richest person on Earth, but if you care only about yourself, I can bet my bottom dollar you will not be happy and joyful. But when you are caring, compassionate, more concerned about the welfare of others than about your own, wonderfully, wonderfully, you suddenly feel a warm glow in your heart, because you have, in fact, wiped the tears from the eyes of another.
Conversation on Joy
Dharamsala, HP, India - April 22-24, 2015
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75. Be joyful
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76. Be joyful though you have considered all the facts.
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77. Be joyful though you have considered all the facts. Plant sequoias.
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78. Andrew Chen schen@EduTron.com
Be joyful though you have considered all the facts.
Plant sequoias. Say that your main crop is the forest that you did not plant, that you will not live to harvest.
Think Stick-and-Sand
Be Humble
Andrew Chen
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