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

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.

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

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

"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

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

Free App: Photo Math EduTron

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 EduTron

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? EduTron

Prep “Classroom”

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).

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. EduTron

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?

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 ?  EduTron

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

Mathematical Problems Solving Real World and Mathematical Problems

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 EduTron

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.   EduTron

Conceptual? EduTron

2011 TIMSS 8th Grade Mathematics Item ID M052228 Which Leg Is Missing? Conceptual, not computational. 3-legs. EduTron

What Does It Take to _____? EduTron

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 =?

Butterfly Method

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

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 EduTron

Visualizing the Backbone of Common Core State Standards Grades K-8 Mathematics EduTron

The Coherence Map CCSSM-Graph Coherence Map EduTron This will be covered in today’s session. EduTron

From Whole Numbers to Fractions EduTron

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

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?”

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 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 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 EduTron

From Fractions to Ratios EduTron

Encapsulation: Maturing of Representations Dogs Discrete diagrams based on counts Cats Concrete 0 4 8 12 16 Dogs based on lengths Double number lines Cats 0 3 6 9 12 Dogs 4 Tape diagrams based on lengths* Cats 3 3 Encapsulation: Maturing of Representations for Ratio Relationship Dogs 0 4 8 12 16 abstract Ratio tables Abstract Cats 0 3 6 9 12 Cats 12 abstract Equations & Graphs Cats = 𝟑 𝟒 Dogs ( y = k x ) Dogs 16

From Equivalent Ratios to Proportional Relationships ? EduTron

From Proportional Relationships to Linear Functions EduTron

EduTron

Significant Milestones 123 = 1  102 + 2  101 + 3 (x2 + 3x – 4) = 1x2 + 3  x1 – 4 123 + 41 = 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 + 3  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).) -8 + 6 = -2 -3  -2 = 6 a = 4.2 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 EduTron

Quizzes: What is Coherence in CCSSM? How do I take advantage of it? EduTron

Dissecting “Units” in CCSSM Andrew Chen The Short Asian

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 + 0.3 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

3 Numerator 8 Denominator Enumerate (count units) with this number 1 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

Story of Units Adding quantities only when they have the same unit 123 + 74 1 hundred + 2 tens + 3 ones + 7 tens + 4 ones 1 hundred + 9 tens + 7 ones 12.3 + 0.64 1 ten + 2 ones + 3 tenths + 0 ones + 6 tenths + 4 hundredths 1 ten + 2 ones + 9 tenths + 4 hundredths

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

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) = 8 tens x tens + 10 tens x ones + 12 ones x tens + 15 ones x ones = 8 hundreds + 10 tens + 12 tens + 15 ones = … = 1035

= (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) = 8 ones x tens + 10 ones x ones + 12 tenths x tens + 15 tenths x ones = 8 tens + 10 ones + 12 ones + 15 tenths = … = 103.5

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 7 x 60 minutes 5 x 3 minutes x 1 hour 2 x 7 x 60 miles minutes 5 x 3 x 1 minutes hour 56 miles/hour

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 , 1 11 , 1 27 , 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)

Progression of “Units” in CCSSM K-8 1 2 3 4 5 6 7 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

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?

Lessons EduTron

“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" EduTron

Empire Strikes Back - Raising the X- Wing Video 0:40 to 1:27 EduTron

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" EduTron

I can't promise I'll try, but I'll try to try. EduTron

Adywans Empire Strikes Back - Raising the X-Wing Video 3:40 to 5:13 EduTron

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" EduTron

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. EduTron

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! EduTron

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

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! EduTron

"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

The Music is NOT in the Guitar

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?

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.

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

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

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

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

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

EduTron

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 EduTron

Be joyful EduTron

Be joyful though you have considered all the facts. EduTron

Be joyful though you have considered all the facts. Plant sequoias. EduTron

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 schen@EduTron.com EduTron