Harvard Mathematics Department : Home pagepeople.math.harvard.edu/~engelwar/MathS305/Singapore Model...

19

Transcript of Harvard Mathematics Department : Home pagepeople.math.harvard.edu/~engelwar/MathS305/Singapore Model...

Page 1: Harvard Mathematics Department : Home pagepeople.math.harvard.edu/~engelwar/MathS305/Singapore Model Met… · Created Date: 9/12/2013 3:56:25 PM
Page 2: Harvard Mathematics Department : Home pagepeople.math.harvard.edu/~engelwar/MathS305/Singapore Model Met… · Created Date: 9/12/2013 3:56:25 PM
Page 3: Harvard Mathematics Department : Home pagepeople.math.harvard.edu/~engelwar/MathS305/Singapore Model Met… · Created Date: 9/12/2013 3:56:25 PM
Page 4: Harvard Mathematics Department : Home pagepeople.math.harvard.edu/~engelwar/MathS305/Singapore Model Met… · Created Date: 9/12/2013 3:56:25 PM
Page 5: Harvard Mathematics Department : Home pagepeople.math.harvard.edu/~engelwar/MathS305/Singapore Model Met… · Created Date: 9/12/2013 3:56:25 PM
Page 6: Harvard Mathematics Department : Home pagepeople.math.harvard.edu/~engelwar/MathS305/Singapore Model Met… · Created Date: 9/12/2013 3:56:25 PM
Page 7: Harvard Mathematics Department : Home pagepeople.math.harvard.edu/~engelwar/MathS305/Singapore Model Met… · Created Date: 9/12/2013 3:56:25 PM
Page 8: Harvard Mathematics Department : Home pagepeople.math.harvard.edu/~engelwar/MathS305/Singapore Model Met… · Created Date: 9/12/2013 3:56:25 PM
Page 9: Harvard Mathematics Department : Home pagepeople.math.harvard.edu/~engelwar/MathS305/Singapore Model Met… · Created Date: 9/12/2013 3:56:25 PM
Page 10: Harvard Mathematics Department : Home pagepeople.math.harvard.edu/~engelwar/MathS305/Singapore Model Met… · Created Date: 9/12/2013 3:56:25 PM
Page 11: Harvard Mathematics Department : Home pagepeople.math.harvard.edu/~engelwar/MathS305/Singapore Model Met… · Created Date: 9/12/2013 3:56:25 PM
Page 12: Harvard Mathematics Department : Home pagepeople.math.harvard.edu/~engelwar/MathS305/Singapore Model Met… · Created Date: 9/12/2013 3:56:25 PM
Page 13: Harvard Mathematics Department : Home pagepeople.math.harvard.edu/~engelwar/MathS305/Singapore Model Met… · Created Date: 9/12/2013 3:56:25 PM
Page 14: Harvard Mathematics Department : Home pagepeople.math.harvard.edu/~engelwar/MathS305/Singapore Model Met… · Created Date: 9/12/2013 3:56:25 PM
Page 15: Harvard Mathematics Department : Home pagepeople.math.harvard.edu/~engelwar/MathS305/Singapore Model Met… · Created Date: 9/12/2013 3:56:25 PM
Page 16: Harvard Mathematics Department : Home pagepeople.math.harvard.edu/~engelwar/MathS305/Singapore Model Met… · Created Date: 9/12/2013 3:56:25 PM
Page 17: Harvard Mathematics Department : Home pagepeople.math.harvard.edu/~engelwar/MathS305/Singapore Model Met… · Created Date: 9/12/2013 3:56:25 PM
Page 18: Harvard Mathematics Department : Home pagepeople.math.harvard.edu/~engelwar/MathS305/Singapore Model Met… · Created Date: 9/12/2013 3:56:25 PM
Page 19: Harvard Mathematics Department : Home pagepeople.math.harvard.edu/~engelwar/MathS305/Singapore Model Met… · Created Date: 9/12/2013 3:56:25 PM

engelwar/MathS305/Chapter 1 Sections 2... · + sdetu ueuo '„L + ax = .eweu wop uaum augep asn ueuo am '[g .êldtuexa ayes Isn! ôL1!sn Kq apetu 'zua.toaw 1 '(0 u r aoeldal 1 uvo

engelwar/MathS305/Chapter 1 Sections 2... · + sdetu ueuo '„L + ax = .eweu wop uaum augep asn ueuo am '[g .êldtuexa ayes Isn! ôL1!sn Kq apetu 'zua.toaw 1 '(0 u r aoeldal 1 uvo

people.math.harvard.edupeople.math.harvard.edu/~engelwar/MathS305/Binomial Theorem Chapter.pdfBinomial Theorem: a!b! The coefficients are the entries of the n-th row of Pascal's trian

people.math.harvard.edupeople.math.harvard.edu/~engelwar/MathS305/Binomial Theorem Chapter.pdfBinomial Theorem: a!b! The coefficients are the entries of the n-th row of Pascal's trian

Sequences and Series: An Introduction to Mathematical …engelwar/MathS305/Sequences and Series Te… · Sequences and Series: An Introduction to Mathematical Analysis by Malcolm

Sequences and Series: An Introduction to Mathematical …engelwar/MathS305/Sequences and Series Te… · Sequences and Series: An Introduction to Mathematical Analysis by Malcolm

Harvard Mathematics Department : Home pagepeople.math.harvard.edu/~engelwar/MathS305/Singapore...Jug Mug After 2nd transfer: Jug Mug From the model, students can formulate an algebraic

Harvard Mathematics Department : Home pagepeople.math.harvard.edu/~engelwar/MathS305/Singapore...Jug Mug After 2nd transfer: Jug Mug From the model, students can formulate an algebraic

Math for Teaching Advanced Algebra and Trigonometryengelwar/MathS305/Math305 Summer 2014... · Introduction to course Wait, more algebra?! Course nuts and bolts aka “the fine print”

Math for Teaching Advanced Algebra and Trigonometryengelwar/MathS305/Math305 Summer 2014... · Introduction to course Wait, more algebra?! Course nuts and bolts aka “the fine print”

people.math.harvard.edupeople.math.harvard.edu/~engelwar/MathS305/Chapter 1... · 2014-07-04 · 12 Difference Tables and Polynomial Fits 1 —5 This "two-term recurrence" 4 G) =

people.math.harvard.edupeople.math.harvard.edu/~engelwar/MathS305/Chapter 1... · 2014-07-04 · 12 Difference Tables and Polynomial Fits 1 —5 This "two-term recurrence" 4 G) =

Harvard Mathematics Department : Home pagepeople.math.harvard.edu/.../TaoSolvingMathProblems.pdf · Mathematical problems, or puzzles, are important to real mathematics (like solving

Harvard Mathematics Department : Home pagepeople.math.harvard.edu/.../TaoSolvingMathProblems.pdf · Mathematical problems, or puzzles, are important to real mathematics (like solving

From Cardano - Harvard Universitypeople.math.harvard.edu/~engelwar/MathS305/Math305... · Solve ax3 + bx2 + cx + d = 0 cool idea –can you work with this equation to make it so that

From Cardano - Harvard Universitypeople.math.harvard.edu/~engelwar/MathS305/Math305... · Solve ax3 + bx2 + cx + d = 0 cool idea –can you work with this equation to make it so that

Harvard Mathematics Department : Home pagepeople.math.harvard.edu/~knill/graphgeometry/muir/Muir.pdf · forms: and, speakino ('enerally, the work of the forty years from then till

Harvard Mathematics Department : Home pagepeople.math.harvard.edu/~knill/graphgeometry/muir/Muir.pdf · forms: and, speakino ('enerally, the work of the forty years from then till

From Cardano - Harvard Mathematics Departmentengelwar/MathS305/Math305 Summer 2014... · Girolamo Cardano (1501 –1576) knew this trick… but needed to do more to solve this new

From Cardano - Harvard Mathematics Departmentengelwar/MathS305/Math305 Summer 2014... · Girolamo Cardano (1501 –1576) knew this trick… but needed to do more to solve this new

Harvard Mathematics Department : Home pagepeople.math.harvard.edu/~bullery/math101/Exam3solutions.pdfMath 101 / Final (December 4—5, 2017) page 3 2. [8 points] Consider X = R x [0,

Harvard Mathematics Department : Home pagepeople.math.harvard.edu/~bullery/math101/Exam3solutions.pdfMath 101 / Final (December 4—5, 2017) page 3 2. [8 points] Consider X = R x [0,

The Model-Drawing Method with Algebra - Harvardengelwar/MathS305/Singapore... · Singapore: Ministry Of Education. Fong, H. K. (1994). Bridging the gap between secondary and primary

The Model-Drawing Method with Algebra - Harvardengelwar/MathS305/Singapore... · Singapore: Ministry Of Education. Fong, H. K. (1994). Bridging the gap between secondary and primary

engelwar/MathS305/Singapore Model Method Text... · Created Date: 9/12/2013 3:56:25 PM

engelwar/MathS305/Singapore Model Method Text... · Created Date: 9/12/2013 3:56:25 PM

When it’s the Form that matters… - people.math.harvard.edupeople.math.harvard.edu/~engelwar/MathS305/Math305 Summer 20… · The Model Method –Singapore Math. How about this

When it’s the Form that matters… - people.math.harvard.edupeople.math.harvard.edu/~engelwar/MathS305/Math305 Summer 20… · The Model Method –Singapore Math. How about this