Thursday, October 8, 2020

James Tanton Problem Solving Strategies

 

James Tanton - Problem Solving Strategies - Curriculum Inspirations from MAA

https://www.maa.org/math-competitions/teachers/curriculum-inspirations



Strategy 1 - Successful Flailing. 

Have no idea how to answer the question? - Try successful flailing

Write everything you know related to the question and hope things will fall into place and make some sense.

e.g. if it is about divisibility, try something (or everything) you know about divisibility
if it is about averages, try something (or everything) you know about averages.

draw picture or do something related to the problem


Strategy #1 - Engage in successful flailing



Grade 8


A Tricky Length


Non-Congruent Triangles


Area in a Polygon - TBD - Doesn’t belong here? - Repeated in Strategy #2 as well.


A Sneaky Area


Additional License Plates


Overlapping Triangles


Counting Jelly Beans



Abstract Sums


Unicorns at Play


Counting Coins


Divisible by 13


Trapezoidal Perimeter


Mixed Colors



Grade 10


Logarthim and Exponents


Painted Cube


Sum of Powers of Ten


Hypotenuse Please


Gothic Windows



Selecting Committes



Counting Multiples


An Integer Sequence


Changing Mean


Mowing Lawns


All Read Beads



Grade 12


Hundreds Digit of a Power


Point of a Contact Triangle


Maximum Ratio




Focus and Directrix


Two Digit Means



A Trigonometric Length



Filling a Grid



Logs of Divisors



A Lopsided Pyramid


Strategy #2 - Do Something

https://www.maa.org/node/129113/

https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/essay2.pdf


Grade 8


Area in a Polygon


Units Digit



Counting Wins


An Array of Sums


A Length in a Square


Probably a multiple of Three



A Weird Calculator


Three Special Factors


A Trapezoid Area


Circle Gaps


Grade 10


Stacking Coins


Logarithms and Exponents



Distributive Rules


Walking the Track



Chords in a circle



Length in a Trapezoid



Units of Big Powers



A Tricky Length


Repeated Visits


Successive Triangles



Arranging Mean, Median and Mode


Some Algebra


Multi-Base Three Digit Numbers


Arithmetic Algebra



Lots of Chimes




Grade 12


Quadaratic Values


Frog Leaping



A Third of an input



A Ratio of Areas


A Complex Minimum



Dividing by 100


Strategy #3 - Engage in wishful thinking

https://www.maa.org/math-competitions/teachers/curriculum-inspirations/Essay3

https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/essay3.pdf


Grade 8


Three Digit Reversal


One Versus Two Coin Tosses


A Triangle Area


Grade 10


Eliminating Roots



Grade 12


The Biggest Circle


Quadaratic Values


Elite Players and Logarithms



Strategy #4 - Draw a picture

https://www.maa.org/math-competitions/teachers/curriculum-inspirations/Essay4

https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/essay4.pdf


Grade 8


Two Trees


Dealing with Averages


Grade 10

Intersecting Tetrahedra


Areas of Nested Squares


Chords in a circle


Skipped counts



Two Counterfeit Coins




Rectangular Region


Counting Two Sets


Cut the Cube


Biking Towards Each other


Selecting Donuts


A Ferris Wheel Ride


Grade 12


Focus and Directrix


Frog Leaping


Parking Probability


Bug Walking



Strategy #5 - Solve a smaller version of the same problem

https://www.maa.org/math-competitions/teachers/curriculum-inspirations/Essay5

https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/essay5.pdf



Grade 8


Units Digit

http://youtu.be/161SYIL4sR0

https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB015_Units-Digit.pdf



Stair Climbing

http://youtu.be/nAP2npokFok

https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB028_Stair-Climbing.pdf


A Big last Digit 

http://youtu.be/gjfJSNAoqjU

https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB043_A-Big-Last-Digit.pdf



Rows and Columns Sums

http://youtu.be/DTl4QAgJK0s

https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB076_Row-and-Column-Sums.pdf


Overlapping Squares

http://youtu.be/MMwnQN7RaAw

https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB115_Overlapping-Squares.pdf



Grade 10


A Cross Section Area

http://youtu.be/pNmWiynmaPc

https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB069_A-Cross-Section-Area.pdf



Circle Area

http://youtu.be/5t9M5TwJgw4

https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB007_Circle-Area.pdf


Grade 12


No Grade 12 Problems.



Strategy #6 - Eliminate the incorrect choices

https://www.maa.org/math-competitions/teachers/curriculum-inspirations/Essay6

https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/essay6.pdf


Grade 8


Consecutive Squares


Matching Cards


A Sailing Ship



Grade 10 


Stacking Coins



A Curved Area


Largest Common Divisor


Avid Reading




Grade 12


Differences of Four Numbers


Mean, Median and Mode



Strategy #7 - Perseverance is Key

https://www.maa.org/math-competitions/teachers/curriculum-inspirations/Essay7

https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/essay7.pdf


Grade 8

At least as many heads


Angles in a Star


Counting Non-Congruent Triangles


A Dart Probability


Best Value


Sitting and Standing


Circles in Squares


A Complicated Area




Grade 10

Probably Above a Parabola


Coloring a Pentagon


Sum of the Ends


Counting Events


A Random Sequence


Selecting Digits


Removing Square Tiles


Ending with 23


Rounded Roots



Grade 12

Focus and Directrix


Arthimetic Logs


Iterated Function Domain


Strategy #8 - Second Guess the author



Grade 8

Hidden Primes


Grade 10

Pencil Prices


Town Population



Given a Bye


Melted Icre Cream


A Reflected Triangle


Grade 12

Whats the Domain


Bug Walking



Strategy #9 - Avoid Hard Work

Grade 8


Units Digit


Shaded Triangles


Pinwheel Area


A curious surface area


Oneless Numbers


Percent Shaded



Running Lemming


Overlapping Circle and Square


Remainders of Two


Circle Moves


Hands of a clock


One Zero


99 Digit Products



Grade 10

Intersecting Tetrahedra



Red and White Chips


Grade 12


Renumbered Dice


A Compound Complex Function



Strategy #10 - Go To Extremes

https://www.maa.org/math-competitions/teachers/curriculum-inspirations/Essay10

https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/essay10.pdf



Grade 8


Hats and Gloves


Different Darts


False Relation


Grade 10


A Line through Lattice Points


Differences of Four Numbers


Union of Two Sets


How Many Twos?


A Magic Square


Very Eight-Centered


Perfect Square Fraction


Grade 12


No Grade 12 problems



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