Math Curriculums and Recommendations

This page is an attempt to list my list of math curriculums, books, programs that covers K-12

Basic Math knowledge - Basic Literacy 

I have not reviewed all of them, but sampled most of them. Provides varying level of engagement for kids. One is not necessarily better than the other. Just pick one and stick with it.

• Saxon Math
• Math Mammoth
• Teaching Textbooks
• RightStart
• MathUSee
• JumpMath

Standard Math Curriculum - Solid Foundation

• Arithmetic for Parents - Ron Aharoni
• Kitchen table math - Volume 1 - Chris Wright
• Singapore Math - Primary Mathematics - 1 through 6 OR  Math No Problem 1-6
• Elementary Algebra - Harold Jacobs
• Geometry Seeing Doing Understanding - Harold Jacobs

Recommended Math Curriculums - Enhanced Foundation

Art of Problem Solving

• Arithmetic for Parents - Ron Aharoni
• Kitchen table math - Volume 1 - Chris Wright
• Singapore Math - Primary Mathematics - 1
• Beast Academy 2
• Beast Academy 3
• Beast Academy 4
• Beast Academy 5
• Pre-Algebra
• Introduction Algebra - Chapters 1-9
• Introduction to Counting and Probability (Chapters 1-8)
• Introduction to Number Theory (Chapters 1-11)
• Introduction Algebra - Chapters 16-22
• Introduction to Counting and Probability (Chapters 9-15)
• Introduction to Number Theory (Chapters 12-15)
• Introduction to Geometry (Chapters 1-12)
• Intermediate Algebra
• Intermediate Counting and Probability
• Introduction to Geometry (Chapters 13-19)
• Pre-Calculus
• Calculus

Elements of Mathematics

• Upto Pre-Algebra in Art of Problem Solving
• Elements of Mathematics  Courses (1-18)

Unified Modern Mathematics - see here for history

• NOTE: Not all materials are available for this curriculum
• Upto Pre-Algebra in Art of Problem Solving
• Course 1
• Part 1 - Number Systems, Sets, Mappings, Probability, Lattice Points
• Part 2 - Geometry, Number Theory, Rational Numbers
• Teachers Commentary
• Course 2
• Part 1 - Proofs, Groups, Geometry, Fields, Real Numbers, Co-ordinate Geometry
• Part 2 - Real Functions, Statistics, Geometry, Combinatorics
• Teachers Commentary
• Course 3
• Part 1 - Matrix, Graphs and Functions, Combinatorics
• Part 2 - Functions, Geometry
• Teacher Commentary
• Course 4 - 
• Course 5 - 
• Course 6 - Introduction to differential equations

Contest Preparation 

Basic Contest Preparation 

The Art of Problem Solving Volume 1 - The Basics

The Art of Problem Solving Volume 2 - And Beyond

Grade Five Competition from Leningrad Mathematical Olympiad - Andy Liu & Garaschuk

Lecture Notes On Mathematical Olympiad Courses: For Junior Section - Volume 1 by Jiagu Xu 

Lecture Notes On Mathematical Olympiad Courses: For Junior Section - Volume 2 by Jiagu Xu 

Junior Balkan Mathematical Olympiads - Dan Branzei; Ioan Serdean; Vasile Serdean

Olympiad Level Contest Preparation

A Gentle Introduction to the American Invitational Mathematics Exam - Scott Annin

First Steps for Math Olympiads - Douglas Faires

First Step to Mathematical Olympiad Problems - Derek Holton

A Primer for Mathematics Competitions - Zawaira and Hitchcock

Problem Primer for Olympiad - Pranesachar

Euclidean Geometry in Mathematical Olympiads - Evan Chen

Supplementary

Supplementary Books

Elementary

• Calculus By and For Young People - Don Cohen
• 50 Problem Solving Lessons - Marilyn Burns
• Exploding Dots - James Tanton
• Shapes in Math, Science and Nature - Ross and Slavin
• Math from Three to Seven - Zvonkin
• Math for Smarty Pants - Maryln Burns
• Olympiad Math Weekly Practice - For 4th to 8th Grader - Cheney Gao

Middle school

• Arithmetical Wonderland - Andy Liu
• Mathematical Circle Diaries - Year 1 - Anna Burago
• Mathematical Circle Diaries - Year 2 - Anna Burago
• S.M.A.R.T Circle Projects - Andy Liu
• Cryptography
• The Cryptoclub: Using Mathematics to Make and Break Secret Codes by Janet Beissinger, Vera Pless
• Geometry
• Triangle Constructions with only Rulers and Compass - Arvind Subramanian
• James Tanton - Edfinity Books
• 8 Tips to Solve Any Problem
• Numbers and the Number System
• Structures, Patterns & Logic
• Counting & Probability
• Relationship and Equations
• 
  

High School

• Mathematics, a Human Endeavor - Harold Jacobs
• Math Problems for children 5 to 15 - Arnold
• One Hundred Problems in Elementary Mathematics - Hugo Steinhaus
• Math Better Explained - Kalid Azad
• Calculus Better Explained - Kalid Azad

Problem Solving and Proofs

• How to Solve Mathematical Problems - Wayne Wickelgren
• Problem Solving Strategies - Engel
• Art and Craft of Problem Solving
• Solving Mathematical Problems: A Personal Perspective - Terence Tao

Recreational/Casual 

• Mathematics Can Be Fun - Yakov Perelman
• Solve this: Math Activities for Students and Clubs
• Aha Solutions - Erickson
• A Mathematical Mosaic - Ravi Vakil

Math Education

• Enrichment Math for Elementary and Middle School - 27th Yearbook
• Enrichment Math for High School - 28th Yearbook
• Nix the Tricks - Tina Cardone
• Mindstroms: Children, Computers and Powerful Ideas - Seymour Papert

Math Help

Grade 9 - Exemplar Tips - Ottawa School District Board Booklet

Math to Avoid

The following are books/curriculum/programs that teach 19th century skills in 21st century. At best they won't add any value and at worst have a great ability to make you dumb.

• Kumon
• UCMAS
• Aloha

Blockchain 101

 

The Basics

• Crypto Currency Capitalism - The business uses of cryptocurrency and blockchain technologies - http://www.cryptocapitalism.center/
• How to explain Bitcoin to your grandmother - http://suitpossum.blogspot.ca/2013/04/how-to-explain-bitcoin-to-your.html
• How the Bitcoin protocol actually works - Very technical - http://www.michaelnielsen.org/ddi/how-the-bitcoin-protocol-actually-works/

News/Media

• Will Blockchain replace swift - http://www.americanbanker.com/bankthink/will-the-blockchain-replace-swift-1079740-1.html
• IBM, J.P. Morgan, and Others Build a New Blockchain For Business - http://fortune.com/2015/12/17/ibm-blockchain-for-business/

 

 

 

Grades Vs. Efforts

 Yesterday,  I received my son's final assessment report for Grade 2. He did get good grades (mostly A+, a few A's and one B+). I chuckled at the overall assessment because I wasn't sure what I could make out of it. Being the skeptic I am on any non-independent assessment in this rampant grade inflated era, I wasn't sure if the report is actually helping me or my son. While he tried explaining to me why he got a B, I told him that wasn't my concern at all and that I am indeed happy because there is scope for improvement. I told him that I was concerned about the A+s and As.  He didn't quite understand. I thought about how I could explain this to a 2nd grader. Then I drew a version of the picture below and told him that the most preferred place to be is #1 and least preferred is #4. And I told him that I don't have enough information whether he is placed  #1 or #4 as the assessment is not outside his school and more importantly difficulty is not known. . Since he had previously written Math Kangaroo, I managed to use that as an example for independent assessment.

I don’t know if he actually understood what I told him, but he sure understood that just getting a A+ or A will not impress me

Ubuntu 18.04 and Unison

 I have been using Unison for several to sync files and I recently upgraded to 18.04 LTS.

Unision will no longer synch between the upgrade machine and my local machine. When a file is copied from my local machine to the upgraded machine, it copied well but the otherway around got an error
unison loadlocale.c _nl_intern_locale_data: Assertion `cnt < (sizeof (_nl_value_type_LC_TIME) / sizeof (_nl_value_type_LC_TIME[0]))' failed

After some trial and error the following workaround helped

1. Rename the unison executable. You can find it under (/usr/bin/unison-x.xx (to for e.g. /usr/bin/unison-x.xx.exe)
2. Rename the unison symbolic link /usr/bin/unison (to for e.g. /usr/bin/unison.exe) and  make it point to the new renamed executable in Step 1.
3. Create the following shell scripts and save it under the 2 original names
#!/bin/bash
LANG=C unison.exe "$@"

Worked like a charm. I know I will have issues when upgrading unison but I am hoping the bug in loadlocale.c is fixed before that.
Notes

a) You will have to be logged in as root for steps 1-3
b) Step 1 is necessary because when synching from a Windows machine through ssh, it searches and invokes unison
c) Step 2 is necessary because when synching from a Mac machine through ssh, it searches and invokes unison-x.xx
d) This workaround could've been made simpler for e.g. creating only one script, etc. but I wanted to retain the original deployment structure. When the issue is fixed all I have to do is to delete the scripts and do a rename.

Learning from Top Students

The video is about research findings across thousands of high school students in Australia, UK and the US.
Key observations

1. IQ does not matter for success in schools
2. Hard work is necessary but not sufficient.
3. Behavioural traits of top students include - self motivation, self discipline and resiliency (i.e. keeping at it even when marks go down in a test).
4. Memorizing doesn't help - Tests are about how you use what you remember, not what you remember.

What Top students do that you can do

1. Do more practice exams.
2. Create a study timetable with first putting all the times you will not study (where you do other things), and then fill in with the times you will study.

Some notes Feynman Technique for learning anything

Summarized from Genius: The Life and Science of Richard Feynman.

1. Write up all you know or want to explain about the topic. This is will be a work in progress and the material will increase when your knowledge increases. In the electronic medium you want to want to write up a blog page for that or a separate One Note page.
2. Pretend to teach it to a classroom - or to self.
3. Identify areas you are shaky, stuck or not confident - Go back to sources and review.
4. Identify any technical jargons in your explanations, simplify them using analogies/metaphors.

Some Notes from Five Principles of extraordinary math teaching

1. Start with the question.
2. Students need time to struggle. Dont provide solutions/answers. Some math problems should take hours or days to solve.
3. You are not the answer key. Dont provide answers, instead ask why it is true.
4. Say yes to ideas - even wrong ideas - don't dismiss them. Rather explore them.
5. Math is not about following rules - but playing

https://youtu.be/ytVneQUA5-c

 

AMC 8

 What is it?

• American Mathematical Contest is a middle school math contest conducted by Mathematical Association of America (MAA)
• Anyone Grade 8 or lower can participate
• First of the AMC tests - Others being AMC 10 (covers first 2 years of high school) and AMC 12(covers all 4 years of high school except calculus)
• Around 200,000 kids write the exam (~2016 stats)

Contest Format and Duration

• 25 Questions - 40 Minutes - Arranged in increasing order of difficulty
• Questions 1-10 are considered easy - If you can't solve these, seek help for school math. It is extremely unlikely you will do well in high school. 
• Questions 11-20 are considered moderately difficult. If you can solve these, you can consider yourself average in math.
• Questions 21-25 are considered difficult. If you can solve these, then you are proficient in Math
• No Penalty for wrong answers
• All multiple choice

Topics Covered

• Number Sense (16%) 
• Number Theory (32%) 
• Odd and Even Parities
• Divisibility Rules
• Counting (8%)
• Double Counting
• Complimentary Counting
• Casework
• Measurement and Probability (12%)
• Algebra (16%)
• Geometry (16%)
• Exterior Angle Theorem
• 
  

Why should I write AMC 8

• Most of the math problems in many textbooks are close to being useless. You cannot learn useful math. Solving them is tantamount to copying a large book by hand with the objective of learning literature.
• An objective assessment of your math skills. Math contests in the erstwhile USSR and most of Asia is for mathematically talented kids. The beginning level of the problems is pretty high. Not being able to solve them doesn't necessarily mean you lack math skills.  But Math contests in North America is for the masses. There will be problems that students every level can solve. Doing well in these mean you are good at math and not being able to do any or only able to do 1 or 2 problems mean that you are bad at math even at a basic level. You need help at school if you perform at the bottom. So contests like AMC 8 and CEMC are good diagnostic tools.
• Opportunity to practice problem solving. There is no material advantage of writing AMC 8 (unlike AMC 10 and 12). You don't get special admission or recognition anywhere based on your AMC 8. The reward is itself. 
• How contest writing helps

Strategies & Tips

Preparing for AMC

• Take Old Practice Exams in a simulated test environment
• Keep a record of every practice test - marking 1 for correct, 1! for correct guess, 0 for wrong, 0! for incorrect guesses,  0? for attempted (but no answer) and blank for skipped
• Questions 1-10 are all about using tricks for school math. If you don't use the tricks or shortcuts you may still solve it but will spend time that you can't use for other problems.
• In geometry problems draw additional lines or grids to see if the problem gets simplified
• Learn the basics - divisibility tests, 

On Exam Day

• Have a test kit ready - Pencil, Paper, Graph paper, rulers, protractors, erasers
• Organize your scratch paper so you can check your work faster
• Divide paper to grid
• Box answer, draw clear diagram.
• Put a circle on unsure answers (put on problem numbers)
• No eraser on scratch paper
• Even write down mental math answers (don't skip writing down answers)
• Don't solve more than what is required.
• Even if guessing answers write choices down e.g A or B (dont forget to circle the question)
• Leave last 3-5 minutes to check answer (starting with the ones you circle)

Problem Solving Tips

• A great tactic to start most geometry problems is to just figure out all information you can to get started and then mark them on the diagram.
• If something is too complex try to break it up into smaller pieces that are easier to handle
• Dont panic if you don't understand a problem. Take a deep breath!!
• When computing areas of complex/irregular figures try to start computing areas of simple figures (triangles, rectangles, circles) and then adding or subtracting the smaller areas to get the area of the complex figure.
• In counting problems, check for boundary items. It is easy to make one-off errors and undercount or overcount.
• It is important to be systematic when solving a counting problem. When it's easy to get lost, it's even more important.
• In counting problems, it can be helpful to come up with a different way of getting the answer, so you can check if your answer is correct.

Awards

• Certificate of distinction - Score of 22-25 (Top 2%)
• Honor Roll - Top 5% - 18-21
• Certificate of Merit - 6th Grades or lower - Top 15% (Score >=15)

Resources

• Mathematical Association of America AMC 8 Home Page
• Ardent Academy for Gifted Youth - Preparation Tips 
• Videos of Titu Andreescu solving AMC 8 problems
• Part 1
• Part 2
• James Tanton Problem Solving Strategies - Look at Grade 8 problems for each strategy  
• Edfinity Online Course
• AoPS Past Problems and Solutions
• Art of Problem Solving Math Jams
• May 2020 - Number theory excursions
• May 2020 - Geometry Excursions
  
• May 2020 - Counting and Probability Excursions
  
• April 2020 - Algebra Excursions
• Nov 2019 - AMC 8 General Discussion
• Nov 2018 - AMC 8 General Discussion
• Feb 2010 - AoPS Classes (Mathcounts/AMC 8)
• Oct 2009 - AoPS Classes (Mathcounts/AMC 8)
• Aug 2009 - AoPS Classes (Mathcounts/AMC 8)
• May 2009 - AoPS Classes (Mathcounts/AMC 8)
• May 2009 - AoPS Classes (Mathcounts/AMC 8)

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

• https://www.youtube.com/watch?v=zkY4M3a022Q&feature=youtu.be

• https://www.maa.org/math-competitions/teachers/curriculum-inspirations/Essay1

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/essay1.pdf

Grade 8

A Tricky Length

• https://www.youtube.com/watch?v=mRiN6dd-Hpo&feature=youtu.be

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB114_A-tricky-Length.pdf

Non-Congruent Triangles

• http://youtu.be/eKUbFUHIrPQ

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB012_NonCongruent-Triangles.pdf

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

• http://youtu.be/RRPywVJ0LJo (Video not available)

• https://www.youtube.com/watch?v=isP_v5C20Ss&feature=youtu.be

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB004_Area-in-a-Polygon.pdf

A Sneaky Area

• http://youtu.be/3Nsx628qb6E

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB045_A-Sneaky-Area.pdf

Additional License Plates

• http://youtu.be/ROqRvGGHCoQ

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB044_Additional-License-Plates.pdf

Overlapping Triangles

• http://youtu.be/lYnibC_o3dc

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB061_Overlapping-Triangles.pdf

Counting Jelly Beans

• http://youtu.be/NWh5AcA91X8

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB074_Counting-Jelly-Beans.pdf

Abstract Sums

• http://youtu.be/-cliFnMIpZA

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB073_Abstract-Sums.pdf

Unicorns at Play

• http://youtu.be/a6jdLqyu8HY

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB099_Unicorns-at-Play.pdf

Counting Coins

• http://youtu.be/YF_BsB9GztE

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB103_Counting-Coins.pdf

Divisible by 13

• http://youtu.be/GtnDPgXsQrc

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB104_Divisible-by-13.pdf

Trapezoidal Perimeter

• http://youtu.be/bUKt8XBUSmg

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB105_Trapezoidal-Perimeter.pdf

Mixed Colors

• http://youtu.be/Zr2H9Q25ioI

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB126_Mixed-Colors.pdf

Grade 10

Logarthim and Exponents

• http://youtu.be/vb4ps9fblwg

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB011_Logarithms-and-Exponents.pdf

Painted Cube

• http://youtu.be/ryK5tDSc9_4

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB013_Painted-Cube.pdf

Sum of Powers of Ten

• http://youtu.be/HDNpoh9jnio

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB018_Sums-of-Powers-of-Ten.pdf

Hypotenuse Please

• http://youtu.be/XGWa3xpQPn0

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB068_Hypotenuse-Please.pdf

Gothic Windows

• http://youtu.be/HgSGWoVusfc

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB082_Gothic-Windows.pdf

Selecting Committes

• http://youtu.be/WW8xQxMRU1A

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB087_Selecting-Committees.pdf

Counting Multiples

• http://youtu.be/pXslOcHkd2A

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB130_Counting-Multiples.pdf

An Integer Sequence

• http://youtu.be/NrQg-fgsInY

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB136_An-Integer-Sequence.pdf

Changing Mean

• http://youtu.be/N7BKIcxx4lQ

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB137_Changing-Mean.pdf

Mowing Lawns

• http://youtu.be/AxI7av3Rzpk

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB138_Mowing-Lawns.pdf

All Read Beads

• http://youtu.be/1H7YKVjcUWk

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB146_All-Red-Beads.pdf

Grade 12

Hundreds Digit of a Power

• https://www.youtube.com/watch?v=dZiPAram2Vc&feature=youtu.be

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB094_Hundreds-Digit-of-a-Power.pdf

Point of a Contact Triangle

• http://youtu.be/_KuXFbH47m8

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB092_Point-of-Contact-Triangle.pdf

Maximum Ratio

• http://youtu.be/z4pRKMebUgs

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB010_Maximum-Ratio.pdf

Focus and Directrix

• http://www.youtube.com/watch?v=OZUBVHhaRVs

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB005_Focus-and-Directrix.pdf

Two Digit Means

• http://youtu.be/GVZ5XDYq7Ww

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB020_Two-Digit-Means.pdf

A Trigonometric Length

• http://youtu.be/nmNitZCxN2k

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB033_A-Trigonometric-Length.pdf

Filling a Grid

• http://youtu.be/khSojsPuy2w

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB035_Filling-a-Grid.pdf

Logs of Divisors

• http://youtu.be/0Dikp-DXYF8

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB057_Logs-of-Divisors.pdf

A Lopsided Pyramid

• http://youtu.be/8y21SN_4Itk

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB060_A-Lopsided-Pyramid.pdf

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

• http://youtu.be/isP_v5C20Ss

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB004_Area-in-a-Polygon.pdf

Units Digit

• http://youtu.be/161SYIL4sR0

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

Counting Wins

• http://youtu.be/Pl2eferg4j0

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB062_Counting-Wins.pdf

An Array of Sums

• http://youtu.be/M-ETUKZGq3k

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB063_Array-of-Sums.pdf

A Length in a Square

• http://youtu.be/aIiXrQAYX_U

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB042_A-Length-in-a-Square.pdf

Probably a multiple of Three

• http://youtu.be/5mWh1YAiY0Q

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB066_Proabably-a-Multiple-of-Three.pdf

A Weird Calculator

• http://youtu.be/BRz3MtcQEGk

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB109_A-Weird-Calculator.pdf

Three Special Factors

• http://youtu.be/jalGiVq0SUg

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB116_Three-Special-Factors.pdf

A Trapezoid Area

• http://youtu.be/zkzxfj5nt-c

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB118_A-Trapezoid-Area.pdf

Circle Gaps

• http://youtu.be/LRa7EbofLL0

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB125_Circle-Graphs.pdf

Grade 10

Stacking Coins

• http://youtu.be/CZH4i1HZukE

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB008_Stacking-Coins.pdf

Logarithms and Exponents

• http://youtu.be/vb4ps9fblwg

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB011_Logarithms-and-Exponents.pdf

Distributive Rules

• http://youtu.be/4cZMwYmZkI0

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB017_Distributive-Rules.pdf

Walking the Track

• http://youtu.be/wIgaGvLLvC0

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB022_Walking-the-Track.pdf

Chords in a circle

• http://youtu.be/k58sOM-eWwM

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB030_Chords-in-a-Circle.pdf

Length in a Trapezoid

• http://youtu.be/ud2IaqAgO6M

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB048_Lengths-in-a-Trapezoid.pdf

Units of Big Powers

• http://youtu.be/XGWa3xpQPn0

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB067_Units-of-Big-Powers.pdf

A Tricky Length

• http://youtu.be/YwaGnhIbT3w

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB080_A-Tricky-Length.pdf

Repeated Visits

• http://youtu.be/y6EpKz3DnoU

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB084_Repeated-Visits.pdf

Successive Triangles

• http://youtu.be/FACKovCLv04

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB096_Successive-Triangles.pdf

Arranging Mean, Median and Mode

• http://youtu.be/b-Gik-QkgOY

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB128_Arranging-Mean-Median-and-Mode.pdf

Some Algebra

• http://youtu.be/N18MK00QlVw

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB135_Some-Algebra.pdf

Multi-Base Three Digit Numbers

• http://youtu.be/BZWxH2EOMd4

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB141_Multi-Base-Three-Digit-Numbers.pdf

Arithmetic Algebra

• http://youtu.be/pu5DGMD82xg

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB143_Arithmetic-Algebra.pdf

Lots of Chimes

• http://youtu.be/RZaSPtrQxEU

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB147_Lots-of-Chimes.pdf

Grade 12

Quadaratic Values

• http://youtu.be/_WuE7u0tKEM

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB016_Quadratic-Values.pdf

Frog Leaping

• http://youtu.be/GIXVVjEQcK0

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB024_Frog-Leaping.pdf

A Third of an input

• http://youtu.be/uvWw9Lzba8w

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB034_A-Third-of-an-Input.pdf

A Ratio of Areas

• http://youtu.be/Z89as7TqFKU

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB055_A-Ratio-of-Areas.pdf

A Complex Minimum

• http://youtu.be/UD2-RftIfSg

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB059_A-Complex-Minimum.pdf

Dividing by 100

• http://youtu.be/leIhtubeC14

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB093_Probably-above-a-Parabola.pdf

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

• http://youtu.be/he-ZKznE44U

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB029_Three-digit-Reversal.pdf

One Versus Two Coin Tosses

• http://youtu.be/HISqi4ij2aE

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB047_One-versus-Two-Coin-Tosses.pdf

A Triangle Area

• http://youtu.be/gVDP4WBnc2o

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB108_A-Triangle-Area.pdf

Grade 10

Eliminating Roots

• http://youtu.be/8fKhZ0D8ZJ8

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB019_Eliminating-Roots.pdf

Grade 12

The Biggest Circle

• http://youtu.be/dKE9UkIRnVY

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB091_The-Biggest-Circle.pdf

Quadaratic Values

• http://youtu.be/_WuE7u0tKEM

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB016_Quadratic-Values.pdf

Elite Players and Logarithms

• http://youtu.be/JYIiSj5lnf0

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB003_Elite-Players-and-Logarithms.pdf

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

• http://youtu.be/tvkI4Bx1tBU

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB001_Two-Trees.pdf

Dealing with Averages

• http://youtu.be/9iyc7pTatgQ

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB046_Dealing-with-Averages.pdf

Grade 10

Intersecting Tetrahedra

• http://youtu.be/35aC2mBkJpM

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB025_Intersecting-Tetrahedra.pdf

Areas of Nested Squares

• http://youtu.be/hAp-LYpBVvY

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB026_Areas-of-Nested-Squares.pdf

Chords in a circle

• http://youtu.be/k58sOM-eWwM

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB030_Chords-in-a-Circle.pdf

Skipped counts

• http://youtu.be/peu6YDlR-Oc

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB039_Skipped-Counts.pdf

Two Counterfeit Coins

• http://youtu.be/wauxZJgx8is

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB040_Two-Counterfeit-Coins.pdf

Rectangular Region

• http://youtu.be/uwTQYYk3rzs

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB036_A-rectangular-Region.pdf

Counting Two Sets

• http://youtu.be/SHkDYPfE3G8

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB071_Counting-Two-Sets.pdf

Cut the Cube

• http://youtu.be/4R9jwpldP4k

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB079_Cut-the-Cube.pdf

Biking Towards Each other

• http://youtu.be/NH41whvborI

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB083_Biking-Towards-Each-Other.pdf

Selecting Donuts

• http://youtu.be/dFh_h3me7_g

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB131_Selecting-Donuts.pdf

A Ferris Wheel Ride

• http://youtu.be/63QnORU0r4o

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB140_A-Ferris-Wheel-Ride.pdf

Grade 12

Focus and Directrix

• http://www.youtube.com/watch?v=OZUBVHhaRVs

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB005_Focus-and-Directrix.pdf

Frog Leaping

• http://youtu.be/GIXVVjEQcK0

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB024_Frog-Leaping.pdf

Parking Probability

• http://youtu.be/QMt-8oLgiMI

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB058_Parking-Probability.pdf

Bug Walking

• http://youtu.be/29pcBoAMFPQ

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB056_Bug-Walking.pdf

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

• http://youtu.be/51my8yRtAJg

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB098_Consecutive-Squares.pdf

Matching Cards

• http://youtu.be/YAjJAIC_O9Q

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB100_Matching-Cards.pdf

A Sailing Ship

• http://youtu.be/1Ov8Dt7DxOI

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB120_A-Sailing-Ship.pdf

Grade 10 

Stacking Coins

• http://youtu.be/CZH4i1HZukE

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB008_Stacking-Coins.pdf

A Curved Area

• http://youtu.be/qMzLmQvcLNw

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB050_A-Curved-Area.pdf

Largest Common Divisor

• http://youtu.be/OqPWjr6YaiY

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB053_Largest-Common-Divisor.pdf

Avid Reading

• http://youtu.be/dneMli5GLss

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB097_Avid-Reading.pdf

Grade 12

Differences of Four Numbers

• http://youtu.be/exj9F-X35Lk

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB009_Differences-of-Four-Numbers.pdf

Mean, Median and Mode

• http://youtu.be/GYB7O5G91fM

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB032_Mean-Median-and-Mode.pdf

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

• https://www.youtube.com/watch?v=SlOCS09kxWw&feature=youtu.be

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB123_At-least-as-Many-Heads.pdf

Angles in a Star

• http://youtu.be/rWRqqwzMIow

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB002_Angles-in-a-Star.pdf

Counting Non-Congruent Triangles

• http://youtu.be/5n250Xyx7O8

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB077_Counting-Non-Congruent-Triangles.pdf

A Dart Probability

• http://youtu.be/gRM_-4T7WPo

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB102_A-Dart-Probability.pdf

Best Value

• http://youtu.be/XQujml4XXHU

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB107_Best-Value.pdf

Sitting and Standing

• http://youtu.be/6dWd-l4Xx-o

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

Circles in Squares

• http://youtu.be/_LEzKLls4Mk

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB119_Circles-in-Squares.pdf

A Complicated Area

• http://youtu.be/Go11-OZ_f3I

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB121_A-Complicated-Area.pdf

Grade 10

Probably Above a Parabola

• https://www.youtube.com/watch?v=-kz29tSVBeA&feature=youtu.be

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB093_Probably-above-a-Parabola.pdf

Coloring a Pentagon

• http://youtu.be/m51Lkb4KgOo

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB031_Coloring-a-Pentagon.pdf

Sum of the Ends

• http://youtu.be/6Ci3PLexdsk

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB038_The-Sum-of-the-Ends.pdf

Counting Events

• http://youtu.be/GLiO05wdvqo

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB037_Counting-Evens.pdf

A Random Sequence

• https://www.youtube.com/watch?v=W9VESWxz32I&feature=youtu.be

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB070_A-Random-Sequence.pdf

Selecting Digits

• http://youtu.be/4G3EbwTj7Fg

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB132_Selecting-Digits.pdf

Removing Square Tiles

• http://youtu.be/FWlalzJ-rUk

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB134_Removing-Square-Tile.pdf

Ending with 23

• http://youtu.be/61t1amXsc5U

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB144_Ending-with-23.pdf

Rounded Roots

• http://youtu.be/82T0EzbL_uc

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB145_Rounded-Roots.pdf

Grade 12

Focus and Directrix

• http://www.youtube.com/watch?v=OZUBVHhaRVs

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB005_Focus-and-Directrix.pdf

Arthimetic Logs

• http://youtu.be/DntN_nQ9LuQ

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB086_Arithmetic-Logs.pdf

Iterated Function Domain

• http://youtu.be/cdSp-bdkIdE

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB089_Iterated-Function-Domain.pdf

Strategy #8 - Second Guess the author

• https://www.maa.org/math-competitions/teachers/curriculum-inspirations/Essay8

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/essay8.pdf

Grade 8

Hidden Primes

• https://www.youtube.com/watch?v=h-h0OEWCP7s&feature=youtu.be

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB064_Hidden-Primes.pdf

Grade 10

Pencil Prices

• https://www.youtube.com/watch?v=WVQhmDdJ1Bo&feature=youtu.be

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB021_Pencil-Prices.pdf

Town Population

• https://www.youtube.com/watch?v=T5nzQ69yMxI&feature=youtu.be

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB014_Town-Population.pdf

Given a Bye

• https://www.youtube.com/watch?v=IAhYaIbQ6F8&feature=youtu.be

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB051_Given-a-Bye.pdf

Melted Icre Cream

• https://www.youtube.com/watch?v=cspEh5FC-pc&feature=youtu.be

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB052_Melted-Ice-cream.pdf

A Reflected Triangle

• https://www.youtube.com/watch?v=P3R6FTPodWQ&feature=youtu.be

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB085_A-Reflected-Triangle.pdf

Grade 12

Whats the Domain

• https://www.youtube.com/watch?v=tNs1q1olg_o&feature=youtu.be

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB054_Whats-the-Domain.pdf

Bug Walking

• https://www.youtube.com/watch?v=29pcBoAMFPQ&feature=youtu.be

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB056_Bug-Walking.pdf

Strategy #9 - Avoid Hard Work

• https://www.maa.org/math-competitions/teachers/curriculum-inspirations/Essay9

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/essay9.pdf

Grade 8

Units Digit

• https://www.youtube.com/watch?v=161SYIL4sR0&feature=youtu.be

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

Shaded Triangles

• https://www.youtube.com/watch?v=ACpq-1Fb7n0&feature=youtu.be

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB041_Shaded-Triangles.pdf

Pinwheel Area

• https://www.youtube.com/watch?v=exyO45yuEbs&feature=youtu.be

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB065_Pinwheel-Area.pdf

A curious surface area

• https://www.youtube.com/watch?v=GjSTJo52wPk&feature=youtu.be

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB072_A-Curious-Surface-Area.pdf

Oneless Numbers

• https://www.youtube.com/watch?v=uze-wORVjN4&feature=youtu.be

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB075_Oneless-Numbers.pdf

Percent Shaded

• https://www.youtube.com/watch?v=GayD9lwybeM&feature=youtu.be

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB088_Percent-Shaded.pdf

Running Lemming

• http://youtu.be/KpV6pkAW5P4

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB101_Running-Lemming.pdf

Overlapping Circle and Square

• http://youtu.be/dABZgSiIaqk

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB110_Overlapping-Circle-and-Square.pdf

Remainders of Two

• http://youtu.be/JS9R7VK_pgE

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB112_Remainders-of-Two.pdf

Circle Moves

• http://youtu.be/sx3IVKTIn_4

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB106_Circle-moves.pdf

Hands of a clock

• http://youtu.be/R2H2wpWGcIM

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB117_Hands-of-a-Clock.pdf

One Zero

• http://youtu.be/tbL2QWmfTWc

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB122_One-Zero.pdf

99 Digit Products

• http://youtu.be/wBOSfYgutEI

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB127_99-digit-Products.pdf

Grade 10

Intersecting Tetrahedra

• https://www.youtube.com/watch?v=35aC2mBkJpM&feature=youtu.be

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB025_Intersecting-Tetrahedra.pdf

Red and White Chips

• https://www.youtube.com/watch?v=oQwDSWGzR_0&feature=youtu.be

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB049_Red-and-White-Chips.pdf

Grade 12

Renumbered Dice

• https://www.youtube.com/watch?v=YIwBcn3Jp4o&feature=youtu.be

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB081_Renumbered-Dice.pdf

A Compound Complex Function

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB090_A-Compound-Complex-Function.pdf

• http://youtu.be/CMdlXpAJ8yc

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

• http://youtu.be/IKlKQ3o2nVQ

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB027_Hats-and-Gloves.pdf

Different Darts

• http://youtu.be/H-efSnP-bkQ

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB111_Different-Darts.pdf

False Relation

• http://youtu.be/XRCIvFabv3E

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB124_False-Relation.pdf

Grade 10

A Line through Lattice Points

• http://youtu.be/j2J6NEGTMsY

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB095_A-Line-through-Lattice-Points.pdf

Differences of Four Numbers

• http://youtu.be/exj9F-X35Lk

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB009_Differences-of-Four-Numbers.pdf

Union of Two Sets

• http://youtu.be/Jj5ftapuDPo

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB023_Union-of-Two-Sets.pdf

How Many Twos?

• http://youtu.be/gzZyvEW1lOI

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB078_How-many-twos.pdf

A Magic Square

• http://youtu.be/NhX8nO3lHyE

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB129_A-Magic-Square.pdf

Very Eight-Centered

• http://youtu.be/zB2SCSD33UU

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB133_Very-Eight-Centered.pdf

Perfect Square Fraction

• http://youtu.be/8KQS9naVINg

• https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB139_Perfect-Square-Fraction.pdf

Grade 12

No Grade 12 problems