Math Resources, Competitions, and Curriculum Suggestions

Competitions:

Math Problems:

NRICH enriching mathematics
NRICH Geometry and Measures

AMC 8, AMC 10/12, AIME:
AMC 10/12
AMC 8
AMC 8 Registration Form
AMC 8 Problems and Solutions
American Invitational Mathematics Exam

Resources:

MathCounts

MathCount Resources (MIT site)

MATHCOUNTS Trainer App

Interactive MATHCOUNTS Platform
How to Write MathCounts Competition Answers

MathCounts Topics (JHU MathCounts Syllabus):

1. Fundamentals: Arithmetic
2. Proportional Reasoning
3. Radicals and Exponents
4. Algebra A: Polynomials, Linear Equations and Functions
5. Algebra B: Applications, Nonlinear Equations, Inequalities, Functions.
6. Plane Geometry
7. Coordinate Geometry
8. Solid Geometry (addresses also transformational geometry)
9. Statistics and Probability
10. Sequences and Series
11. Problem Solving

Art of Problem Solving Videos
Khan Academy Mathematics Videos

Math Typesetting Tool
SAGE Math Cloud
Geometry Sketching Tool

Math Curriculum Suggestions from AOPS
Curriculum Inspirations by James Tanton, PhD (videos)

Thinking and G'Day Mathematics (resources for students and teachers):
http://www.jamestanton.com/
http://gdaymath.com/

Book of Proof (Free PDF available under Creative Commons License)

Other Competitions:

Math Olympiad for Elementary and Middle Schools (MOEM)

Purple Comet 

Math Kangaroo 
Math League

Pi Math Contest ( FIFTH GRADERS and below)
Continental Math League

Division M2 Session 5/8/2016

Instructor:	Mr. Ahmed Hefny
Attendance:	Adan, Omar, Areej
Handout:	Pre-Algebra Chp 2
Problems Solved in Class:	Chosen exercises from chapter 2
Concepts:	* Definition of exponent * Properties of exponent:     - Not commutative     - Not associative (default order is top to bottom)     - Does not distribute over addition     - Distributes over base multiplication (ab)^c = a^c * b^c     - 1 is a "right identity" element.  * (a+b)^2 = a^2 + b^2 + 2ab. It can be proven using distributive property.  * Negative powers.  * 0th Power. * Powers of 0.
Student Difficulties:	. Students still have difficulties using variables to prove general statements. . A problem that took un expected long time is showing that: (2a+2b)^m = 2^m (a+b)^m Students had trouble figuring out that this is a simple application of distributive properties.
Homework:	· Chapter 2: Please watch teh videos and make sure you can solve example problems. . Solve exercises: 2.1.2, 2.1.5, 2.1.9, 2.2.6, 2.2.10, 2.2.11, 2.4.6 . Solve review exercises: 2.45, 2.50. 2.76
Notes:

Division M1 session on April 17, 2016

Instructor:	Mr. Zia Hydari
Attendance:	AbdulRafay, Sohaib, Abiha, Abdul Qadir, Adeel, Rami, Kamal
Handout:	Pre-Algebra http://aops-cdn.artofproblemsolving.com/products/prealgebra/exc1.pdf
Problems Solved in Class:	Problems illustrating the distributive property
Concepts:	Operators, distributive property
Student Difficulties:	Using variables to prove properties e.g. if the operator “@” is defined as: a @ b = 2a + 2b and I asked students to prove that “@” is commutative, the students used specific numbers to create examples but did not use variables to construct a general proof.
Homework:	·         Read Section 1.1, 1.2, and 1.3 ·         Watch all of the videos for Section 1.1, 1.2, and 1.3 from https://www.artofproblemsolving.com/videos/prealgebra ·         If you need more help, please watch the following videos and work through the online exercises at: o    https://www.khanacademy.org/math/pre-algebra/order-of-operations/arithmetic_properties/v/commutative-law-of-addition o    https://www.khanacademy.org/math/pre-algebra/order-of-operations/ditributive_property/v/the-distributive-property ·         Solve all of the exercises and problems from Section 1.1, 1.2, and 1.3 ·         Solve problem 1.71 on page 51. Then solve these additional items: 1.     Does multiplication distribute over “@”? 2.     Does addition distribute over “@”? 3.     Does “@” distribute over addition? 4.     Does “@” distribute over multiplication? HINT: First, try to solve on your own; then use the hint below. Recall that problem 1.71 in the book defines the operator “@” as:  a @ b = 2a + 2b Part 1 asks if the following is true: a ( b @ c) = ab @ ac Part 2 asks if the following is true:  a + (b @ c) = (a + b) @ (a + c) Part 3 asks if the following is true: a @ (b + c) = (a @ b) + (a @ c) Part 4 asks if the following is true: a @ bc = (a @ b) (a @ c)
Notes:

Division M1 session on April 10, 2016

Instructor:	Mr. Zia Hydari
Attendance:	AbdulRafay, Sohaib, Abiha (Abdul Qadir?, Adeel?, Rami?, Kamal?)
Classwork:	Problems illustrating the distributive property
Homework:	All problems from Section 1.3

April 3, 2016—CONTEST for All Levels (E, M1, M2)

March 27, 2016—NO AKCMP sessions

AKCMP closed as MCCGP Sunday School was closed.

Division M1 session on March 20, 2016

Instructor:	Mr. Isa Hafalir
Attendance:	AbdulRafay, Abiha, Rami
Classwork and Homework	In the first half, we did Pre-Algebra book Section 1.3 and exercises 1.3.5 to 1.3.11 were assigned as homework. In the second half, we went over Set 10 Olympiad 5 and Set 11 Olympiad 1. 5 questions in Set 11 Olympiad 2 were assigned as homework.

Division M2 session on March 13, 2016

Instructor:	Mr. Ahmed Hefny
Attendance:	Ayan, Adan, Areej, AbdulRafay, Bilal, Baseer, Omar
Handout:	Pre-Algebra Chapter 1
Problems Solved in Class:	* Probability problems: throwing a die and drawing from a deck of cards. * Disproving false statements about properties of operators: commutative and associative properties of subtraction, addition distributes over multiplication.
Concepts:	[Session 1] A brief introduction to probability:* Probability and statistics are two opposite inference paths; probability tells us, given knowledge about a random process, how to answer questions related to samples from that process. [Ex: what is the probability of getting 3 heads in a row if I throw a fair coin three times ?]. Statistics tells us, given a sample from the random process, how to gain knowledge about that process. [Ex: Given a sample of 10000 voters, how much is the American community biased towards Republicans ?] * Basic probability laws and the conditions for their correctness: Let A and B be two conditions (usually called events) - P(A) = # of outcomes that satisfy A / # of all possible outcomes      [Assuming all outcomes are equally likely] - P(A and B) = P(A)P(B)              [iff A and B are independent] - P(A and B) = P(A)P(B|A)          [P(B|A) is the probability of B happening given that A happened. P(B|A) = P(B) iff A and B are independent]- P(A or B) = P(A) + P(B)             [iff A and B are disjoint i.e. A and B cannot happen together]- P(A or B) = P(A) + P(B) - P(A and B)      [This is the same inclusion-exclusion principle for counting the union of two sets]     [Session 2] Pre-algebra: - Commutative property- Associative property - Distributive property - Disproving a property by a counter-example - Negation vs subtraction. Negation is a unary operator (takes one number) and gives its negative. Subtraction is a binary operator (takes two numbers) and returns the difference. They happen to use the same symbol '-' but they are different things.
Student Difficulties:	Thinking in terms of equations Generalizing distributive property to arbitrary operators.
Homework:	Download PDF Note: There are some hints in the end of the file. Try to solve first without looking at them.
Notes:	You can access video resources at: https://www.artofproblemsolving.com/videos/prealgebra Videos related to today's session are the first four videos of chapter 1.

Division M1 session on March 13, 2016

Instructor:	Mr. Zia Hydari
Attendance:	AbdulRafay, Sohaib, Abiha, Abdul Qadir (not present: Adeel, Rami, Kamal)
Handout:	Pre-Algebra http://aops-cdn.artofproblemsolving.com/products/prealgebra/exc1.pdf
Problems Solved in Class:	All exercises from section 1.2.
Concepts:	Commutative, associative, and identity for addition operator
Student Difficulties:	Avoiding unnecessary computations.  Working out the problems step-by-step. Using mathematical vocabulary e.g. commutative property in explaining solution. Identity for addition.
Homework:	Read Section 1.1 and 1.2. Watch all of the videos for Section 1.1, 1.2, and 1.3 from https://www.artofproblemsolving.com/videos/prealgebra Solve all of the exercises and problems from Section 1.1 and 1.2
Notes:	You can download the handout for Section 1.1 and 1.2 from http://aops-cdn.artofproblemsolving.com/products/prealgebra/exc1.pdf

Feb 28, 2016—Math Contest

No classes—students participated in Math Contest. The winners were announced on March 6th:

M2: Basir, Omar
M1: Bilal M, Abdur-Rafay
E:   Abiha

Division M1 session on March 6, 2016

Instructor:	Mr. Isa Hafalir, Mr. Zia Hydari
Attendance:	AbdulRafay, Adeel, Bilal, Remy, Sohaib, Areej
Handout:
Problems Solved in Class:	MOEMS Volume 3 p. 73: 3C, 3D, and 3E MOEMS Volume 3 p. 74: 4D, 4E From the contest on Feb 28th:  1, 2, 4, 5, and 6.
Concepts:	Mean, median, mode. Percent change. Area. Congruent shapes.
Student Difficulties:
Homework:	MOEMS Volume 3 p. 75 (all problems from Set 10 Olympiad 5). Due date is March 20th.
Notes:

Division M1 session on Feb 21, 2016

Instructor:	Mr. Isa Hafalir, Mr. Zia Hydari
Attendance:	AbdulRafay, Adeel, Bilal, Ramy, Sohaib, Areej
Handout:	MOEMS Vol 3, pp. 72–85 (please bring this handout to every class)
Problems Solved in Class:	MOEMS Volume 3 handout: All problems on p. 72 From Geometry Chapter 2 handout: 2.44, 2.45, 2.53, 2.54,
Concepts:	Angles, parallel lines, triangles (esp. exterior angle), counting, greatest common divisor
Student Difficulties:	Not counting systematically. Proofs.
Homework:	Finish all problems from Geometry Chapter 2 handout If you face any difficulties, please make sure that you complete the old homework on Khan Academy missions: Lines, Angles, Shapes
Notes:	CONTEST on Sunday Feb 28th. To prepare for the contest, please make sure that you have solved all problems in Geometry Chapter 2 handout. There will be additional problems similar to the ones in the MOEMS handout.

Division E session on Feb 21, 2016

Instructor:	Rudina Morina
Attendance:
Handout:	MOEMS Vol 3, p. 36
Problems Solved in Class:	MOEMS Volume 3 handout: All problems on p. 36 except the last one
Concepts:
Student Difficulties:	Students have not studied probability, which is why the last problem had to be left out.
Homework:
Notes:

Division M2 session on Feb 21, 2016

Instructor:	Mr. Isa Hafalir, Mr. Ahmed Hefny
Attendance:	Ayan, Adan, Omar, Baseer
Handout:	Purple comet problems
Problems Solved in Class:	- Problems 1-5 of 2015 Purple Comet test - Examples from "Introduction to Counting and Probability"
Concepts:	Counting: - Counting number of elements in a list: Off-by-one errors, problem reduction: reduce a more difficult problem to a simpler one; transforming elements in a list does not change the number of elements. - Counting using Venn diagrams- Constructive Counting: Define a generative process to create solutions such that the number of possibilities in each step of the process can be counted. - Complementary Counting: When counting the number of solutions that satisfy a condition, sometimes it is easier to count the number of solutions that do NOT satisfy the conditions (let's call that x). The answer then would be:answer = number of all solutions - x
Student Difficulties:
Homework:	Homework due 3/6: Purple Comet Problems: Problems 6-15 Counting:  https://www.dropbox.com/s/zy3vdbrdj4ifrsw/CountingDay1.pdf?dl=0
Notes:	* Please bring working sheets and pencils to upcoming sessions. * A competition will be held on 2/28. It will cover all concepts discussed so far. Use purple comet handout for preparation.

Division M1 session on Feb 07, 2016

Instructor:	Mr. Zia Hydari
Attendance:	AbdulRafay, Adeel, Bilal, Ramy, Sohaib, Areej
Handout:	No new handout today; I returned graded competition questions
Problems Solved in Class:	Problem 5–10 from the competition given out last week
Concepts:	Angles, parallel lines, triangles (esp. exterior angle)
Student Difficulties:
Homework:	Please complete the following problems from the handout that I gave a few weeks ago: Monday: 2.31, 2.35 Tuesday: 2.36, 2.39 Wednesday: 2.42, 2.44 Thursday: 2:45, 2.46 Friday: 2.49, 2.50 Saturday: 2.51, 2.52.  If you face any difficulties, please make sure that you complete the old homework on Khan Academy missions: Lines, Angles, Shapes
Notes:
Winner for Jan 2016 Competition	AbdulRafay (winner); Areej (runner-up)

Division M2 session on Jan 24, 2016

Instructor:	Mr. Ahmed Hefny
Attendance:	Ayan, Adan, Omar, Baseer
Handout:	Combinatorics Problems I
Problems Solved in Class:	2,9 and 11
Concepts:	Counting, Factorials, Permutations and Combinations
Student Difficulties:	Although the terms factorials, and combinations seemed to ring a bell. There was difficulty solving more general counting problems. I believe the general material may be new to the students.
Homework:	Attempt rest of problems in the handout, For questions that ask for probabilities, solve for "In how many ways could X happen" instead of "what is the probability of X happening".
Notes:	Most students had difficulty with problem 1 in the last geometry homework.
Winner:
Main ideas:	* The number of outcomes of a multistep decision sequence is the product of the number of possibilities for each decision. Example 1: Number of ways to order n elements = n * (n-1) * (n-2) * ... * 1 = n! * If there are different alternatives to decide (part of) the outcome, the number of possibilities of these alternatives should be added. * When confused, draw a tree of decisions and then go bottom-up: each leaf represents a single outcome. The number of outcomes from a on-leaf node is that sum of outcomes from its children. Usually, you won;t need to draw the tree down to the leaves. * One strategy to find the number of possible values of part of the outcome you care about (e.g. 4 out of 10 numbers) is to use the following factorization: number of possible full outcomes = number of possible values of the part we care about * number of ways to decide the values of the part we don't care about. The quantity in red is the one we want to compute, the other two are usually easy to compute. Example 2 - number of ways to select r elements from n elements where order matters (nPr): number of ways to order n elements = nPr * number of ways to order the remaining n-r elements --> n! = nPr * (n-r)! --> nPr = n! / (n-r)! Example 2 - number of ways to select r elements from n elements where order does not matter (nCr):number of ways to select r elements from n elements where order matters = nCr * number of ways to order the selected r elements --> nPr = nCr * r! --> nCr = nPr / r! = n!(n-r)! / r!

Division M1 session on Jan 24, 2016

Instructor:	Mr. Zia Hydari
Attendance:	AbdulRafay, Adeel, Bilal, Ramy, Sohaib, Areej, Abdul Qadir
Handout:	Angles (definitions, review problems, challenge problems)
Problems Solved in Class:	2.28, 2.29, 2.30, 2.31
Concepts:	Axioms, Euclid's Axioms, Angles, Parallel Lines
Student Difficulties:	Students who did not do homework had difficulties which slowed down the class as I had to review concepts.
Homework:	Complete Khan Academy missions: Lines, Angles, Shapes Solve (or at least attempt) Problems 2.32 to 2.46 (p. 46–47) in the handout. Bonus points for finishing challenge problems (2.47–2.57).
Notes:	Most student did not complete the Khan Academy mission on Lines and Angles before class. Those who did, found the material easy.
Winner:	Areej (highest class score for solving problems on the board)

Division M2 session on Jan 17, 2016

Instructor:	Ahmed Hefny
Attendance:
Handout:	Level 5 Geometry Problems (All homework except problem 5). Please download the handout by clicking here.
Problems Solved in Class:	Problem 5
Concepts:	Pythagorean theorem, congruent triangles, similar triangles
Student Difficulties:	Square roots, solving geometry problems by constructing intermediate shapes.
Notes:	Congruent Triangles Two triangles are congruent if they have equal side lengths and angle measures.  We do not need to test ALL lengths and measures; there are minimal tests for congruency.   Usually the solution strategy goes as follows:  There is missing piece of information about triangle A (e.g. missing side length)  The information we have about A is sufficient to establish congruency with another triangle B using one of the minimal tests.  Once congruency is established, we determine missing information about A from what we know about B.  Minimal tests for congruency:  Three sides  Two sides and the angle between them  Two angles and the side between them  If the two triangles are right. Any two sides suffice (due to Pythagorean theorem)  How do we know these tests are sufficient ?  The information used in the tests uniquely identify all lengths and angles of a triangle.  Example 1:  Knowing the lengths of all sides uniquely determines the shape of a triangle. Figure 1 shows how to draw a triangle knowing the lengths of the three sides using a ruler and a compass.  Example 2:  Knowing the lengths of two sides and the measurement of an angle other than the one between them does not uniquely determine the shape of a triangle.  Similar triangles:  The ratios of side lengths are the same for all corresponding sides.  Corresponding angles have equal measures.  Each property implies the other one.  If two shapes are similar with side length ratio r, the are ratio is r*r and the volume ratio is r*r*r.  Important right triangles:  See figure 3.  Resources: https://www.khanacademy.org/math/geometry/cc-geometry-circles/area-inscribed-triangle/v/area-of-inscribed-equilateral-triangle-some-basic-trig-used