Los Angeles Math Circle

LAMC Meetings • 2019-2020 Academic Year

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For meetings prior to Fall 2019, visit the Circle Archive.

Advanced 1AAdvanced 1BAdvanced 2AAdvanced 2BBeginners 1ABeginners 1BBeginners 2ABeginners 2BBNPIntermediate 1A
Intermediate 1BIntermediate 2AIntermediate 2BOlympiads 1Olympiads 2
10/6/2019
To start out the quarter, we will be developing logic skills by looking at problems with hats and doors. The goal of this handout is to learn how to make an assumption, test the assumption, and readjust the original assumption if necessary.


Handouts: handout | solutions
10/13/2019
An alternate method of multiplication based in binary numbers and the basic ideas of the distributive property.




Handouts: Handout | solutions
10/20/2019

We will continue with different ways to multiplying 2 numbers. This week we will look at Russian Peasant Multiplication, which, surprisingly, has no relation to Russia or Peasants. However, this will be another good way to show the students how to write numbers as sum of powers of 2



Handouts: handout | answers
10/27/2019

This packet introduces the topic of exponents, some of their properties, and size comparison!

11/3/2019

Continuing last week's handout!

Handouts: handout | pg 4 answers
11/10/2019

Review what we learned about exponents and continue to build how to compare numbers

11/17/2019

A look at how we can organize multiple sets of objects/people/things using venn diagrams!

11/24/2019

This week we will be looking at what it means for shapes to be similar, as well as exploring how we can add on to a shape to create another that is similar to the original.

12/1/2019
12/8/2019

For the last meeting of 2019, we will be playing a Math Review Game!

1/12/2020

We started a warm-up discussing auction theory. We will begin our exploration of game theory by starting with the example of subtraction games of varying subtraction sets.

Handouts: handout | solutions
1/19/2020

This week we started off class discussing "I cut you choose." We then continued will be continuing our discussion of subtraction games, in particular the Game 21. With 21 sticks, each player can either take away 1,2, or 3 sticks each turn, what is the winning strategy if you don't want to take the last stick? If you want to take the last one? How are these two related?

1/26/2020

This week, we will be preparing for the Math Kangaroo contest by working out various types of problems!

Handouts: solutions | handouts
2/2/2020

Intro: How many days are in a year? How are leap years counted? Why do we include every 400 years, but not 100, 200, or 300? Hint: a year is technically about 365.25 days - 11 minutes.

In this handout we examine how to systematically perform calculations to find the day of the week (Sunday, Monday, Tuesday, etc.) a particular date is, e.g., your birthday

Handouts: handout | solutions
2/9/2020

Warm-Up: What is the trick to square numbers ending with 5 and why does it work?

More math kangaroo problems!

Handouts: handouts | solutions
2/16/2020
2/23/2020

Warm-Up: Multiply two-digit and three-digit numbers using the criss-cross method! It really reduces the amount of work required!

Today we will be introducing the topic of Polyhedras and learning the terminology.

Handouts: handout | solutions
3/1/2020

Warm-Up: If I give you two numbers, like 998 and 992, and I ask you to multiply them together using conventional math techniques, you end up writing a lot of numbers to generate the answer. But notice that 998 is just 2 shy of 1000, and 992 is just 8 shy of 1000. If you multiply 2 times 8, you get 16. And if you take 8 away from 998, or you take 2 away from 992, you get 990. And guess what? The correct answer is 990016. Similarly, if I ask you to multiply 990 times 991, you could work it out ... or you could recognize that 990 is 10 below 1000, 991 is 9 below, the product of 9 and 10 is 90, and 990 minus 9 is 981, and 991 minus 10 is also 981. The answer: 981090.

The insight: if you rewrite 998 as (1000-2) and 992 as (1000-8), multiply the two we get 1000*1000 - 2*1000 - 8*1000 + 8*2. Hence we get (1000-2-8)*1000 + 16 = 990,016.

We will be continuing our topic on Polyhedra from last week!

Handouts: handout | solutions
3/8/2020

This week we will be continuing our topic of Polyhedras, but this time developing a more rigorous relationship between edges, vertices, and faces!

Handouts: handout
3/15/2020

This week we will be continuing our topic of Polyhedras, but this time developing a more rigorous relationship between edges, vertices, and faces!

Handouts: handout
4/5/2020

This helps students see what age-appropriate math problems look like in a different country!

Handouts: handout | solutions
4/12/2020

This week, we will be introducing the distance formula!

Handouts: handout