ORMC Meetings • 2020-2021 Academic Year

For our first lesson, we will introduce pooled testing in the context of coronavirus.

We will be introduced to modular math. We completed pages 1-6 of the handout.

We will be continuing the second half of the handout on modular math. We will also learn modular math applications, such as checksums.

We will finish up our review on modular math, learning how to subtract and divide in modular math as well as learning how to prove divisibility rules with modular math.

We will be exploring an ancient Egyptian technique of splitting fractions into their unit parts. We completed pages 1-16.

We will continue our exploration of Egyptian fractions (pages 17-24). Homework is pages 25-26.

To conclude our exploration of Egyptian Fraction Representation, we will complete the Egyptian Fractions part 1 handout and begin Egyptian Fractions part 2. Pages 6-8 EFR part 2 are assigned as homework.

We will look a method to prove mathematical hypotheses: proof by induction.

We will continue to explore proof by induction and introduce proof by contradiction. *Last class of fall quarter, Happy Holidays!

Suppose we break a stick into three pieces randomly. What are the chances the resulting pieces will form a triangle?

We will continue and complete our packet on breaking sticks. In which scenario are we most likely able to form a triangle from our broken sticks?

This week we will learn how to convert between fractions and decimals, while also exploring the properties of terminating and non-terminating decimals.

We will continue to explore terminating and non-terminating decimals. WHY do decimals have these properties? How can we write non-terminating decimals as fractions?

We will write and define sequences and numbers through explicit and recursive definitions. We will also explore arithmetic sequences and how we can generalize the sum of n-terms in the sequence.

We will continue our work on arithmetic sequences, then transition to learning about arithmetic series.

We will introduce geometric sequences and explore how using geometric series can help us convert non-terminating decimals to fractions.

Today, we introduce combinatorics: the mathematics of counting.

We will complete the combinatorics worksheet from last week. Furthermore, we will explore what happens if the order of the items in our list matters.

Can you move the earth with a lever? Today's math circle lesson will require creativity, physics, and a little intuition to balance levers.

We will refresh our minds on combinations and permutations from before spring break, and we will also begin to explore probability.

To test our knowledge of combinatorics that we learned over the past few weeks, we will go over 4 tough problems.

How can we estimate our dartboard score by using probabilities? Today we explore the first 7 problems (pages 1-4) of our probability packet.

Back to the basics: how can we describe probability for rolling dice and flipping coins? Today we tackle pages 5-10 of our probability worksheet.

Today, we will complete the probability packet and explore set notation.

How can probability be applied to more than dartboards, dice, and coins? Genetics! Today we will explore how we can use probability in biological applications to figure out blood types, hair colors, nose shapes, and more!

We will finish our genetics worksheet from last week and then start with a new topic: herd immunity! What needs to happen in a population to reach herd immunity? How can we approach it mathematically?

For our last class, we will review all of the best problems and topics from the school year.