October 25, 2020

## What Is The AMC 8?

AMC 8 stands for American Mathematics Competition for students Grade 8 and below. According to the Mathematical Association of America (MAA), “the AMC 8 is a 25-question, 40-minute, multiple choice examination in middle school mathematics designed to promote the development of problem-solving skills”. The goal of AMC 8 is to provide an opportunity for middle school students to enjoy analytical thinking and problem solving. Students apply their mathematical skills to unique problem-solving challenges.

## What Are The Topics Covered In AMC 8?

The AMC 8 includes topics from a standard middle school mathematics curriculum. The AMC 8 website lists potential topics such as:

- Counting and probability
- Estimation
- Proportional reasoning
- Elementary geometry including Pythagorean Theorem
- Spatial visualization
- Everyday applications
- Reading/interpreting graphs and tables
- Linear or quadratic functions and equations
- Coordinate geometry

and other topics traditionally covered in a beginner’s algebra course.

## Who Administers and Scores These Tests?

The AMC is registered and administered by a Competition Manager (CM). These are usually middle schools, colleges & universities, learning centers, or math circles.

Recognitions are given to students who receive a perfect score (Certificate of Distinction), a high score (Distinguished Honor Roll and Honor Roll Certificate), and to high scoring students in the 6th grade or below (High Achiever Merit Certificate). In 2019, roughly 100,000 middle school students took this test. The MAA (Mathematical Association of America) AMC office will typically publish the test results from early to mid-December through the AMC 8 in November.

## What’s Different for AMC 8 in 2020?

Due to the current pandemic, many schools and universities, which used to be centers for paper-based testing, have decided not to host these competitions. Many parents are trying to engage their math-enthused children who have spent their year preparing for these competitions. These parents are not up to date with the latest changes and are looking for ways to enroll their students in these math competitions.

To encourage maximum participation, the AMC provided an **online option **at the beginning of Fall 2020, in addition to the conventional paper-based option. In fact, MAA recommends participants take the competition(s) online for greater ease and convenience.

The online option also gives the participant the freedom to sign up with the AMC 8 center of his or her choice (as long as the competition managers allow it). This year, The Study Huddle will be hosting the AMC 8 through our online platform. Our competition managers are in constant communication with MAA members and AoPS competition platform teams to conduct these tests fairly by understanding and enforcing the rules of the competition within the new, virtual environment.

If the students are taking the test from home in a virtual setting, proctoring options include parent/guardian proctoring and Competition Manager proctoring. However, you may want to **check with the Competition Manager to see which option they have chosen for the participant**. For details on the rules, please visit the MAA website.

In addition, there are changes in regards to what you’re allowed to bring during the test. Permitted materials are – writing utensils, blank scratch paper, rulers, and erasers. Prohibited materials include – calculators, smart watches, phones, computing devices,** compasses, protractors, and graph paper**. In earlier years, protractors, graph paper, and compasses were allowed, but are now prohibited this year.

## How Can Students Prepare For AMC 8?

**Practice, practice, practice…**- Many times, students struggle with comprehension of the problem and miss out on clues that may lead them to forming a strategy. The more you can make sense of these problems, the easier it is for you to understand the problem.

**Explore the mathematical pattern that happens around you**- Explore the connections between algebra, geometry, and some of the most elegant theorems in math like Pythagorean theorem.
- Understand the power of primes, factors, and numerical patterns.
- Actively explore all mathematical concepts you have learned; recognize why it works when the conditions are met and what those conditions are. The previous AMC-8 tests are a good source for practice and these types of mathematical explorations.

**Learn and practice with a group**- Get together with a group of math enthusiasts or join a math club. Learning involves exchanging ideas without inhibition. This happens around a group of people students feel comfortable with.
- Join a group that makes the student feel at home so he or she can share ideas as well as challenge the ideas of others and vice versa.
- Having a discussion of your explorations and findings are key to building and securing mathematical concepts. Make sure the group meets regularly once to a few times a week.

**Understand the tenets of a good problem solving strategy**- This AoPS article explains how to deal with difficult problems that can be easily summarized as follows:
- Read the problem multiple times and check if you missed any useful information.
- Start somewhere. Go through a trial and error of different numbers. Try working backwards to check if the conditions in the problems are met.
- Simplify the problem. Try the same problem with smaller numbers or whole numbers (sometimes, fractions can be hard to visualize in a division problem).
- Take a break and come back to it.
- Ask for help, a clue, or discuss it with someone.
- If you give up and look at the solution, actively solve it along with the solution provider. That means doing the same problem after watching the video or reading through the solution by yourself from beginning to end.

- This AoPS article explains how to deal with difficult problems that can be easily summarized as follows:
**Know the AMC 8 schedule and prepare ahead**- AMC-8 is typically conducted in early November each year. As you get closer to taking these tests, you can complete anywhere from 3 to 5 practice tests per week using a 40-minute countdown timer. This helps students get into a rhythm. If you’re taking the test online, you might have to draw your own diagrams; so be prepared to draw good diagrams with roughly accurate dimensions.

**Understand the progression of problems and allocate time wisely**- The problems get progressively harder and in some cases, more time-consuming towards the end. It is better to plan roughly 20 minutes for the last 10 problems and the other 20 minutes for the first 15.

**Know the rules of the competition and have the proper tools**- Permitted materials are: Writing utensils, blank scratch paper, rulers and erasers.
- Prohibited materials include: Calculators, smart watches, phones, computing devices,
**compasses, protractors and graph paper**.

December through May is a good time to learn the concepts and explore specific strategies in depth. June through November is an ideal time to practice the previous AMC 8 problems.

## How Can The Study Huddle Help?

The Math Circle programs at The Study Huddle give our students an edge over others through our competition prep classes. Our effective lesson plans, discussion groups, problem solving sessions, and math jams allow students to learn effectively. We also offer a 3-tiered math club (beginner, intermediate, and advanced) where students regularly meet and practice problem solving based on the questions from previous math competitions. Our semester-long courses allow students to learn concepts more in depth. In addition to test practice, this allows them to absorb concepts in an organized fashion.

Both the math clubs and our semester-long programs provide students with a place where they feel like they belong and are empowered to express themselves through problem solving sessions. Students immediately feel at home in our learning environment. As a result, they’re comfortable challenging each other’s ideas while learning the many ways of solving a problem and appreciating the elegance behind the solutions.

## Example Problems From AMC 8

AMC 8 2012:

**A square with area 4 is inscribed in a square with area 5, with one vertex of the smaller square on each side of the larger square. A vertex of the smaller square divides a side of the larger square into two segments, one of length ***a***, and the other of length ***b***. What is the value of ***ab***?**

One approach: In this case, as soon as you recognize the difference between the two areas (which is 1 square unit) is getting created by the four triangles of area half of ** ab**, the problem is solved. In this case, spatial visualization helps you recognize immediately that the four triangles are all congruent. Without the proper mathematical exploration of the connection between algebraic identities and spatial modeling, the students are almost sure to miss this very simple problem (with an elegant solution).

AMC 8 2010:

**Everyday at school, Jo climbs a flight of ***6 ***stairs. Jo can take the stairs ***1***, ***2***, or ***3 ***at a time. For example, Jo could climb ***3***, then ***1***, then ***2***. In how many ways can Jo climb the stairs?**

Students could solve this problem by the brute force method. They will organize a pattern around how many ways can Jo move in each step. Another approach is much more elegant and faster. First they analyze the pattern.

Step-1: 1 step

Step-2: 1,1 or 2

Step-3: 1,1,1, 1-2 or 3

From here on, it’s about building a pattern. If you haven’t seen the pattern already, you may think of it like this–to get to step 4 from step 1, he could have done a 3-step leap. Similarly, to land on 4, he could have jumped two ways using a 2-step leap. (a 1,1,2 or 2,2). And finally from step 3, he could have landed on 4 in 3-ways using a single step. This brings us to a beautiful solution that is an extension of the Fibonacci sequence; we are adding the last three numbers to get to the next number. Without proper exploration of this pattern, students would have struggled organizing and recognizing this pattern.

If you are interested in learning more about AMC 8 prep and similar academic competitions, The Study Huddle’s math department offers dedicated, live online prep courses for AMC 8 (beginner) and AMC 8 (advanced). We also offer Mathcounts prep courses for the upcoming Mathcounts competitions. Browse our online talent programs and contact us to learn more today!