These MATHCOUNTS Practice Plans are designed to help you prepare for competition. They cover a variety of topic areas and generally increase in difficulty as you progress through them. Each plan is intended to cover 45 minutes to 1 hour of practice time. The plans are divided into four sections:

Mathcounts Tips for Beginners. Twenty Problem Solving Skills for Mathcounts. Twenty More Problem Solving Skills for Mathcounts. 50 Mathcounts Lectures. 50 Mathcounts Lectures Solutions. Mathcounts Speed and Accuracy Practice Tests. Mathcounts State Competitions Preparation Books. Eleven Years Mathcounts Chapter Solutions. October 2019 This video shows how to approach any probability problem without fear. Download the Activity Sheet here. Download the Solutions here. Video by Art of Problem Solving's Richard Rusczyk, a MATHCOUNTS alum. Interesting Math Problems ABOUT MathCON MathCON is a nonprofit national mathematics organization recognized for its annual student math competition for students in grades 4-12, with more than 200,000 participants since 2008. Mathcounts is a club at Mendive for students to practice problem solving and have fun learning math! We will compete in a school competition, district competition, and state competition. Mathcounts in a national organization for middle school students to learn build confidence and great attitudes in math. The goal of this 12 week course is to give students an introduction to the problem solving strategies required to succeed in the Mathcounts competitions at the school and chapter levels. In a collaborative platform with guidance from the coaches, students will share their ideas, challenge their own understanding of several mathematical concepts.

Counting Paths Along a Grid

How To Study Mathcounts: Math Problem Solving Inequalities

Explore combinatorics by looking at a common type of MATHCOUNTS counting problem – counting paths between two points. End with an extension that connects counting paths to another type of combinatoric problem.

Counting Shapes in a Complex Figure

This plan will help Mathletes to develop a strategic approach to counting the occurrences of a certain shape in a more complex figure made of multiple intersecting lines.

Difference of Squares

An important formula to know, the difference of squares identity is derived geometrically in the video for this practice plan. Mathletes will then try to recognize the difference of squares structure in various expressions and use the identity find the value.

Distance = Rate x Time

Explore the formula d = rt by starting with unit conversion problems. Mathletes will solve for distance, rate and time by paying attention to the units given in the problem and using the appropriate equivalent version of the formula: d = rt, r = d/t or t = d/r.

Divisibility Rules

Students will apply divisibility rules of various integers to simplify computation, better understand number composition and aid in problem solving. In the extension, Mathletes can prove why each of these rules work!

Faster Arithmetic Methods

Using the commutative, associative and distributive properties, Mathletes will arrange arithmetic problems in a different order that allows them to be solved more readily.

The Fundamental Counting Principle

This plan will introduce students to The Fundamental Counting Principle – a faster method to determining the total number of possible outcomes of an event without listing them all out!

Least Common Multiple

Calculating the least common multiple is something many students are asked to do, but in this plan they will use their understanding of the least common multiple to stretch themselves to solve more complex problems.

Order of Operations & Defining New Rules

After refreshing Mathletes on the order of operations, the video will then focus on how to solve problems where an unfamiliar symbol is defined to be a new type of operations that follows given rules.

Ratios & Simple Probability

This plan builds on what students already know about ratios to introduce the definition of probability as a ratio of desired outcomes to total outcomes. Mathletes will then practice calculating the likelihood of single events.

Representing Patterns Numerically

In this practice plan, Mathletes will recognize visual patterns and practice defining them numerically in order to find the number of elements in the pattern after a large number of repetitions.

Special Right Triangles

Mathletes will become familiar with properties of 45-45-90 and 30-60-90 triangles. In this plan, the relationships between the sides of these two special right triangles will be derived. Then, Mathletes will apply these to solve for unknown lengths in geometric figures.

You Don’t Have to Solve for x!

Often the immediate reaction when Mathletes see an algebraic equation is to solve for the unknown but depending on what you are looking for it might be easier to manipulate the equation without solving it.

MATHCOUNTS Minis

Mathcounts Problem Of The Week

Need more practice? Check out the similarly structured MATHCOUNTS Minis from Art of Problem Solving's Richard Rusczyk! These minis explore even more topics and go in depth on areas touched on in these practice plans.

Mathcounts Past Problems

LinkedIn Coaches Group

How To Study Mathcounts: Math Problem Solving Equations

Connect with fellow coaches and MATHCOUNTS staff on the LinkedIn MATHCOUNTS Competition Coaches page. This is a great opportunity for dialogue with the coaching community about best practices, share resources and to get answers to questions plus additional support!