# Free Resources for Any Middle School Math Concept

MATHCOUNTS provides many free problem sets, videos, lesson plans and activities that can complement in-person and online learning. We've categorized some of the best resources for several middle school math topics:

- Arithmetic Skills
- Introduction to Counting
- Basic Number Sense
- Exploring Equations
- Properties of Right Triangles
- Multiple Approaches to Problems
- Squares
- Using Similar Figures
- Area and Perimeter
- Sequences, Series and Patterns (Part 1)
- Sequences, Series and Patterns (Part 2)
- Probability
- Circles
- Rates and Proportional Reasoning

Use these resources to help you plan your next online learning session!

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

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.

In The Multiplication Game players take turns chosing factors to obtain a product on the game board. The first player to four squares in a row wins. The game can be used to practice multiplication tables and factor pairs as well as to discuss prime and composite numbers.

In a heads up style game, students use inverse operations to guess the card on their forehead. They may or may not realize they are doing algebra! Register for the free National Math Club to access this game and dozens of others!

Operations with fractions are often hard for students to conceptualize. With this exploration's dry erase maze boards and four basic arithmetic operations, Mathletes can begin to uncover the secrets of fractions by finding a path that results in the least value or the greatest value. Register for the free National Math Club to access this activity and dozens of others!

Help students improve their basic arithmetic skills by competing in a club counting bee. Given a starting number and counting number, see how far students can count in 15 seconds! Register for the free National Math Club to access this game and dozens of others!

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.

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.

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!

This video focuses on using diagrams and organized lists to ensure that each possible outcome is counted once, and only once.

Moving beyond the fundamental counting principle, students will be introduced to the difference between combinations and permutations, and presented with multiple methods for solving these types of problems.

Two sets of ten practice problems from the 2002-2003 and 2015-2016 MATHCOUNTS School Handbook that cover basic counting including some number sense, shapes and paths.

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!

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.

In the Marble Challenge students will take turns removing marbles with the goal of not taking the last marble. This game encourages students to notice patterns in the numbers and can even be used to introduce modular arithmetic. Register for the free National Math Club to access this game and dozens of others!

Using increasingly popular KenKen® puzzles, Mathletes will use teamwork, number sense and logic skills to solve challenges. Register for the free National Math Club to access this activity and dozens of others!

Often in MATHCOUNTS you find yourself with a unique problem you don't already have a prescribed method for solving. This mini gives examples of such problems that can be solved with a little logic, number sense and understanding of divisibility rules.

In these number sense stretches, there are three problem sets (10 problems each) from old MATHCOUNTS School Handbooks that covers number sense topics such as factoring and divisibility. These are great additional practice in after trying the Practice Plans and MATHCOUNTS Minis.

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.

This exploration is a great way to practice translating word problems into algebraic equations and to develop understanding of the concept of inverse operations. Mathletes will be amazed at first by what appears to be magic, but they will come to understand that the tricks can be explained using algebra. Mathletes can come up with their own magic examples to impress their friends and families and become true mathemagicians! Register for the free National Math Club to access this activity and dozens of others!

This exploration lets Mathletes manipulate functions in order to explore and better understand translating, stretching, compressing and other transformations of functions. Through the Desmos platform, with the added twist of similarity to the board game Battleship, Mathletes can graph functions and see the effects of changing coefficients and exponents and adding and subtracting integers. Register for the free National Math Club to access this activity and dozens of others!

In a heads up style game, students use inverse operations to guess the card on their forehead. They may or may not realize they are doing algebra! Register for the free National Math Club to access this game and dozens of others!

These problems and video focus on translanting the information in word problems into representative algebraic equations.

When dealing with systems of equations, if you are able to recognize symmetry between the equations, you can simplify the steps to a solution. This Mini will look at some problems and demonstrate how to find and use the symmetry to your advantage.

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.

From special right triangles to Pythagorean Triples, this video shows how to use properties of right triangles to solve problems.

This exploration gives Mathletes a brief introduction of the Pythagorean Theorem, then guides them through what we call Proofigami. This fun exploration will feel a lot like origami, but will provide Mathletes with a better understanding of the Pythagorean Theorem and gives club leaders a visual and tactile tool that makes explaining this proof easier. Register for the free National Math Club to access this activity and dozens of others!

This MATHCOUNTS Mini will look at ways to use known ratios of 30-60-90 triangles to help solve more complex geometric problems.

Practice solving problems by using the Pythagorean Theorem, recognizing Pythagorean triples and applying properties of special right triangles.

This video explores how we can decompose a figure into trapezoids and triangles to determine its area. The problems associated with this mini will help students determine when and how to apply their right triangle knowledge to solve more complex geometry problems.

This video demonstrates multiple problem-solving strategies and emphasizes the importance of solving problems in more than one way to verify that you've solved a problem correctly.

This video reinforces the concept of solving a problem multiple ways to validate your answer.

Being able to take multiple different approaches to solve problems is an invaluable skill. In this problem set, students will look at four techniques - creating a model, acting out a situation, drawing a picture and making a list.

Chances are students are familiar with tic-tac-toe, but these rule variants on the traditional version will challenge students to rethink their strategy. Use this game to talk about symmetry, logic and proof writing.

This video explores how to solve problems by drawing a picture to organize the given information.

This video demonstrates how making a sketch of a given scenario can be a useful strategy when solving problems.

This video focuses on recognizing squares and using them to solve a simpler problem.

This video explores how to use the difference of squares to solve problems and why this method works.

Apply the difference of squares formula in order to solve problems involving systems of equations.

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

This video demonstrates how to use perfect squares to find a simpler case to help solve a problem.

This video demonstrates how to solve problems using the difference of squares.

This video shows how to identify and use similar triangles to solve geometry problems.

This video explores how to apply properties of similar triangles in solving problems about two-dimensional and three-dimensional figures.

Practice with the concept of similarity by answering questions about similar figures, and see how similarity relates to proportional reasoning and geometric transformations.

This video demonstrates how to use similarity and proportional reasoning to solve difficult geometry problems.

Sometimes it is necessary to create the similar triangles you'll need in order to solve a problem. This video shows how to look at and build on given diagrams to create similar figures.

This video explores how to use parallel lines and angles to identify similar triangles and solve problems.

After rolling dice to determine the size, in part, of a rectangle, players then use perimeter and area formulas to determine dimensions. The goal is to try to fill up the board first.

This video demonstrates two strategies for how to find the area of an irregular convex polygon.

Find the areas and perimeters of various figures, and see how area and perimeter measurements can be used to solve other types of geometry problems.

This video demonstrates how to find the area of an irregular polygon by dividing the figure into smaller regions for which the area is more easily determined.

This video explores how we can decompose a figure into trapezoids and triangles to determine its area.

Practice calculating area and perimeter measurements using the image of a shamrock.

This video focuses on techniques for solving problems by looking for patterns that emerge among the digits in large numbers.

Recognizing patterns in objects in order to express them mathematically is an important skill for students to learn. In this game students will attempt to recognize visual and numeric patterns in a group of cards.

This video shows how to find patterns in both visual and numerical sequences and how to use patterns to identify an unknown value in a sequence.

This video demonstrates how to find a pattern in a sequence or series, and prove that it works, to solve problems.

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.

Practice with patterns through problems about visual and numerical sequences and series, the digits of large numbers and other real-world and math topics.

This video explores how to solve problems about arithmetic and geometric sequences.

This video demonstrates how to use mean and median in solving problems about arithmetic sequences.

This video focuses on techniques for solving problems involving arithmetic sequences, including finding the *n*th term.

Practice with standard arithmetic and geometric sequences and series, as well as with other special types of sequences and series, like the Fibonacci sequence.

This video shows a few techniques for solving problems using patterns in sequences and series.

This video demonstrates how the relationship between measures of central tendency and sequences can be used to solve problems.

This problem set 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.

For years, the Monty Hall Problem has been debated and examined. Mathletes will play the game in groups and use mathematical reasoning to decide - Do you switch? Do you NOT switch? Or is it a 50/50 chance either way?

This video demonstrates how to solve certain probability problems using geometric representations.

Players compete to roll the numbers on their product cards without rolling their opponents. They will have to use their understanding of probability to win.

Practice with probability through a wide variety of probability problems from many years of MATHCOUNTS School Handbooks.

This video explores some helpful strategies for approaching probability problems.

This π-themed problem set, created to celebrate Pi Day, has problems involving π on a variety of topics, including solid geometry, plane geometry and number theory.

This video focuses on finding area using properties of circles.

This Problem of the Week from 2009 on circles focuses on finding the areas of various regions.

Practice with circles, and see how they can be used in a variety of problems to answer questions about other shapes.

This video explores solving problems using properties of circles and triangles.

This Problem of the Week from 2007 explores where π came from, how it was approximated and some of its many uses.

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*.

This video desmonstrates some alternative approaches to problems traditionally solved by using *d* = *rt*.

This video explores algebra rate problems, using a variety of problem-solving techniques.

Practice with rates and proportional reasoning through a wide variety of problems from many years of MATHCOUNTS School Handbooks.

Using marathon statistics, practice applying the formula *d* = *rt* and equivalent versions in this 2001 Problem of the Week.

Practice with rates and proportional reasoning in this 2007 Problem of the Week using some statistics from the Indianapolis 500 race.