PRACTICE PLANS
Practice is on us this week! Use these plans to prepare your students to compete or to review math skills.
Practice Plans cover a variety of math topics and skills in 35-60 minutes. We are so grateful to Taren Long and Tyler Erb—past DoD STEM
Ambassadors for MATHCOUNTS—who created many of the awesome plans below, based on their experiences coaching.
Learn more from Taren and Tyler in our MATHCOUNTS for Educators interview series.
Warm-Up
We start with a short problem set so Mathletes can practice related skills that will be expanded upon throughout the practice plan.
The Problems
Next, a video introduces a common type of competition problem or a helpful problem-solving strategy with 2-3 example problems.
Piece It Together
Next, Mathletes solve a set of related problems to build on the strategies and skills they learned in the Warm-Up and problems video.
Extension
We'll end with a related activity, puzzle or game to give Mathletes a fun opportunity to apply their problem-solving skills creatively!
Addition and subtraction may sound easy for middle schoolers, but what if you are missing some digits? What if you want to maximize or minimize a result? This plan focuses on some common types of MATHCOUNTS problems in which Mathletes will need to apply number sense and logic to a variety of scenarios.
Explore measures of central tendency, specifically mean and median, by solving common types of MATHCOUNTS problems related to sets of numbers. Use the extension at the end to develop a rule for finding the average of a sequence of numbers.
Mathletes are likely most comfortable working with numbers in base 10, but there are many other number systems to explore - other integer bases, fractional bases, and even negative bases. This plan introduces Mathletes to the basics of bases and how to convert from one to another.
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 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.
Mathletes will analyze frequency tables, histograms, stem-and-leaf plots and other visual representations to solve problems about sets of data. In the extension, Mathletes will analyze a set of data to draw their own conclusions.
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 to find the value.
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.
Mathletes 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!
Using the commutative, associative and distributive properties, Mathletes will arrange arithmetic problems in a different order that allows them to be solved more readily.
This plan will introduce Mathletes to The Fundamental Counting Principle – a faster method to determining the total number of possible outcomes of an event without listing them all out!
Mathletes will explore interior angles of various polygons and understand how to find the number of sides a polygon has using information about its interior angles.