# PRACTICE PLANS

### Practice is on us this week! Use these plans to prepare your students to compete or to review math skills.

These plans cover a variety of math topics and skills, and are designed to cover 45-60 minutes of practice time.

##### A special thank you to Taren Long, our 2020-2021 DoD STEM Ambassador!

Taren created many of the awesome Practice Plans below, based on her experience as longtime MATHCOUNTS coach.

What's in Each Practice Plan
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##### Warm-Up

We start with a short problem set so Mathletes can practice related skills that will be expanded upon throughout the practice plan.

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##### The Problems

Next, a video introduces a common type of competition problem or a helpful problem-solving strategy with 2-3 example problems.

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##### 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.

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##### Extension

We'll end with a related activity, puzzle or game to give Mathletes a fun opportunity to apply their problem-solving skills creatively!

Summary:

Calculating the least common multiple is something many Mathletes 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.

DIFFICULTY:
Medium
Summary:

Learn what Mass Points are and how to use them to solve problems involving side lengths and areas of triangles. Mass Points Part 1 (above) covers the fundamentals of Mass Points, while Mass Points Part 2 is more advanced, covering what happens when you have too many cevians and how to "split the mass".

DIFFICULTY:
Difficult
Summary:

Explore Modular Arithmetic by working with remainders to solve problems about very large numbers.

DIFFICULTY:
Difficult
Summary:

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.

DIFFICULTY:
Easy
Summary:

This plan focuses on all things percents. Mathletes will practice with tips, markups, markdowns, interest and percent of quantity scenarios. Use the 'would you rather' questions in the extension to explore which shopping discounts are the better deals.

DIFFICULTY:
Medium
Summary:

Understanding and applying ratios can be used in a variety of problems, from finding a missing measurement to determining scale between similar figures. Mathletes will solve problems using ratios, then play a dice game for additional practice.

DIFFICULTY:
Medium
Summary:

This plan builds on what Mathletes 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.

DIFFICULTY:
Easy
Summary:

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.

DIFFICULTY:
Medium
Summary:

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.

DIFFICULTY:
Medium
Summary:

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.

DIFFICULTY:
Difficult