柠檬导航

Students like you are the future of mathematics. Our resources are designed to ignite your curiosity and enhance your learning journey.

The 柠檬导航offers K-12 students engaging and enriching resources to explore the wonders of mathematics. Delve into fun challenges, competitions like the American Mathematics Competitions (AMC), and interactive materials that make math come alive. Discover various mathematical fields, learn problem-solving skills, and get a glimpse into exciting STEM careers.

Start navigating our resources by interest, level, or type, and consider participating in 柠檬导航competitions to showcase your skills and passion for mathematics. Embark on this exciting journey to uncover the beauty and potential of math in your world!

Featured Resources

Freaky Fraction Splitting

Take a pile of nine pebbles, nine coins, or nine cucumbers (but you can't use zucchini!) and split it into two piles. Then, split each of those piles into two piles. Keep doing this until you have nine piles, each with one object. What could be mathematically astounding about such a process? There is a...

Curriculum Inspirations: Pencil Prices

James Tanton takes viewers through this question from the 2011 柠檬导航AMC 10a Competition. Appropriate for the 10th grade level, this question covers Algebra. Common Core State Standards (CCSS): A-SSE.2; 7.G.4 Read the Curriculum Burst essay that goes with this question here: Pencil Prices This video demonstrates problem-solving strategy #8: Second-Guess the Author Curriculum Inspirations...

Sample Competition: 2023 AMC 8

Test out your creative problem-solving skills! Try your hand at these problems from the 2023 American Mathematics Competition (AMC) 8 competition. This mathematical competition is for students in grades 8 and below. Interested in more? Purchase collections of past competitions from our store or participate in our next 柠檬导航AMC competition.

Sample Competition: 2022 AMC 10 A

Test out your creative problem-solving skills! Try your hand at these problems from the 2022 American Mathematics Competition (AMC) 10 A competition. This mathematical competition is for students in grades 10 and below. Interested in more? You can purchase collections of past competitions from our store or participate in our next 柠檬导航AMC competition.

Curriculum Inspirations: Walking the Track

James Tanton takes viewers through this question from the 2011 柠檬导航AMC 10 B Competition. Appropriate for the 10th grade level, this question covers the topic of the circumference of a circle formula in Geometry. Common Core State Standards (CCSS): A-SSE.2; 7.G.4 Read the Curriculum Burst essay that goes with this question here: Walking the...

Problem-Solving Strategy #10: Go to Extremes

It is fun to be quirky and push ideas to the edge! Taking the parameters of a problem to an extreme can give insight to the workings of the situation described. And such insight can often illuminate a path for success. Read more about this strategy here: Problem-Solving Strategy #10: Go to Extremes Find other...

Problem-Solving Strategy #9 Avoid Hard Work

No one enjoys hard computation or a tedious grind through formulas and equations. Brute-force work should be undertaken only as a last resort! Do what a mathematician does - think very hard first to devise a creative, elegant approach that avoids hard work! Read more about this strategy here: Problem-Solving Strategy Essay #9 Avoid Hard...

Problem-Solving Strategy #1: Engage in Successful Flailing

One can often identify to which topic a challenge belongs 鈥� this question is about right triangles; this question is about repeating decimals 鈥� but still have no clue as to how to start on the challenge. What should you do? Engage in successful flailing! Think about everything you know about right triangles or repeating decimals....

Problem-Solving Strategy #8: Second-Guess the Author

If a curriculum or textbook problem is staged, then use that to your advantage! Read more about this strategy here: Problem-Solving Strategy Essay #8: Second-Guess the Author Find other problem-solving strategies you can use on the 柠檬导航American Mathematics Competitions and other competitions here.

Problem-Solving Strategy #7: Perseverance is Key

What impression of the mathematical pursuit do we often give students? Answers are pre-known (they are at the back of the book or are in the teacher鈥檚 mind), all can be accomplished in a fixed amount of time (quizzes and exams are usually timed), and the goal is to follow a pre-set intellectual path (as...

Problem-Solving Strategy #6 Eliminate Incorrect Choices

Eliminating what cannot be right helps determine that which must be correct! Read more about this strategy here: Problem-Solving Strategy Essay #6: Eliminate Incorrect Choices Find other problem-solving strategies you can use on the 柠檬导航American Mathematics Competitions and other competitions here.

Problem-Solving Strategy #5: Solve a Smaller Version of the Same Problem

A large, complex task can be made comprehensible by examining a smaller, analogous version. This powerful technique applies to mathematics research too. Read more about this strategy here: Problem-Solving Strategy Essay #5: Solve a Smaller Version of the Same Problem Find other problem-solving strategies you can use on the 柠檬导航American Mathematics Competitions and other...

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