Think You've Got Problems?

Each month we will discuss one math problem from any of our K-12 classes. We hope these posts will serve to illuminate the many exciting and intriguing aspects of math, and possibly even help interested parents learn how to inspire their children in a subject that is crucial to their development.

Here follows our inaugural post:

Math education is anything but boring.  Not unlike philosophy or art, it requires deep thought and debate. It is visual and provoking. And it is also a subject that should spark lively classroom discussion. When students are taught math this way, they find it more compelling, and naturally develop a deeper understanding of the subject.

Here's an example of how our mathematics programs apply this approach to a 4th grade math problem:

Jane and Andrew had $50 together. After Jane bought a present for $12, she and Andrew had the same amount of money. How much money did Jane and Andrew each have initially?

This seems like a fairly simple problem. And tempting to solve the straightforward way: algebraically. But instead, we encourage our students to solve the problem visually. This way, they develop clarity around why the algebra works.

Here are a few segments from our teacher-training seminar as an example:

1. We know that initially, Jane must have had more money than Andrew:

 4th grade algebra explained

2. And after Jane spent $12, they had the same amount. Which, combined, was $50-$12=$38:

 

4th grade algebra explained

3. Meaning that if both Jane and Andrew had equal amounts, then each had $19. And initially, before spending the $12, Jane had $31.

 

4th grade algebra explained

Algebra is a powerful and useful tool for elementary math problems like these. But by taking a visual approach and encouraging classroom debate, we encourage students to grapple with the problem and envision what the algebraic translation really means.  This understanding is essential; as problems become more complex, rewriting them in algebraic terms becomes increasingly difficult. Building a solid foundation in elementary school is the key to developing excellence in mathematics and critical thinking.

 

 

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