Because we have to teach so much “content” in math classes in schools, parents and students often miss an essential thing about math learning: it requires thinking. Not just a quick learning of procedures and facts, but getting into problems and grappling our way to solutions, using anything and everything we know.
That’s math. Sweating with our brains. Struggling forward when we can’t find an easy answer.
One of the best ways to help kids in math is to let them know this is not only normal, but essential. One of the best ways to counteract math anxiety is to give them experience with this, in comfortable environments, and do it with them. It’s okay if you don’t know “the math.” Because that’s how we can help augment school math the most - not to teach content, but to model methods for struggling with the content.
Problem Solving
The following are two problems designed to challenge students in connecting mathematical concepts.
Problem 1
The divisors of a natural number, excluding the number itself, are called the proper divisors . If the sum of proper divisors is equal to the number we call the number perfect. For example, the divisors of 28 are 1, 2, 4, 7, 14, and 28, so the sum of proper divisors is 1 + 2 + 4 + 7 + 14 = 28.
Similarly, if the sum of the proper divisors exceeds the number we call the number abundant. For example, 12 is abundant because the divisors of 12 are 1, 2, 3, 4, 6 12, and the sum of proper divisors 1 + 2 + 3 + 4 + 6 = 14 
12.
Prove that every even n 
48 can be written as the sum of two abundant numbers.
Problem 2
Use each digit 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 exactly once to form two five-digit numbers that when multiplied produce the largest quantity.
Resources
Problem Solving Learning Centers in Mathematics
Algebraic Thinking through Problem Solving
Math Teaching Strategies that Challenge Students
Tags: math activities, math problem solving, problem solving, solving problems, teaching math
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