Each pathway is different, but there are trends that occur.You can find the Landscapes in the following documents: Addition & Subtraction and Multiplication & Division. There’s a lot of words in these documents that you might have to look up, but the idea that I want to emphasize is that students are continually finding new ways to solve problems.
They understand that the same strategy doesn’t work for all problems and are able to apply the best, most effective strategy to solve a problem. I discovered, by being taught a few key foundational ideas, that I could approach a difficult problem and reason through it, figuring out my own way to do it. It is such a clear example of how to use 10 to solve addition facts. With new standards and professional development, the idea of teaching multiple strategies has come to the forefront again. Next time you figure out an addition problem in your head, think about how you solve the problem. You probably aren’t thinking about the traditional algorithm (although you might be if that’s all you’ve been taught). Ideally, we want students to be flexible mathematical thinkers.
I wonder how much I was missing by being taught just one way. It was boring, mundane, and we did the same thing every day. I became involved with some professional development that taught me all about the different ways to solve multi-digit addition and subtraction problems as well as work with fractions. Do you make a ten or round to the next friendly number? Teaching students different strategies helps them transition between paper and pencil calculations and mental calculations. We want them to be good at math and feel confident about their ability to math.
They are much more motivated to work during math than I ever was growing up.
I have given students entry points into the problem and allowed them to approach it at their level, tackling it with the foundational skills that they know and understand.
From addition to fractions, decimals to percentage, you can find a wide array of math problems right here.
What if your child could be taught place value with the help of diagrams?
One of the best tools I have seen to explain this journey is Contexts for Learning.
The Landscape for Learning outlines the pathways students can take for understanding Addition & Subtraction and Multiplication & Division.
Now there’s a fine line between scaffolding learning and providing a crutch.
The key is always encouraging students to try something that is just outside their comfort level, which is called their zone of proximal development.