Inventing Addition and Subtraction Algorithms

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Here's the description:

• My collections represented 475 and 358, and I wanted to combine them.
• I first combined 400 and 300, making 700.
• To the 700, I added 10 from the units, leaving 3.
• Next, I added 90 to the 710, making 800
• There are 33 left over, so the sum is 833
• In general, I try to combine all of some piece from one 'side' so it's easy to remember what's left.

Here's the recording symbolically:

Here's another symbolic approach. Can you describe this person's thinking?

Or even

There are a number of ways to perform the calculation 475 + 358. If each of us uses our own way of regrouping, our symbolic communication may look a bit different, but they lead to the same result. What is an efficient strategy for one of us may not be efficient for another, but we can understand each other! We could show subtraction strategies with the take-away and the difference models, as well - I'll leave that for you to explore. Click here or here, if you need some guidance.

In both addition and subtraction, regrouping is the key to mental computation. Recording our thinking helps us communicate our strategies and ideas to others.