Whole Number and Decimal Adding and Subtracting
We can use the base ten pieces to create models that lead to mental computation strategies with whole numbers and decimals.
For example, 57 + 35 can be represented by combining the base ten pieces that represent the numbers:
Either way (and there are other strategies, too) the result is 92. We can add 57 and 35 in our heads. It's just regrouping and keeping track of where our thinking is at. Try these mental gymnastics for fun; see what kinds of strategies you use...
Here's a subtraction problem: 93 - 56 = ?...
We can look at it a couple of ways...
There are a variety of ways to think about the numbers; these are just two examples. All will tell us the difference is 37. By trying to think about these models mentally we can compute differences flexibly, using the method that seems to work best for any given problem, regrouping as necessary.
Here are some more problems to try to think through...
The process is similar for decimal numbers, just imagine the square unit being the size of a Mat - a 10 x 10 square:
We can use the models to add and subtract decimal numbers, too.
Let's look at .467 + .391:
Here's a subtraction problem: 3.42 - 0.7:
If we just think about the computations we want to do, addition and subtraction are basically just regrouping processes. We can jot down rough sketches, or keep track of numbers as we're thinking. It can be faster than using a calculator!
Here's a few problems to try out your mental strategies on.
In the next lesson, we'll discuss inventing some ways to keep track of our thinking processes, and make some generalizations about adding and subtracting.