addition and subtraction
There are lots of ways to solve
addition or subtraction problems.
There are various strategies that can be used.
*There is always more than one way to solve a problem!
Visualizing number quantities....visual images
What do you see? How do you see it?
You won't need to count all if you find a way (a strategy) to keep track of what you see.
Number Bonds or Math Mountains in Expressions.
Number bonds are a visual model that connect a total, the WHOLE to the two PARTS that create it.
Number bonds help us to see a number TOTAL or WHOLE broken up or decomposed into its PARTS.
This is a helpful concept which will aid in mental math problem solving throughout life.
One strategy is referred to as a MAKE 10 strategy.
The following video clip does a nice job of explaining this. important strategy.
You will note the use of NUMBER BONDS here as well. 4
/ \
2 2
The use of ten frames support the visual nature of math.
The concept of making tens can transfer to making 100, 1,000, 10,000, 100,000 and even 1,000,000!
Now that you've worked on making 10, try number bonds from 11-19.
The following video clip is full of fun, fancy-dancy music.
Boogie kids! Get up and move!
Using Expanded Form to Add
Expanded form breaks up, or decomposes a number into its place value parts.
This is helpful for students to to relate the place value of the digits as they add.
Below you will view arrangements for adding numbers in expanded form (in short form and in long form). The numbers are written in column form; the digits are arranged in expanded form and then finally added to find the sum of the given numbers.
Solved examples on adding numbers in expanded form:
1. Add 32 and 25
Solution:
Numbers are written in column form T O
3 2
+ 2 5
5 7
Adding ones: 2 ones + 5ones = 7 ones
This 7 is written in one’s column.
Adding tens: 3 tens + 2 tens = 5 tens
This 5 is written in tens column.
So, the answer is 57
2. In other way, add the expanded form of the numbers 32 + 25
Solution:
32 = 30 + 2 Expanded form of the numbers
+ 25 = 20 + 5
= 50 + 7
= 57
Use expanded notation
Adding 2 two digit or three digit numbers
Watch the video clip below for examples of adding two and three digit numbers.
Adding three digit numbers using expanded notation
Watch the video clip below for an example of adding three digit numbers together.
Here is another strategy to add or subtract. Common Core refers to this as ARROW MATH.
Can you see how number bonds are related to this?
Subtraction using expanded notation form
Above are demonstrations of the expanded form with subtraction. You will see this used without regrouping, and with regrouping. The important piece to remember is the value each number stands for (place value.)
Understanding Subtraction- Part 1
As shared by Dan Finkle: Math For Love
Dan talks about the importance of starting from where things make sense. This may be one of the best ways to help your kids with math at home. If you don’t know what to do, take a step back. Then take another. Keep going back until things make sense. Then follow the bread crumbs back up till you’ve figured out the new thing.
That’s all good in theory. But what’s missing is the details. (And there are a lot of details in math!) So I’m going to try to touch on some of the foundational visuals and representations that ground the meaning of mathematical symbols and operations at an elementary level.
When it comes to arithmetic, there are always two parts: understanding the operation, and understanding how it works in base 10. Today, I want to do just part 1 of that, as it pertains to subtraction.
Folllowing this post, is another for subtraction 2.- which includes place value and regrouping.
Understanding Subtraction- Part 2 -place value
As shared by Dan Finkle: Math For Love
This will, I hope, help you understand the algorithm, the meaning behind it, and how to explain it clearly.
Understand subtraction with respect to place value well and you can do it at any level (huge numbers, decimals, algebra, etc.). It all comes down to genuinely making sense of the simple case.