I have recently been introducing my daughter (4th grade) to decimals. We began by understanding what decimals are and what they represent (and how they relate to fractions). We also spent a great deal of time understandingdecimal place valueand relating decimals to money (because this is an already familiar skill). With this solid foundation in place, we moved todecimal operations, beginning withhow to add decimals。伟大的事情是，一旦基础decimal place valueis there and an understanding of加钱,添加小数很容易。
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Adding Decimals: Begin with Visual Models
Long before we sat down to use the formal algorithm (lining up the decimals correctly and then adding with regrouping), we represented decimals withgrids,数线andmoney。
For example, we represented decimals usinga hundred grid(andbase ten blocks) so she could visualize the tenths and hundredths as being less than one whole or part of the whole.
We also spent timerelating tenths to fractions and mixed numbers。This allowed her to understand how decimals relate to whole numbers and we then practicedplacing numbers on a number line to order and compare them。
We also usedplace value chartsand图片to show how the decimal parts relate to the whole number parts.
For example, if we have 12 tenths, we can then see that 10 tenths is equal to one whole. Therefore 12 tenths is equal to 1.2 or 1 and 2/10.
Thisbuilds a foundation for adding decimalsthat is not dependent on rules or formulas or algorithms.
So by the time we got to adding decimals to two and three decimal places with regrouping,I never actually taught her ‘how to do it,’她只是利用她对自己的价值的了解来解决问题。
How to Add Decimals Using Place Value:
For example, let’s say you want to add 0.43 + 0.05.
Again, understanding place value helps us to recognize right away that the tenths don’t change because we are adding 0 tenths to the 4 tenths.
Therefore, all we have to worry about are the 3 hundredths and 5 hundredths, which equals 8 hundredths when you add them together.
If you know that 0.7 means 7 tenths and 0.8 means 8 tenths, then you can add them and think of the answer as 15 tenths.
We then know that 10 tenths is equal to one whole. Therefore the answer is 1.5.
And although these are pretty simple and straightforward examples, it lays a foundation formental math calculationandadding decimalsthat will strengthen and solidify an understanding of the formal procedure with larger numbers.
Adding Decimals Using Money:
When kids can think of decimals as money, whole numbers represent dollars, tenths and hundredths represent pennies and dimes,it’s less intimidating。
Kids in fourth or fifth grade are likely fairly competent at adding up their loose change or money they received for their last birthday.
So I would encourage you to challenge them with金钱相关问题such as这加入和减去了小数课程before you actually teach them strategies or procedures for how to add decimals.
They will likely pull from their prior knowledge andcome up with their own strategiesfor adding or subtracting decimals without formally being taught.
我还会鼓励你让他们use play money(or actual money) to work out problems, again so that they can visualize the decimals.
So for instance, if they are adding 6.78 + 3.43, let them think of this as $6.78 + $3.43 and用戏剧代表他们to add.
这将有助于他们看到0.78 + 0.43创造另一个整数，有些剩余的。
Again, this helps them to connect what’s happening to the formal algorithm or procedure down the road.
How to Add Decimals: Formal Algorithm
Finally, after kid are familiar and comfortable with representing decimals, understand decimal place value, and can do simple decimal addition mentally, then they can move toward正式程序。
所以开始，all place values must be lined up。This includes the integer or whole number part and the decimal part.
Then you添加以最小的地方值开头。For example, if the numbers go out to the thousandths (3 decimal places) you begin by adding the thousandths.
然后是你add each place valueuntil the entire problem is solved, continuing to carry when necessary.
Here’s an example for you to see what I mean if you’re not familiar with this procedure:
And that’s it!
我希望这些提示和策略对你有所帮助，也知道这一点you can use the same visuals and strategies when subtracting decimals。
Want ready to use resources to help kids visualize decimals? Try my complete添加和减去小数集合！！要查看包含的内容，您可以点击此处了解详情。
这里有一些更多的小数资源you might enjoy:
- Adding & subtracting decimals partner challenge(using grids and number lines)
- Decimal operations mazes(low-prep practice)
- Converting fractions to decimals game
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