Addition and Subtraction Strategies

Hi! Here are some of the strategies we have been using for adding and subtracting decimals:

Compensation is an addition strategy in which you adjust one of the addends to make it a friendly number by taking an amount from the other other addend.  This strategy works because of the Associative Property of Addition, which allows us to group addends in any way way we want. In the SmartBoard grab below, you will see how we used compensation to take .1 from 3.14 and group it with 2.9 to make 3 wholes. Our new expression was 3.04 (this was the previous 3.14) + 3 (the previous 2.9). 3.04 + 3 can easily be solved using mental math. Also, to the right, you can see how you could use compensation to adjust 16.18 + 5.94 to 16.12 + 6 = 22.12.

Our next two strategies are for subtraction. The first is using finding the difference by building up, and we can use an open number line to model this. Here we started by placing the subtrahend and minuend on the number line. Then we began at the subtrahend, and took jumps to get to to the minuend. Every times we took a jump, we record the distance traveled on top of the jump. We went from 1.83 to 2 (+.17), from 2 to 4 (+2), and from 4 to 4.67 (+.67). Then we added up the total distance traveled between the minuend and subtrahend and that was the difference.

The last strategy is called constant difference, and it is useful when the subtrahend is close to, but slight less than, a friendly number. In constant difference, we adjust both the minuend and the subtrahend by adding the same amount  to both (however much you need to make make the subtrahend friendly will determine this amount) in order to make a friendly expression. See below how we added .09 to the minuend and subtrahend of 5.03-2.91 to change it to 5.12-3= 2.12. Underlying this strategy is the concept that if the minuend and subtrahend both increase by the same amount, the difference between them will not change.

Division Strategy: Partial Products and Ratio Tables

With this strategy, we use a ratio table to build multiples of the divisor, starting with 1 set.  We can use place value, doubling, and halving to make 10, 2, and 5 sets of the divisor. We want to try to build a big "chunk" of the dividend using the ratio table, which we will then subtract from the remaining amount of dividend. We will continue to subtract sets of the the divisor from the dividend until we cannot subtract anymore sets. If we have any left over, this will be our remainder. We then add up all of the sets we made, and this is our quotient.

Here are some screenshots of this strategy

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Using Open Arrays and the Distributive Property to Solve Division Problems

Using the Distributive Property is a  great strategy for solving division problems - and you can use an open array as a model. When you use an open array in division, the dividend is the area, the divisor is one side length, and you are solving for the other side length (this will be your quotient). You can use the Distributive Property to break the dividend into multiples of the divisor (this is really important because it allows you to divide easily by the divisor!),  and then add the distances along the unknown side to find the quotient.  I like to make a mini array with the area next to my large array to keep track of total area because I will be breaking it apart in my large array. Here are some screen shots from today's lesson - hope they help!

WELCOME FAMILIES!!!

I am so excited for the 2016-17 school year! It was wonderful to meet my new homeroom today. Please check back for updates, and/or follow this blog. I will post information about class and grade events and trips as well as math homework and review resources. Please email me if you have any questions or concerns.  I look forward to a great year! - Ms. Rached

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