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Why Do We Do That? 3 Traditional Algorithms with Decimals

I went to one of the most beneficial decimal and fraction professional developments I have ever been to this summer.  I want to share what I learned with you so you can share it with your children.

1.  Traditionally adding and subtracting decimals:  Just line up the decimals to add or subtract.  Then just add and subtract like normal.  You may have to add zeros to the end of the decimal number on top if you have additional numbers on the bottom.  Why does this work?

Lining up the decimals is like adding like denominators. See:


2. Traditionally multiplying decimals:  Multiply the numbers like there is no decimal point.  Then count the places behind the decimal.  The number of decimal places in the numbers you multiplied is the number of decimal places in the product when you count from the back of the number.  Why does this work?

This works because you are counting the powers of ten in the denominator.  That is why there are three places behind the decimal!  See:


3.  Traditionally dividing decimals:  If their is a decimal in the divisor, move the decimal to the back of the number.  Then move the decimal that many places back in the dividend number.  Divide normally.  Then place the decimal on top of the “house” above where the decimal is in the dividend.  Why does this work?

Well, if you, again, turn the decimals into fractions, you can see what is happening.  If you divide straight across the fractions, you get the resulting 25 tenths.  Like with multiplication, this works the same.  You count the zeros OR powers of ten to know how many decimal places to include in the quotient.  See:


Free Fraction Cards for Tonight Only!!!

I just finished these fraction cards per request to go with a Decimal Wall Number Line I have in my TPT store.  The cards include halves, fourths, thirds, fifths, sixths, eighths, tenths, and hundredths.  They are free for tonight only.  They are pointy so that they can precisely point to a number on the Decimal Number Line.  Just click the picture to be taken to the freebie.

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Below is a sample of the Decimal Number Line that I made the cards to match…

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Use This to Build a Foundation with Decimals

After trudging through decimal teaching the last two years, I decided that students needed a stronger visual to help them see the patterns within decimal numbers…after all when students count to 20 in kindergarten, we have pictures of 1-20 plastered everywhere with visual models for students to see.  Because students need to see a longer set of decimal numbers to see patterns, I created this decimal number line (and a few other items).  The number line has numbers from 0.001-1 on it counting by thousandths.  On numbers where the zeros occur at the end of the decimal number the zeros are printed very lightly to remind students that these do not change the value of the decimal number and can be left off.  There are picture and number representations of each decimal and optional word cards that can be added by the teacher with the students through class discussion.

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Below are the first few numbers on the number line…

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and the last set of numbers on the number line…

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the word cards…

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To top this all off, you can find the Wall Decimal Number Line on sale for 50% off through Wednesday, April 23rd, 2014.  Scoop it up while the sale lasts.

You may also like…

Decimal Pocket Chart Number Cards

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or Fill in Decimal Number Charts …Screen Shot 2014-04-21 at 7.42.16 PM

Use These to Help Students Formulate Understanding of Decimals

What does a day out of school equal?  A finished product for Teachers Pay Teachers!  Here is a little something I have been working on that I was able to complete today since we got a surprising day off from work due to the icy weather.

Because decimals seem abstract to students–especially when the zeros fall off the ends, I created these decimal pocket chart number cards.  The zeros are grayed out so that students begin to make the connection that the zeros don’t necessarily have to be on the end of a decimal number.  The number cards are great for 4th graders just beginning to make the connection that the zeros have no value.

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The cards come in 3 different color variations–red backgrounds with white numbers…


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white backgrounds with red numbers….

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and white backgrounds with black numbers.  The black numbers offer a host of variations if printed on colored card stock.  The pattern possibilities using colored card stock are endless.

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The numbers also come in two different variations–without the whole number 1 and with the whole number 1.  This will aid in giving students the understanding that decimal numbers may or may not have whole numbers in front of them.

Come by my store to check these out!


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