Multiplying and Dividing Decimals Using Number Sense

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The Common Core State Standards (CCSS) now have 5th graders computing with decimals.  CCSS 5.NBT.7 reads:

Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

Well, that's certainly a mouthful!  This post is going to focus on place value strategies, or what I call number sense.

First, computing with decimals is essentially the same as computing with whole numbers.  Don't believe me?  Multiply 12.1 x 34, 121 x 34, and 121 x .34  What do you get?  All three products contains exactly the same digits-4114.  The only difference is place value, or in other words, the placement of the decimal point.  We traditionally teach students to count the places after the decimal point in the factors, and move that many places from the right of the product and insert the decimal point.  That certainly works, but it's just a "trick", and tricks can lead to unreasonable answers.

John Van de Walle suggests that instruction on computation with decimals must start with estimating.  If students can accurately estimate products and quotients, they are more likely to correctly place the decimal point.  Look at the card shown below.  The digits in the product of the two numbers are shown below the multiplication problem.  Without multiplying, decide where the decimal point should go.

Did you place the decimal after the 28?  Why?  How would you justify your answer? 

With this next problem, you are placing the decimal points in the factors.  It's trickier, because there could more than one right answer (don't you just love that!).

What solution or solutions did you come up with?  18 x 14.5 would work, but so would 1.8 x 145.  Could you explain your reasoning on both those answers?

Not surprisingly, the same process works with division.  Look at the card below.  Where would you place the decimal in the quotient?  Why?

So, I hope that helps some.  Remember, you always want your kiddos to understand the math they're doing.  I think this little activity is very powerful and really encourages deep understanding.

Click here to download a set of cards like the ones above that you can use in your classroom.  And, please, if you teach math, don't start the year without a copy of the Van de Walle book for your grade level.  Use the link below to grab yours.