Decimal Operations

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The students will be able to apply knowledge of the four basic operations when using numbers with decimals.

Big Idea

Keeping track of math operation rules can be as easy as using a piece of paper.


10 minutes

Today’s lesson will focus on recapping the rules for performing the four basic operations with numbers that include decimals.  I will have students create a foldable to organize the rules and then apply their knowledge by solving problems with each type of operation.

To get my student’s math brains started for the day I begin with a little warm activity called Guess My Rule.  In this exercise I think of a number and a rule.  The students give me a number and I apply the rule to it, without telling them the rule.  After the giving several responses to students I have them guess the rule I have in my head. 

When I think of a rule, I give the students parameters for numbers they may guess.  The numbers and rules I choose to use today are as follows;

Rule 1: Add ten, parameters for guess 1-100

Rule 2: Subtract 2, parameters for guess are 2-100

Rule 3: Multiply by 5, parameters for guess are 0-15

Alright, I have a rule in my head and you have to figure out the rule.  You can guess numbers and I will give you an answer after I have used the rule inside my head.  I will also give you a range of numbers you can guess to solve the rule.  Okay, I have the first one in my head.  You are allowed to guess numbers between 1 and 100.  If you think you figured out the rule, keep the rule a secret until I ask for the rule.

Students guess and I reply with an answer using the applied rule.  The students are able to guess several times.  I read the crowd and look for the majority of the students lightbulbs to go off. 

Alright, who thinks now they know my rule?  (Student responds with add 10).  That’s right, you guys got it.  Those of you who gave numbers, think of what my answer to you was.  Did I add ten to your number?

I repeat this process for the remaining two rules. 


30 minutes

The foldable that students are creating today is intended to be a reference and reminder of how to apply the four basic operations to numbers that include decimals.  My students are comfortable using the operations with whole numbers but sometimes get a little confused with what to do with the decimal.  It’s so tiny of a dot yet so scary to students. 

This particular foldable is an adaptation from a foldable I found on Pintrest.  I modified it to fit the needs of my learners and the concepts we are covering.  The inside of the foldable is intended to be a guided activity to solidify procedures using decimals.  Students will be recalling the rules used and then creating examples of each type of operation. 

I start by passing out the foldable and showing students how to fold the flaps as quarters.  When I redesigned the foldable I put lines in the inside which will guide where the students need to fold the paper.  I go over the addition portion of the foldable first by reading the rules to the students and pausing to have them think about what goes in the blanks of the rule.  I give students about 30 seconds to think and then ask them to respond.  We fill the blanks as a class and then move to the creating an example together.

I want students to have a correct example of each type of decimal operation to use as a guide and resource.  That's why I'm moving step-by-step, to ensure students' create a correct example.  It is important to highlight the importance of keeping the numbers neat and organized on the page; meaning, ones lined up with ones, and tenths lined up with tenths, and so forth.  Once we are done doing the example together, students share with their partner the thinking of how we did the example.

Okay, now that we have the example written, let’s share with our partner the thinking that was involved in solving this problem.  I would like the person who sits on the left to explain to the person on the right each step that was involved in solving the problem.  If the person explaining gets stuck, the other person may help them with their thinking.

I have students go this process of recording the rule, writing an example and then sharing with their neighbor for the remaining three operations.  When the foldable is finished the rules should read as follows;

Addition: Line up the DECIMAL then add as with whole numbers.  You may have to write zeroes. Bring down the decimal point.

Subtraction: Line up the DECIMAL then subtract as with whole numbers.  You may have to write zeroes and borrow.  Bring down the decimal point.

Multiplication: Multiply as you would multiply whole numbers.  Then place the DECIMAL POINT in the product the SAME number of decimal places in the factors.

Division: Divide as with whole numbers.  Place the decimal point in the quotient ABOVE the point in the dividend. 


15 minutes

In order to assess if students are able to use the four basic operations when working with decimals, I provide one problem of each type to students.  The students work individually to solve the problems and may use their foldable if they get stuck on the rules or steps.

I display these problems on the board and have students complete the work on a piece of lined paper.

7.5 + 1.42, 7.56 - 4.235, 4.25 x 1.2, 47.6 ÷ 4

I tell students to show all work when creating problems, and be prepared to share their thinking.  After about ten minutes I call students up to the document camera to display one of the problems.  When students are finished explaining their work and thought process I ask some furthering questions to determine if they have a flexible understanding of the rules of decimals. 

Alright, we determined that the answer for the addition problem was 8.92.  What would happen if we added 75 instead of 7.5?  Without doing the computation, does anyone know what the answer would be to the problem?  What if we changed the numbers to 7.5 and 14.2, would we have to do anything differently then?

My goal is to assess the flexibility of my students’ understanding. If students are relying on procedural knowledge they are less likely to grasp that adding 7.5 and 75 has no impact on the numerical outcome, but it does affect the place value outcome. 

I continue to have students share the remainder of the operations and ask furthering questions to the class after the presentation of work.