Montessori Addition and Subtraction of Fractions

Sharing some updates with regard to my elementary boy.  Though it may seem that I’m posting a lot about preschool activities, in the background my 9 years old is doing a lot of work too in math, geography/history, and science.  Now, one of the things he worked on last year was his fractions.  After working fractions and fraction equivalence, Mavi worked on addition and subtraction of fractions.  He did very well on this.  With one simple presentation, he grasped the concept right away, and after which he did a lot of practise using our fraction cut-outs.  Somehow, I find this straightforward, meaning if your child knows about their basic addition and subtraction they can breezily work on this and move on to multiplication of fractions or working with unlike fractions.

Materials Needed:

• Montessori Fraction Cut-outs
• Addition Task Cards/Tickets
• Subtraction Task Cards/Tickets
• Arithmetic Sign Box (optional)

Addition and Subtraction with Same Denominator

Note that you only work on this once the child has a good grasp of the basic concept of fractions.

Addition:

1. Using the ticket, take three 1/6 cut-outs and say “This is three 1/6 or 3/6”.
2. Place two 1/6 and place them next (to the right) of the 3/6 and explain that you need to add all the fraction cut-outs.  Place the addition sign (or just write this on paper) in between the two fraction cut-outs to form the equation.
3. Combine the two groups of fraction cut-outs, and count the total fraction cut-outs.  Say 3/6 plus 2/6 is (or equals) 5/6.
4. You can reduce the sum to it’s equivalence.  In our case 5/6 is already in its reduced form.

Subtraction:

1. Place five 1/8 cut-outs and have the child take away two 1/8 cut-outs.  For the sake of presentation, Mavi showed me what’s 2/8 thus, he placed two 1/8 cut-outs on the rug on the right of the first set of fraction (5/8).  Place a minus symbol or you can just write it in a piece of paper instead
2. Once you have removed two 1/8 cut-outs from the first fraction, ask the child what’s left.  Reduce the fraction if needed.

NOTE:  In most homeschool and Montessori schools, they write tickets and place them underneath the fraction (see a sample of it here).  We didn’t do this at home because Mavi used the answer sheets in our Fraction printable instead.

Mixed Fractions

This is the case when the sum is more than one whole.  For example, in 3/4 + 2/4 = 5/4, Mavi replaced the 4/4 with 1 to reduce the fraction to 1 and 1/4.  The same happens to the second set of equation, replacing the answer to 1 and 4/10.

Subtraction involving Whole Numbers

Now when you encounter a problem like this, the first thing to do is to convert the whole number to its equivalent fraction.  In the first equation, we replaced 1 whole to four 1/4 cut-outs, and removed two 1/4 cut-outs from it.

Similarly, replace 1 in 1 and 4/7 to seven 1/7 cut-outs so you can subtract six 1/7 cut-outs from the total number of 1/7 cut-outs in the equation.

The method of using fraction cut-outs is undeniably effective in making the child understand how to manipulate fractions by using concrete materials.  Through first hand experience of how these fractions work, how they are added and subtracted, the child can easily retain the concepts of fraction operations.  And they can easily master reducing fractions as the cut-outs can provide a visual demonstration of the operation.  We worked on these materials for two months (since December)and just last week Mavi started abstract work (working with worksheets).  This is the second series of my elementary fraction posts (see first part here - Hands-on Learning of Equivalent Fractions), and hopefully we’ll get to work on other equations too so I can share them with you.

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