You shall teach them diligently to your children, and shall talk of them when you sit in your house, and when you walk by the way, and when you lie down, and when you rise. -Deuteronomy 6:7

Sunday, July 14, 2013

Montessori Fractions - Beginning through Basic Operations

One of the first activities when teaching Fractions with Montessori materials, is to have the child explore and eventually label the fraction circles.  I use the red fraction circles in the green frames for this.

I make my on labels on small papers that have fractions written on them:  1, 1/2, 1/2, 1/3, 1/3, 1/3 and so on.  These can probably be found online in a search, and you could print them.

PRESENTATION 1 (Age 4-6 typically)

The Fraction Circles

Sensorial Exploration
  • Have the child bring over the first tray of fractions (1-5).
  • Tell the child that a fraction is a dividing of a whole into equal parts.
  • Take out the first circle and place it in front on the tray.
  • Take our 1/2 and place it in front of the tray.
  • Take out 1/3 and place it in front of the tray.
  • Show the child how to carefully replace each one back into it's spot.
  • Once the child is comfortable with the first tray, have the child replace it and take out the second tray (6-10)
  • Have the child explore this tray as with the first tray.
  • Once the child is familiar with the second tray, use the two trays together

  • Have the child bring over the first tray of fractions.
  • Take out the whole circle.
  • Tell the child: "This is a whole"
  • Place the whole in front of the tray.
  • Take out one of the group of 2 and say,m "This is a 1/2".
  • Place it in front of the tray.
  • Repeat this way up to the group of 5.
  • You can continue this with the second tray.  Some children may already have a grasp on this so it will go quickly, just depending on what age you've started them.
  • When the child knows the names, begin with the two trays.
  • Point to a few fractions and ask the child what it is.  This will serve as your confirmation that the child knows the names.
  • Tell the child taht you will show him how to write fractions.
  • Point to the group of 2.  Ask the hcild how many pieces there are. (2)
  • Say, "Yes, there are two pieces, so I will write a 2."
  • Take one 1/2 and place it in front of the tray.
  • Ask the child how many pieces are here.  (One 1/2)
  • Say, "There is one."
  • Place a line over it and write 1 over the 2.
  • Replace the 1/2 back onto the tray. 
  • Repeat this way for all of the fractions.
  • You can remind the child that we place how many piees are all together under the line and the piece we have taken out goes over the line.
Labeling   Get Fraction Circle Labels here

  • Once the above has been practiced (sometimes many times - depending on the child) you can begin labeling.
  • Take out all the labels and place them in their corresponding piles in front of the fraction circles.
  • Have the child label each part of each fraction reading each leabel as he does.
  • Some children go through this very quickly.  Others like to do this activity over and over again!

PRESENTATION 3: Operations

Addition with the same denominator  (I start this as soon as my child has learned addition)

  • Have the child bring out the two trays.
  • Write two fractions (with the same denominator) as shown:
2/6 + 3/6 =

  • Show the child that we first take out 1/6 two times (2/6)
  • Place these in front of the tray.
  • Then take out 1/6 three times (3/6)
  • Have the child count how many 1/6 there are (5)
  • Show the child how to write the answer as shown:
2/6 + 3/6 = 5/6
  • Read the whole equation with the child.
  • Write another addition problem and have the child do it.
This is work the child can continue to do on his own, if you supply the equations!

Subtraction with same denominator

  • Write a subtraction equation on the paper.  (4/8 - 1/8=)
  • Create 4/8 and place it in front of the tray.
  • Point to the 1/8 and tell the child, "I will now take away 1/8"
  • Move 1/8 from the 4/8 and move it off to the side.
  • Ask the child to count how many 8ths are left.  (3/8)
  • Have the child write the answer.
  • Repeat a few times!
Younger children like to do this work over and over.  I started at 1st grade.  Older children will quickly see the pattern and may want to move on without using the materials.  Keep them using the materials as long as you can - this will increase their deeper understanding.

Multiplication by a whole number

  • Have the child bring over the two trays of fractions.
  • Write a multiplication equation on the paper:  2/8 X 3 =

  • Tell the child, "We will take 2/8 3 times."
  • Take 2/8 one time, two times, three times.
  • Push them all together and have the child count the number of 8ths.
  • Show the child how to write the answer.
  • Do a few with the child.
  • When he understands, he can use the equations written on cards and complete problems on his own.
I had one child that had mastered this by 1st grade.  I have a 3rd grader that is mastering it pretty quickly now.  Currently, she can multiply but does not have multiplication facts all memorized.  With Montessori materials, in this case, I may start showing her division soon because Montessori materials make it VERY easy to move forward with new concepts since everything is quite visual.  I'll teach her division of WHOLE numbers first and then teach divison of fractions.

I'll post more on fractions soon!

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