Fractions

Materials
- Red fraction circles in green frames: ten circles – 1 undivided and the others divided into 2 to 10 equal part.
- Label with fractions written on them: 1, 1/2, 1/2, 1/3
- Pencil and paper
- Skittles


Presentation 1

Sensorial Exploration

• Have the child bring over the first tray of fractions.
• Tell the child that a fraction is a dividing a whole into equal parts.
• Take out the first circle and place it in front on the tray.
• Take out 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 its spot.
• Do this for 1/4, and 1/5. Have the child replace each one back into its spot.
• Repeat a few times, mixing up the parts and having the child replace them in their correct spot.
• Once the child is comfortable with the first tray, have the child replace it on the shelf and take out the second tray.
• Have the child explore this tray as with the first tray.
• Once the child is familiar with the second tray, use the two trays and repeat as above.

Presentation 2

Naming

• 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, “This is a 1/2”.
• Place it in front of the tray.
• Repeat in this way up to the group of 5. (1/2)
• Do a Three-Period Lesson for the group of 1, group of 2, group of 3, group of 4, and group of 5.
• Once the child is familiar with this tray, do the same for the second tray.

Writing

• When he 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 check to see if the child knows the names.
• Tell the child that you will show him how to write fractions.
• Point to the group of 2. Ask the child 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 on 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 it.
• Replace the 1/2 back onto the tray.
• Repeat in this way for all of the fractions.
• You can remind the child that we place how many pieces are all together on the bottom and the piece we have taken out over the line.
• Do a Three Period Lesson for Numerator and Denominator.
• The take out 2/3 or 7/9 or 2/5, etc and have the child write these fractions. Then read these with the child.

• Have the child bring over the two trays of fractions.
• Take out all of the labels and place them in their corresponding piles in front of the tray.
• Have the child label each part of each fraction reading each label as he does so.
• Two children can work together by mixing all of the labels together and then labeling each piece of each fraction.
• Ask the child for the names of the numerator and denominator to check for understanding.
• The children who may need more work can play a game  in pairs, one picking a slip with a fraction written on it and the other child pointing to it or taking it out of the tray.

Presentation 3: Operations

Addition with same denominator

• Have the child bring out the two trays.
• Write two fractions (with the same denominator) as shown:
  
  

• 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:

• Read the whole equation with the child.
• Write another addition problem and have the child do it.
• After a few equations, point out to the child that we can only add fractions with the same denominator. See below:

Substraction with same denominator

• Have the child bring over the two trays of fractions.
• 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 8th are left. (3/8)
• Have the child write the answer.
  
  

• Repeat a few times. See example below

Multiplication by a whole number

• Have the child bring over the two trays of fractions.
• Write a multiplication equation on the paper:

• Tell the child, “We will take 2/8 four times.”
• Take 2/10 one time, two times, three times and four times.
• Push them all together and gave the child count the total number of 10ths.  (8)

• Show the child how to write the answer.

• Do a few with the child.
• When he understands, he can use the equations written on the prepared cards. See below for another example.





Division by a whole number

• Have the child bring over the two trays of fractions.
• Have the child also bring the skittles.
• Write a division equation on the paper:


• Read the equation. Ask by how many will we be dividing.
• Have the child place two skittles in a row below the trays.
• Ask the child how many 4ths we need to start. (four 1/4)
• Place all of the 4ths below the tray.
• Tell the child that we need to share these 4ths evenly between our two skittles.
• Have the child give each 1/4 and then another 1/4.
• Remind the child that in division we always want to know how many 1 got.
• Ask the child how many 4ths one skittle got. (2/4)

• Have the child write the answer.
• Do a few examples with the child. Such as:






Equivalencies

This can be done during or after the work with the Operations .Look with the child to see if it is possible to fill 1/3 with any other fraction. For example two 1/6 will fit for one 1/3. Guide the child to this discovery, but do not tell him. This should be experienced by the child.

As a final piece of work with the fractions, the child can make his own chart of the equivalencies.


Purpose

Direct
To help the child gain a sensorial impression of fraction.
Introduction to the concept and notation of fractions.
Sensorial exploration of equivalency among fraction.
Introduction to simple operations.


Control of Error
The Directress and the child’s own ability.


Age
4 1/2 years


Note
This may be introduced after work with Group 1: Numbers through 10




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