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# Fractions

#### Material

Ten green metal plates each with circular red insets.
One inset is whole.
The other circles are divided into 2, 3, 4, 5, 6, 7, 8, 9 and 10 equal parts.
Each segment has a knob.

One set of tickets labeled:
1
2 tickets of 1/2
3 tickets of 1/3
4 tickets of 1/4
Etc. all the way through 10 tickets of 1/10.

Problem slips for the operations, grouped separately by operation.

#### Presentation

##### Introduction and Naming
1. Invite the child to the lesson.
2. Show him Fraction Board 1, and ask him to bring it to a table.
3. Bring one bead and a bowl to a table.
4. Place the bead on the table surface.
5. Place the first inset – the “whole inset” – on the table surface.
7. “This is one.”
8. Point to the whole inset.
9. “This is also one.”
10. Put the bead back in the bowl.
11. Place the inset back into its frame.
12. Place the first three frames and insets on the table surface:
whole, halves, and thirds.
13. Take the whole inset out again.
14. “This is one, again! One whole.”
15. Put the whole inset back in its frame.
16. Ask the child to take it out of its frame and to set it on the table right below its frame.
17. Take out the halves inset and place them below their frame.
18. Pick them up and show how they are the same exact size.
19. Say “halves” then place them down on the table.
20. Pick up one half and say “this is one half.”
21. Place the half in the whole inset’s frame.
22. Place the other half in the whole inset’s frame.
23. Take them out and place them back below their frame.
24. Take the thirds out of their frame and place them below their frame.
25. Pick two of the thirds up and show that they are the same size, then pick up a different third and compare it, showing that they all are the same size.
26. Say “thirds.”
27. Place the thirds down.
28. Pick up a third “this is one third.”
29. Place a third in the whole frame.
30. Put the other thirds in the same frame; take time to admire them.
31. Take the thirds out and place them back below their frame.
32. Take the fourths out and repeat the process.
33. Proceed with a three-period lesson.
34. Repeat this process for all fractions.
35. Introduce combining fractions of the same category such as 2/3’s and 3/5’s etc.
36. Point to the combined fractions and name them.
37. Point to combinations and ask the child to name them.
38. Ask the child to make fractions and name them.
##### Symbols
1. Invite the child to the lesson.
2. Bring pencil and paper.
3. Place all 10 frames and insets on the table, in a sort of rainbow formation: starting with the whole on the bottom left, followed by halves above it, thirds above halves, fourths to the right of thirds, fifths then sixths, then sevenths then eights, followed by ninths below eights, and tenths below that.
4. Set the halves insets on the table.
5. Be sure that the line separating the halves is horizontal.
6. Trace over the line with your finger.
7. Draw a line on the paper.
8. “This line means ‘fraction.'”
9. “How many pieces do I have here? Yes, two.”
10. Write a 2 on the paper below the line.
11. “This is the family of two.”
12. Place one inset back in its frame.
13. “How many do I have now? Yes, just one.”
14. Place a 1 above the line.
15. “What do we call this piece again? Yes, we call it one half?”
16. Point at the fraction you’ve written on the paper:
“When we see this symbol, it means one half.”
17. Repeat this process for all fraction categories; using a numerator of 1.
18. On the same day, or on another day, invite the child to make his own combinations and ask him to write the symbols, such as 2/6 or 4/7 etc.
19. On the same day, or on another day, introduce the labels.
20. Bring the box of labels and place it on the table.
21. Open the box and take some of the labels out.
22. “You can read these labels and then place them where they are supposed to go!”
23. Match a few labels to their fractions, then let the child work independently.
##### Equivalence
1. Invite the child to the lesson.
2. Place the halves frame with insets on the table.
3. Remove one half inset, place it on the left side of the table.
4. “I wonder what else could fit in here.”
5. Attempt to fill in the empty side of the halves frame with thirds.
6. “Oh, that isn’t going to work.”
7. Place the thirds insets back in their frame.
8. Repeat this process with the fourths; admire the two fourths insets and how they fit perfectly.
9. Place the two fourths insets next to the one half inset on the table.
10. Repeat this process for the rest of the insets, handing it off to the child, trying to fill in the one half section of the frame, keeping only the successful equivalent matches on the table with the others.
11. When the child is done, he should have the following on the table:
1/2 next to 2/4 next to 3/6 next to 4/8 next to 5/10.
12. “I can show you how to write this.”
13. On paper, write:
1 = 2 = 3 = 4 = 5
2 4 6 8 10
14. Repeat this process, solving for different equivalencies, such as filling in for 1/3, letting the child work independently.
1. Invite the child to the lesson.
2. Write on paper a fraction such as 1/7.
3. Place 1/7 on the table.
4. Write + 4/7 =
5. Place 4/7 on the table.
7. Give many more problems for the child to solve.
##### Subtraction
1. Same process as addition but place, for example, 4/5 on the table and write 4/5 on the table.
2. Then write on the paper – 1/5 =
3. Slide 1/5 away and ask the child to count and write the answer: 3/5
4. Give more problems for the child to solve.
##### Multiplication
1. Write on paper, a problem such as 1/4 x 2 =
2. Place two fourths on the table.
3. “One fourth, taken two times.”
4. Slide the fourths together.
6. Give more problems for the child to solve.
##### Division
1. Write on paper a fraction such as 8/9
2. Place 8/9 on the table.
3. Write รท 4 =
4. Place 4 skittles on the table and ask the child to share out.
6. Give more problems for the child to solve.

#### Exercises

Child works independently.

#### Purpose

To acquire the concept and knowledge of fractions.
To acquire the concept of equivalence.
To acquire an understanding of the operations.

5 1/2 to 6

#### Notes

This material can be presented at an earlier time for sensorial purposes.