1. To provide sensorial exploration of fractions as well as equivalency among fraction.
2. To introduce the concept of fractions and how fractions are named.
3. To show how to add, subtract, multiply and divide with fractions.
Materials:
1. Metal Fraction Circles (or you can also use Montessori Cut-Out Labeled Fraction Circles)
2. Labels with fractions written on each of them: 1, 1/2, 1/3, 1/4... 1/10
3. Pencil and paper
4. Skittles to present people (for division)
Presentation 1: Sensorial Exploration & Naming
1. Ask your child to bring out the 1st tray of fractions.
2. Explain that a fraction is sharing a whole "cake" into equal parts with your friends.
3. Take out the whole metal circle from its base and place it in front on the tray.
4. Say, “This is one whole.”
5. Take out a 1/2 and say, “This is a 1/2, one cake cut into 2.”
6. Ask, "How many pieces do you need to make a whole cake?" The child should say 2.
7. Say, "2 pieces of 1/2 make a whole cake," and put the two 1/2 together to make one whole.
8. Take out a 1/3 metal circle and say, “This is a 1/3.”
9. Ask, "How many pieces do you need to make a whole cake?" The child should say 3.
10. Say, "3 pieces of 1/3 make a whole cake," and put the three 1/3 to make one whole.
11. Do this for 1/4, and 1/5. Have the child replace each one back into its spot.
12. Do a Three-Period Lesson for the group of 1, group of 2, group of 3, group of 4, and group of 5.
13. Mix up the metal circle parts, invite your child to place them back in their correct spot and repeat several times.
14. Proceed in the same manner to the 2nd tray, when your child is ready.
15. Repeat the activity with both trays, when your child is ready.
1. Point to a few fractions and ask your child what it is. This will serve as your check to see if the child knows the names.
2. Show him how to write fractions.
3. Point to the second circle and ask, "How many pieces there are?" He should answer 2.
4. Say, “Yes, there are two pieces, so I will write a 2.”
5. Take out a 1/2, place it on front of the tray and ask, "How many pieces are here?" He should answer 1.
6. Say, “There is one." and write a line above 2 and write 1 over it.
7. Put back the 1/2 back onto the tray.
8. Repeat for all of the remaining fractions.
9. Explain that we place the total number of pieces on the bottom and we call it the "Denominator"
10 Explain that we place the piece we have isolated and taken out over the line and we call it the "Numerator."
11. Do a Three Period Lesson for Numerator and Denominator.
12. The take out 2/3 or 7/9 or 2/5, etc and invite your child to write these fractions. Then read these with the child.
1. Ask your child to bring out the 2 trays of fractions.
2. Place the fraction labels in their corresponding places in front of the tray.
3. Ask your child to label each part of each fraction and read it as he goes about doing it.
4. Ask the child for the names of the numerator and denominator to check for understanding.
5. Play a game: you pick a slip with a fraction written on it ask your child to point to it or take a piece out of the tray.
1. Ask your child to bring out the 2 trays.
2. Write and read an addition equation with 2 fractions:
2/6 + 3/6 =
3. Show your child that we take out 1/6 metal circle twice = 2/6.
4. Place these two pieces in front of the tray.
5. Take out 1/6 metal circle pieces three times = 3/6.
6. Ask, "How many 1/6 are there?" Your child should answer 5.
7. Show your child how to write the answer as shown:
2/6 + 3/6 = 5/6
8. Read the whole equation to your child.
9. Write another addition problem and invite your child to try.
10. After a few rounds, explain that we can only add fractions with the same denominator such as:
2. Take out 4/8 pieces and place it in front of the tray.
3. Point to a 1/8 piece and say, “I am going to take away 1/8”
4. Remove 1/8 from the 4/8 to the side.
5. Ask, "How many 8th are left?" Your child should answer 3/8.
6. Ask your child to write the answer on the equation.
7. Repeat a few times. See example below
2. Say, “We are going to take 2/8 three times.”
3. Take 2/8 one time, two times and three times.
4. Place them together and ask your child to count the total number of 8ths. He should answer 6.
5. Ask your to write the answer on the equation.
6. Repeat a few times. See example below:
1/4 x 3 =
7. When he understands, he can use the equations written on the prepared cards.
Presentation 6: Division by a whole number
1. Write and read a division equation:
4/4 ÷ 2 =
2. Ask, "How many will we be dividing?" and ask your child to place two skittles or Lego men in a row below the trays.
3. Ask your child how many 4ths we need to start. (four 1/4)
4. Place all 4 of the 1/4 pieces of metal circles below the tray.
5. Tell the child that we need to share these 4 pieces evenly between our two skittles or people.
6. Ask your child to give each person evenly the 1/4 pieces of circle.
7. Explain that in division we always want to know how many 1 got.
8. Ask your child how many 1/4 pieces each person got? He should answer 2 i.e. 2/4 meaning 2 of the 1/4 pieces each.
9. invite your child to write the answer on the equation.
10. Repeat several times. See examples below:
3/8 ÷ 3 = 1/8
Presentation 7: Equivalence
1. 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.
2. Guide the child to this discovery, but do not tell him. This should be experienced by the child.
3. Invite your child can make his own chart of the equivalencies.
This was J's first Advent Calendar. This is a Danish tradition, whereby the child gets to open a small gift every day until Christmas Eve. I was a little in doubt whether we should get J such a calendar, as I think it is a little too over-indulgence to open a small gift everyday. J did not ask for one himself, so we could have easily slipped it this Christmas. However, we subcumbed to it and bought the Lego Advent Calendar. Many of such calendars contains chocolate or sweets for each day, and the LEGO calendar is a healthier choice. So, each day, J will get to build a small LEGO figurine.
I intend to reuse the Calendar box for next year. I will put a Bible verse in each of the pocket that J will get to open each day in December until Christmas.
1 suppy box containing golden beads materials i.e. units, ten-bars, hundred-squares, thousand-cubes to serve as "Bank"
1 tray containing 10 unit beads, 9 ten-bars and 9 hundred-squares
AGE: 4.5 years old
OBJECTIVE:
To demonstrate that 10 units can be exchanged for a ten-bar, 10 ten-bars can be exchanged for a hundred-square, and 10 hundred-squares can be exchanged for a thousand-cube.
MATERIALS:
1. 1 suppy box containing golden beads materials i.e. units, ten-bars, hundred-squares, thousand-cubes to serve as "Bank"
2. 1 tray containing 10 unit beads, 9 ten-bars and 9 hundred-squares
3. 1 mat
PRESENTATION:
1. Arrange the golden beads materials as shown in the tray. Show it to your child and ask, "how much do you think we have here. Let us find out."
2. Layout the leads on the mat as shown above.
3.Count the unit beads in straight vertical line and when you reach the 10th unit, prompt your child to exchange it for 1 ten-bar from the bank and say: "10 units is the same as 1 ten."
4. Place it together with the other ten-bars on the mat.
5. Count the ten bars and when you reach the 10th bar, prompt your child to exchange it for 1 hundred-square from the bank and say, "10 tens are the same as 1 hundred."
6. Place it together with the other hundred-squares on the mat.
7. Count the hundred squares and when you reach the 10th square, prompt your child to exchange it for 1 thousand-cube from the bank and say, "10 hundreds are the same as 1 thousand."
8. Ask your child, "Did you know that we have 1000 beads on the tray? It is much easier to see how much we have on the tray after exchanging. This is the purpose of exchanging."
2. Count the unit beads in straight vertical line and when you reach the 10th unit,
prompt your child to exchange it for 1 ten-bar from the bank and say: "10 units is the same as 1 ten."
3. Place it together with the other ten-bars on the mat.
4. Count the ten bars and when you reach the 10th bar, prompt your child to exchange it for 1 hundred-square from the bank and say, "10 tens are the same as 1 hundred."
5. Place it together with the other hundred-squares on the mat.
6. Count the hundred squares and when you reach the 10th square, prompt your child to exchange it for 1 thousand-cube from the bank and say, "10 hundreds are the same as 1 thousand."
7. Ask your child, "Did you know that we have 1000 beads on the tray? It is much easier to see how much we have on the tray after exchanging. This is the purpose of exchanging."
AGE: 5 and up (after the child who has experience with the Decimal System, Teen Board, Ten Board and Hundred Board)
OBJECTIVE(S):
1. To give the child a means of counting other than one-by-one.
2. Learn to count in bases other than ten.
3. Preparation for multiplication skill.
4. Development of Order, independent, concentration and coordination.
5. Development of mathematical mind.
MATERIALS:
1. 1 hundred chain consisting of 10 ten-bars
2. 1 hundred-square
3. 1 box or an envelop containing arrowed tags:
- Green tags1-9
- Blue tags10-90
- A red tag100
4. 1 pointer for counting
5. 1 large mat
PRESENTATION:
1. Show your child how to hold the 100-chain by both ends and put it vertically on the mat.
2. Slowly fold the 100-chain into a hundred-square and draw your child to notice how it looks like a 100-square.
3. Place the 100-square on top of the folded 100-chain to show that they are the same.
4. Straighten out the 100-chain.
5. Take out the unit arrows (green), tell your child what it they are called and tag them to the left of the 100-chain, by taking a counter, count "1" and tag 1.
6. Take out the green tag 2, count "1, 2" with the counter and tag 2.
7. Continue the same manner for the rest of bead chains.
8. Take out the ten arrows (blue) and continue in the same manner, counting and tagging 10, 20... 90, in multiple of 10 until you reach 100 and place the hundred tag (red) at the 100th bead.
9. Count with the child all the arrow tags: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100
The number of beads,
correct amounts will use up all 45 of the ten bars and unit beads.
POINTS OF INTEREST:
1.Learning the number of different combinations that can be made
from combining these materials.
2.Seeing the ten beads on a bead bar and the single units.
3.The unit beads in the little container.
4.Watching the quantity of golden bead bars grow from 1 to 9.
5.Seeing the relationship between the 45 layout and the ten board.
VARIATIONS:
1.Select numbers and ask the child to provide the quantity
2.Select quantities and ask the child to provide the correct
symbols.
ADDITIONAL INFORMATION:
Although this activity is recommended for children 4.5 years and up, J tried this only for the first time today at 5+ years old (5Y4M7D). We recorded the videos below for memory. He could say the numbers in Chinese very well now, but we are still practicing saying the numbers in English and Danish.
