Montessori Activity: Subtraction with Number Rods - Unit Place Value

AGE: 4.5 and up (after the child has worked with the decimal system and addition using the Number Rods. Other subtraction work could have been done prior to using the rods also.)

OBJECTIVE(S): To teach counting and subtraction of the unit place value in a concrete manner seeing the minuend and then taking away the subtrahend.

MATERIALS:

1.     2 sets of Number Rods.

2.     1 subtraction worksheet and a pencil.
3.     1 mat 

PRESENTATION:

1.     Place the 2 sets of number rods side-by-side.

2.     For each set, build the stair using the rods by placing the longest rod at the top and the shortest rod at the bottom.

3.     Explain to the child that addition puts things together and subtraction takes them apart again.

4.     Read the first problem e.g. “10-4=?” to your childf.

5.     Place the 10 rod in front of the child. Select 2 rods which equal 10 (i.e. 6 and 4) and place them under the 10 rod saying 6+4=10.

6.     Then say, "If we take the 4 rod away, how many are there left".

7.     Point to the 6 rod and say, "There are 6 left. We say that 10 take away 4 equals 6"

8.     Take the appropriate number card and place them under the rod 6.

9.     Ask your child to say, “10-4=6” and write the answer on the worksheet.

10.  Repeat this process for other problems using the 10 rod as your minuend.

CONTROL OF ERROR:

1.     Seeing the incorrect alignment of the rods.

2.     Counting the places on the rods.

REFERENCES:

- Shu-Chen Jenny Yen’s On-line Montessori Albums
  http://web.archive.org/web/20050212085156/http://www.ux1.eiu.edu/~cfsjy/mts/math/_link.htm



Montessori Activity: Static Addition with Number Rods - Unit Place Value (加法 [jiāfǎ])

AGE: 4.5 to 6 years (after the child has mastered the Plus and Equals and the Number Rods counting exercises)

OBJECTIVE(S): To provide a concrete representation of the addition of the unit place value concept.

MATERIAL:

1.     2 sets of Number Rods

2.     1 addition worksheet

PRESENTATION:

1.     Place the two sets of Number Rods side-by-side each arranged in a stair formation each with 1 at the bottom and 10 on top.

2.     Read to your child or have your child read the first question: “1+3=?”

3.     Let your child pick the first addend 1 from the number rods, count it and place it on the mat.

4.     Let your child pick the second addend 3 from the number rods, count it and place it on the mat, making sure that the beads are not taken from the same set of number rods.

5.     Let your child place both number rods in a line on the mat.

6.     Have your child count the total number of sections: “1,2,3…”

7.     Ask your child to write or paste the result onto the equation and say: “1+3=4”.

8.     Return the number rods and encourage your child to try the different combinations from the worksheet.

VARIATIONS:

1.     Addition with colored short bead bars.

2.     Addition with other concrete materials.

REFERENCES:

Shu-Chen Jenny Yen’s On-line Montessori Albums
http://web.archive.org/web/20050212085156/http://www.ux1.eiu.edu/~cfsjy/mts/math/_link.htm

Brilliant Minds Montessori Maths Curriculum

ADDITION INFORMATION:

J tried this on 6 May 2014 (5Y2M1D). He was a little bored with it, but was willing to complete all the sums in the worksheet. Perhaps I had introduced to him a little too late. I don't think I will be repeating this activity. We will move on to other addition activities.

6 May 2014 (5Y2M1D)

http://amzn.to/1SCUlsu

Montessori Activity: Static Addition with Number Rods (加法 [jiāfǎ])

AGE: From 3.5 years old (after mastery of The Number Rods and Sandpaper Numbers)

OBJECTIVE(S):

1.     To associate symbol and quantity.

2.     To prepare for addition.

MATERIALS:

1.     Set of Red Rods or Number Rods

2.     Set of Number Tablets (or Sandpaper Numeral Cards)

3.     1 mat

PRESENTATION:

1.     Arrange the Number Rods in sequential stair formation on the mat.

2.     Take out the cards and place them randomly onto the square mat.

3.     Separate Rod 10 from the others to the top of the mat.

4.     Have the child count it and the mark it with the appropriate card.

5.     Tell your child that you are going to make tens with the number rods.

6.     Move Rod 9 up beside Rod 10.

7.     Have the child say what rod it is, count it and place the correct card.

8.     Ask the child: “I wonder which rod we can put to make this nine the same length as the ten?”

9.     Have the child join Rod 1 to the end of Rod 9 and place Tablet 1 at the end of the Rod 1.

10.  As you point to the numbers, say: “9 + 1 makes 10.”

11.  The Number Tablets may be used to state equation together with the “+” symbol.

12.  Repeat in the same way for the Rod 8 and make it the same length as the Rod 10. Say: “8 + 2 makes 10.”

13.  Repeat for Rod 7 and Rod 6.

14.  When the child gets to Rod 5, show him how to flip it to the right hand side and say: “If we had another 5, we could make 10.”

15.  Ask the child if we have something in the classroom that is similar to the Rod 5.

16.  Have the child bring over the fifth rod from the Red Rods and see if it is the same length as the Number Rod 5.

17.  Place it to the left of the Number Rod 5 and say: “See it makes the same length as Rod 10.”

18.  Take away 5 by flipping the Rod 5 back. Ask the child what is left. State equation: “10 take away 5 is 5.”

19.  Repeat for the other combinations of tens and then nines, eights, etc.

20.  Put back The Red Rod back on the shelf and have the child rebuild The Number Rods in stair formation.

21.  Put back the cards in the box.

TIPS:

Repeat but this time start with the number rod 9 and have the child make 9’s. (Remove rod 10 and place it on the empty mat, out of the way.). For making 8’s, remove the Rod 10 and Rod 9. For making 7’s, remove the Rods 10, 9, and 8 rods, etc.

CONTROL OF ERROR:

The number of partitions on each rod acts as a guide.

NOTES:

The child can work on his own as shown in the presentation as an exercise.

ADDITIONAL INFORMATION:

J (3Y10M24D) tried this for the first time today. He was able to find out that intuitively adding Rod 1 to Rod 9 will make 10 and he could do it all the way to adding to the end by adding Rod 5 to Rod 5. As this was the first time we did this activity, we conducted it in Mandarin. I was hoping that we would repeat this in English the following day, he requested it again to be conducted in Mandarin as well.

  

So far, J has the tendency to name 5 wrongly in English and sometimes also naming 6 wrongly. However, he has no problem in Mandarin.

Research has shown that reaction time tend to be faster when one thinks in Mandarin when doing Maths because numbers in Chinese are single syllabus. Chinese numbers are also very logical when articulated in Mandarin, contributing to the faster thinking time. However, I also want him to be fluent in English so that he can follow the Montessori classes in Singapore, when we are back home on vacation.

I am not sure if I am doing the right thing by repeating the lesson in English, or whether I should just use Mandarin all the way. I will wait and see and observe more, until I decide. Maybe I might only teach and do Maths activities solely in Mandarin.

REFERENCES:

http://www.infomontessori.com/mathematics/numbers-through-ten-number-rods.htm
http://web.archive.org/web/20050212085156/http://www.ux1.eiu.edu/~cfsjy/mts/math/_link.htm
http://www.moteaco.com/albums/casa/casamath.html#anchor2979127
Basic Montessori Learning Activities for Under-Fives

  http://amzn.to/1pNRvsp

http://amzn.to/1SCUlsu

Montessori Activity: Matching Numerals To Number Rods

J (3Y10M22D) - Verifying Rod 5 (aka The No. 5 Train) by counting it, before driving it to its "parking lot" denoted by the number tablet 5.

AGE: From 3.5 years old (after mastery of The Number Rods and Number Tablets or Sandpaper Numerals)

OBJECTIVE(S):
1. To associate symbol and quantity.
2. To prepare for addition, subtraction and multiplication.

MATERIALS:
1. Set of Number Rods
2. Set of Numeral Tablets (you can also use Sandpaper Numbers instead)
3. 1 mat

PRESENTATION 1:
1. Ask the child to set up the Number Rods in stair formation on the mat.
2. Read through the Number Tablets and place it back to the shelf.
3. Take Rod 1 and say: "this is one," count it and ask the child: "Can you find the Tablet 1?"
4. The child goes to the shelf and brings back the Tablet 1.
5. Let him verify by counting the rod.
6. If it is correct, ask the child to place Tablet 1 beneath the last segment on Rod 1.
7. Do the same for all the rods and tablets.
8. Do the Three Period Lesson.

PRESENTATION 2:
1. Place the Number Rods on the mat in mixed order and place the Number Tablets on the mat in mixed order.
2. Pretend that the rods are trains and that each section of the rods is the train’s coaches. Pretend that the tablets are “parking lots” for the trains.
3. Show your child a tablet and ask him to name the numeral: “What number is this?” and place the tablet in a line on the side.
4. Ask your child to find the corresponding train (rod): “Can you find me the correct train and count the number of coaches?”
5. Ask your child to park the corresponding train (rod) beside the tablet.
6. Do the same for all the rods and tablets until all of them have been matched.
7. Always finish the lesson by placing the rods and tablets in correct sequence.

J (3Y10M22D) - "Driving" the "No. 5 train" to its "parking lot", and making the cho cho sound along the way

J counting and self-verifying the no. of "coaches" on the "No. 10 train" i.e. the Number Rod 10, and driving it to its "parking lot" denoted by the number tablet 10

PRESENTATION 3 (Reversed exercise of Presentation 2):
1. Place the Number Rods on the mat in mixed order and place the Number Tablets on the mat in mixed order.
2. Pretend that the rods are trains and that each section of the rods is the train’s coaches. Pretend that the tablets are “parking lots” for the trains.
3. Show your child a rod and ask him to name it and to count it.
4. Ask the child to find the corresponding number tablet and place it beside the rod.
5. Do the same for all the rods and tablets until all of them have been matched.
6. Always finish the lesson by placing the rods and tablets in correct sequence.

TIPS:
To encourage instant recognition without counting, show a child a rod and ask the number, or vice versa, show a number tablet and ask the child to find the rod without counting. Thereafter, count the partitions out loud so that if a child makes a mistake, it is corrected without placing blame. This can be played by a group of children.

VIDEO DEMONSTRATION:
http://www.youtube.com/watch?v=-sbZScRMS4w

ADDITIONAL INFORMATION
J (3Y10M22D) tried this today. J is not very fond of Number Rods, but it is part of the Montessori Maths Curriculum and an important step in it. So I persevere through it. Number Rods had been introduced to J since he was 2.5 years old, and each time he was not interested at all.

Initially I thought that it was because it was home-made - made of LEGO. So I bought the real Number Rods from one of the Montessori educational materials company. But he still wasn't keen on it. I have been very lenient, putting it aside and coming back. As a result, my Maths Montessori attempts last year 2012 was rather hap-hazard. Just going with the flow and not following any sequence.

This year 2013, I am determined to be more structured. I will not move on to the next activity, if he has not mastered the current one yet.

I realized that parental resolve seems to help tremendously. It is just like the car seat belt - there is no discussion.

So for the last one week, I have been doing nothing but various combination of Number Rods. J is not only showing more focus in his work, he is also improving a  lot more. Repetition definitely helps in learning, and this is the case with Montessori.

The Montessori school in Singapore also made me realized that this is the way to go. The children there are free to choose any Montessori Practical Life activity, but when it comes to Montessori Maths activity, it is a one-to-one time with the teacher. The children don't get to choose it. They go through the series of activities, and they don't skip any, until they master it. Also the children there are assessed after each activity to see which level they are at, whether they would proceed to the next Maths activity or continue on. In other words, they follow a structured Maths curriculum.

The only thing is, as Daddy pointed out to me, the teachers there do it with a straight face, and it looked boring. It is after all a job, in a country as stressful as Singapore. His assessment of the Montessori enrichment centre's teachers that we sent J to wasn't too positive. He thinks that I am doing an equally good job, if not better, and with passion and love (Maybe it is just his way of avoiding having to fork out money and listening to my constant request of sending J to a Montessori school, since if I do it, it is free and less painful on his pocket. Well he forgot the expensive materials I have shopped using his money, oh well, our money :-)!!!!) I didn't really see it, until I began to analyze his description. After all the teachers follow the same motion every day and with so many different children, how enthuasistic can one get? So I am not as critical as him. But I am following the same concept of the Singapore Montessori school - no skipping of any Maths activity, but as a parent, I think I am doing it with a lot more passion and love. It is not just a job.

I have found a way to make it fun for J. I pretend that each rod is a train and each section is the train's coach. And I pretend that the number tablet is the parking lot for each train. That helps a lot. J enjoyed pulling the "trains" to the right "parking lot".

REFERENCES:
http://www.infomontessori.com/mathematics/numbers-through-ten-number-rods.htm
http://web.archive.org/web/20050212085156/http://www.ux1.eiu.edu/~cfsjy/mts/math/_link.htm
http://www.moteaco.com/albums/casa/casamath.html#anchor2979127
Basic Montessori Learning Activities for Under-Fives

Montessori Activity: Naming & Counting Number Rods

AGE: 3.5 - 5 years old

ACTIVITY DURATION: 15 minutes

OBJECTIVE(S):
1. To learn to count each number by a single object as a whole separate from others and understand the value of each number (i.e. that each number represents a quantity and distinct

2. To teach the names of one to ten in relation to quantities.

MATERIALS:
1. The Number Rods
2. 2 mats or trays

PRESENTATION:

Day 1: Name the Number Rods

1. Ask your child to spread out a floor mat.

2. Name the Number Rods, show where they are kept and have your child go and fetch them.

3. Have your child arrange the rods into starting with the red section first, from the smallest to the longest (as seen from picture above).

4. When the child is able to arrange the rods in stair formation, isolate the first three rods and teach the Three Period Lesson.

5. Put Rod 1 in front of the child and say its name several times: “This is one.” Touch the rod and count: “one”. Put aside Rod 1. Put Rod 2 in front of the child and say: “This is two.” Point and touch each section and count: “One, two.” Put aside Rod 2. Do the same for Rod 3. (Period 1)

6. Place the three rods in front of the child in mixed order and ask: “Can you give me Rod 1?” then Rod 3 and then Rod 2. Repeat until the child knows the rods by name. (Period 2).

7. Put a rod in front of the child and ask: “What rod is this? Can you count it for me?” Do the same for all three rods (Period 3).

8. Always end your lesson by placing the rods in order.

9. Do the same with Rod 4 – 10 three rods at a time. Depending on the child, teach this in a day or over a few days.

Day 2: Name & Count

1. Mix the Number Rods on the mat.

2. Ask the child for a specific rod and place it on an empty mat.

3. Let the child count the alternating color segment of each rod one-by-one by touching each partition of the rod hand-over-hand (this will help fix the repeated numbers in his mind and helps him associate the spoken number with the concrete quantity of segments.)

4. If he forgets some of them, repeat the Three Period Lessons.

Day 3: Identify Quantity

1. Mix the Number Rods on the mat.

2. Pick a rod and place it in front of the child, ask: “What is this?”

3. Let the child count it and tell you the name of the rod. Then put aside the rod.

4. Do the same for all the rods.

Day 3: Identify Rod in Order

1. Lay out the Number Rods in stair formation order on the mat.

2. Point to a rod in stair formation and ask the child to say the name of the rod.

3. Let him verify by counting it.

4. Do the same for all the rods.

Day 4: Identify Rod Randomly

1. Mix the Number Rods on the mat.

2. Let the child pick a rod, place it on an empty mat, and say its name.

3. Let him verify by counting it.

4. Do the same for all the rods.

VIDEO DEMONSTRATION:
http://www.youtube.com/watch?v=-sbZScRMS4w

CONTROL OF ERROR:
Color and irregular progression of length.

ADDITIONAL INFORMATION:
Our Number Rods arrived today from Absorbent Minds Montessori. It was a very small set, but I do not mind it, as we have limited space at home. However, I was a little disappointed that the red and blue colors were not as bright as the pictures shown from their website, but it does the job.

But J did enjoy it, so I could live with it. I made the Number Rods using lego bricks, but that did not quite work with Joshua, as he kept taking them apart. Joshua (3Y7M21D) tried this set of small, but real Number Rods this evening, and it was the first time we managed to go through the whole activity as it meant to be with the Number Rods, so I was glad. It was just at the right challenge for him. He made some errors using visual judgment of the length. He had to count the partitions to get the size right.

REFERENCES:
http://www.infomontessori.com/mathematics/numbers-through-ten-number-rods.htm
http://web.archive.org/web/20050212085156/http://www.ux1.eiu.edu/~cfsjy/mts/math/_link.htm
http://www.moteaco.com/albums/casa/casamath.html#anchor2979127
Basic Montessori Learning Activities for Under-Fives

10 November 2019 (3Y5M24D): I tried this with C for the first time together. She was not using it as it was intended. She put them together, she made the shape rabbit, that only she can recognize. Finally, I use Montessori mystery bag and she finally use it as what it was intended for, by picking out a rod in the bag and saying its number.

10 November 2019 (3Y5M24D)