Montessori Activity: Small Bead Frame - Dynamic Multiplication

Note: I am showing the large bead frame above, because it is not necessary to buy both the small bead frame and the large bead frame. I am using the large bead frame to do the small bead frame exercises.

AGE: 5.5 (after the child has worked with the Stamp Game)

OBJECTIVE(S):

To show the relationship between the different place values in the decimal system.

MATERIALS:

1. Small bead frame
2. 1 worksheet
3. 1 green, red and blue pencil

PRESENTATION:

1. Read a problem to your child, i.e.:

     423

x       3

---------

   1269

2. Expand the multiplicand 423 on notation paper, i.e. 2, 30 and 400.

3. Slide 3 green unit beads 3 times to the right.

4. Count the beads on the right and write the answer 9 on the worksheet.

5. Slide 2 blue ten beads 3 times to the right.

6. Count the beads on the right and write the answer 6 on the worksheet.

7. Slide 4 red hundred beads 3 times to the right.

8. After the 2nd time, you will find that you don't have sufficient beads. You only have 2 beads to the right, and you are still missing 2 beads.

9. Slide the last 2 beads to the right.

10. Exchange by sliding all the red hundred beads back to the left in exchange for sliding 1 green thousand bead to the right.

11. Then slide 2 red hundred beads you are still missing earlier to the right.

12. Count the beads on the right and record the answer on the worksheet, i.e. 2 red hundred bead and 1 green thousand beads, i.e. 1269.

13. Read the question and answer aloud together.

PHOTO DEMONSTRATION:

1. Read a problem to your child, i.e.:

2. Expand the multiplicand 432 on notation paper, i.e. 2, 30 and 400 (optional).

3. Slide 3 green unit beads 3 times to the right:

 

 

4. Count the beads on the right and write the answer 9 on the worksheet:

5. Slide 2 blue ten beads 3 times to the right:

 

 

6. Count the beads on the right and write the answer 6 on the worksheet:

7. Slide 4 red hundred beads 3 times to the right:

8. After the 2nd time, you will find that you don't have sufficient beads. You only have 2 beads to the right, and you are still missing 2 beads:

 

9. Slide the last 2 beads to the right:

10. Exchange by sliding all the red hundred beads back to the left in exchange for sliding 1 green thousand bead to the right:

 

11. Then slide 2 red hundred beads you are still missing earlier to the right:

12. Count the beads on the right and record the answer on the worksheet, i.e. 2 red hundred bead and 1 green thousand beads, i.e. 1269:

13. Read the question and answer aloud together.

VIDEO DEMONSTRATION:

https://youtu.be/U4y7Wl94nmE

ADDITIONAL INFORMATION:

J tried this for the first time on 30 Oct. 2015 (6Y6M25D). He could do it easily on paper, calculating in his head the right answer and writing it down, but made some mistakes manipulating the beads when exchanging. I must admit that exchanging using the Small Bead Frame is not the most straight forward. One has to remember the remaining beads not moved over, after exchanging and moved those beads over. It seemed that it is easier for him to understand and do the sum on paper using the written vertical format method, then using the Small Bead Frame. But I am not too concerned. In fact, I am questioning a little the usefulness of the Small Bead Frame, when doing exchange is required. This is a Montessori tool that is nice to have, but not absolutely necessary.

REFERENCES:

http://www.infomontessori.com/mathematics/passage-to-abstraction-small-bead-frame.htm

http://www.montessorialbum.com/montessori/index.php?title=Small_Bead_Frame

http://faculty.fullerton.edu/syen/mts/math/8-4.htm
https://youtu.be/wXm3eIb49kc

Montessori Activity: Small Bead Frame - Static Multiplication

Note: I am showing the large bead frame above, because it is not necessary to buy both the small bead frame and the large bead frame. I am using the large bead frame to do the small bead frame exercises.

AGE: 5.5 (after the child has worked with the Stamp Game)

OBJECTIVE(S):

To show the relationship between the different place values in the decimal system.

MATERIALS:

1. Small bead frame
2. 1 worksheet
3. 1 green, red and blue pencil

PRESENTATION:

1. Read the problem to your child, i.e.:

   321

x     3

---------

   963

2. Have your child build 1 unit three times on the small bead frame by sliding 3 green unit beads one at a time to the right one at a time.

3. Count and record the units on the worksheet, i.e. 3.

4. Have your child build 2 tens three times by sliding 6 blue ten beads two at a time to the right two at a time.

5. Count and record the tens on the worksheet, i.e. 6.

6. Have your child build 3 hundreds three times by sliding 9 blue ten beads three at a time to the right three at a time.

7. Count and record the tens on the worksheet, i.e. 9.

8. Read the question and answer aloud together.

9. Invite your child to do the next question and remind him that once he knows his time-tables by heart, he will no longer need to use the beads.

PHOTO DEMONSTRATION:

1. Read the problem to your child, i.e.:

   321

x     3

---------

   963

2. Have your child build 1 unit three times on the small bead frame by sliding 3 green unit beads one at a time to the right one at a time.

 

 

3. Count and record the units on the worksheet, i.e. 3.

4. Have your child build 2 tens three times by sliding 6 blue ten beads two at a time to the right two at a time.

 

5. Count and record the tens on the worksheet, i.e. 6.

6. Have your child build 3 hundreds three times by sliding 9 blue ten beads three at a time to the right three at a time.

 

 

7. Count and record the tens on the worksheet, i.e. 9.

8. Read the question and answer aloud together.

9. Invite your child to do the next question and remind him that once he knows his time-tables by heart, he will no longer need to use the beads.

ADDITIONAL INFORMATION:

I have prepared this since 23 Sep. 2015. For some reason, I waited for a month to introduced it. I have been too tired, lacking the energy. Also I think that multiplication will be too difficult for him. It has been a long while since we do any new Montessori Maths, or even just the usual practice. Today, I finally pulled myself together. J tried this for the first time on 30 Oct. 2015 (6Y6M25D). It turned out to be too easy for him. He could get the answer by just doing the written sum without manipulating the beads. However, I insisted that he manipulate the beads, as I think it will give him a more physical understanding of the concept. So we moved on to dynamic division with Small Bead Frame.

REFERENCES:

http://www.infomontessori.com/mathematics/passage-to-abstraction-small-bead-frame.htm

http://www.montessorialbum.com/montessori/index.php?title=Small_Bead_Frame

http://faculty.fullerton.edu/syen/mts/math/8-4.htm

Montessori Activity: Small Bead Frame - Dynamic Subtraction (With Exchange)

Note: I am showing the large bead frame above, because it is not necessary to buy both the small bead frame and the large bead frame. I am using the large bead frame to do the small bead frame exercises.

AGE: 5.5 (after the child has worked with the Stamp Game)

OBJECTIVE(S):

To show the relationship between the different place values in the decimal system.

MATERIALS:

1. Small bead frame
2. 1 worksheet
3. 1 green, red and blue pencil

PRESENTATION:

1. Read a problem to your child, i.e.:

  4962

- 2347

---------

  2615

2. Have your child build the minuend in beads to the right of the frame, i.e. slide 2 unit green beads, 6 ten blue beads, 9 hundred red beads and 4 thousand green beads to the right.

3. Have your child try to take 7 unit beads away from 2 unit beads by sliding the green unit beads to the left and he will notice that he doesn't have enough to do so, after he has taken away 2 unit beads.

4. Tell your child, "We can exchange a ten blue bead for 10 green unit beads."

5. Slide 1 blue ten bead back to the left and move 10 green unit beads to the right.

6. Ask him to remember that he has already taken 2 units away just now, so he should continue counting from 3 and slide away 5 green unit beads back to the left to show the subtraction 12-7. There should be 5 green unit beads remaining on the right after this process.

7. Ask your child how many blue ten beads he has now and he should answer 5.

8. Have your child slide 4 blue ten beads to the left to show the subtraction 50-40.

9. Have your child slide 3 red hundred beads to the left to show the subtraction 900-300.

10. Have your child slide 2 green thousand beads to show the subtraction 4000-2000.

11. Count the remaining beads on the right of the frame and record the answer on the worksheet, i.e. 2615.

VIDEO DEMONSTRATION:

https://youtu.be/Aa3a0K4pHMg

0. Prepare the materials.

1. Read a problem to your child.

2. Have your child build the minuend in beads to the right of the frame, i.e. slide 2 unit green beads, 6 ten blue beads, 9 hundred red beads and 4 thousand green beads to the right.

3. Have your child try to take 7 unit beads away from 2 unit beads by sliding the green unit beads to the left and he will notice that he doesn't have enough to do so, after he has taken away 2 unit beads.

4. Tell your child, "We can exchange a ten blue bead for 10 green unit beads."

5. Slide 1 blue ten bead back to the left and move 10 green unit beads to the right.

6. Ask him to remember that he has already taken 2 units away just now, so he should continue counting from 3 and slide away 5 green unit beads back to the left to show the subtraction 12-7. There should be 5 green unit beads remaining on the right after this process.

Have your child write 5 down on the worksheet.

7. Ask your child how many blue ten beads he has now and he should answer 5.

8. Have your child slide 4 blue ten beads to the left to show the subtraction 50-40.

Have your child write 1 down on the worksheet.

9. Have your child slide 3 red hundred beads to the left to show the subtraction 900-300.

Have your child write 6 down on the worksheet.

10. Have your child slide 2 green thousand beads to show the subtraction 4000-2000.

 

11. Count the remaining beads on the right of the frame and record the answer on the worksheet, i.e. 2615.

ADDITIONAL INFORMATION:

J tried this for the first time on 21 September 2015 (6Y6M16D). He could do the sum on paper without the small bead frame, but he had trouble understanding that he has to take away 2 first, before exchanging, when using the small bead frame.

REFERENCES:

http://www.infomontessori.com/mathematics/passage-to-abstraction-small-bead-frame.htm

http://www.montessorialbum.com/montessori/index.php?title=Small_Bead_Frame

http://faculty.fullerton.edu/syen/mts/math/8-4.htm