Thursday, 27 August 2015

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Montessori Activity: Large Bead Frame


AGE: 7 years old and up (after the child has worked with The Small Bead Frame)

OBJECTIVE(S):

1. To show the relationship between the different place values of the decimal system.
2. To gain familiarity with understanding large numbers.

MATERIALS:

1. Large bead frame
2. Worksheet
3. Pencil and eraser

PREPARATION:

Using the three period lesson to introduce the child to the categories he may not know. Count the beads beginning with the units, go through each category.

PRESENTATION I (COUNTING):

1. Place the frame before the child and show him the seven numbers along the left side. Begin with all the beads on the left.

2. Count the unit beads, moving them to the right. As you do so, say: "1 unit, 2 units" all the way to 10 units.

3. After having counted 10 units say, "10 units make one ten".

4. As you say this move the 10 units back to the left and move one 10 bead to the right.

5. Continue counting tens - move 10 tens back to the left as you move 1 hundred to the right.

6. Continue in the same manner through the hundreds, thousands, ten thousands, hundred thousands, and millions.

VIDEO DEMONSTRATION:



PRESENTATION II (FORMING NUMBERS):

1. Write a number, i.e. 2,347,231.

2. Show your child how to build this number on the large bead frame by sliding 1 green unit bead, 3 ten blue beads, 2 red hundred beads, 7 green thousand beads, 4 blue ten thousand beads, 3 red hundred thousand beads and 2 green million beads.

3. Invite your child to write a number down and build that number on the large bead frame.

VIDEO DEMONSTRATION:


PRESENTATION III (LARGE BEAD FRAME PAPER):

1. Use the paper with the unit line in green, the tens line in blue, the hundreds line in red, units of thousands line in green, units of ten thousands line in blue, hundred thousands line in red, and units of millions line in green.

2. Slide one unit over to the right.

3. Write the numeral 1 in the first box of units column on notation paper in green or lead pencil.

4. Continue to slide unit beads over to the right one at a time while naming them. Each time record them in the units column.

5. After having counted ten units say, "Ten units make one ten".

6. Immediately as you say this move the 10 units back to the left and move one ten bead to the right.

7. Record 1 ten by placing the digit 1 in the tens column.

8. Continue to count tens, recording each time you slide a ten bead to the right.

9. After having counted ten tens say, "10 tens make 1 hundred".

10. Immediately as you say this, move the 10 units back to the left and move 1 hundred bead to the right.

11. Record 1 hundred by placing the digit 1 in the hundreds column.

12. Continue in the same manner for the thousands, ten thousands, hundred thousands, and millions.

13. After reaching the millions column, tell the child the empty unit spaces are all zero and write "0" all the way down the unit column.

14. Do the same thing for the tens column, hundreds column, thousands column, ten thousands column, and hundred thousands column.

VIDEO DEMONSTRATION:


PRESENTATION IV:

Child composes numbers on the bead frame and composes the number on their notation paper.

PRESENTATION V:

Child writes the number on the notation paper and makes the number on the bead frame.

PRESENTATION VI (STATIC ADDITION):

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

    1,234,567
+  7,654,321
    ------------
    8,888,888

2. Have your child build the 1st addend on the large bead frame, i.e. slide 7 green unit beads, 6 blue ten beads, 5 red hundred beads, 4 green thousand beads, 3 blue ten thousand beads, 2 red hundred thousand beads and 1 green million beads to the right.

3. Have your child build the 2nd addend with the remaining beads, i.e. slide 1 green unit bead, 2 blue ten beads, 3 red hundred beads, 4 green thousand beads, 5 blue ten thousand beads, 6 red hundred thousand beads and 7 green million beads to the right.

4. Count the beads on the right and record the answer on the, i.e. 8,888,888.

PRESENTATION VII (DYNAMIC ADDITION):

Same as presentation V of small bead frame but use 7 digit numbers rather than 4 digit numbers.

PRESENTATION VIII (STATIC SUBTRACTION):

Do problems involving static subtraction using 7 digit numbers (see presentation vii for small bead frame)

PRESENTATION IX (DYNAMIC SUBTRACTION):

PRESENTATION X (MULTIPLICATION – ONE DIGIT MULTIPLIER WITH EXCHANGE):

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

  423
x    3
-------
1,269

2. Expand the multiplicand 423 on notation paper, i.e. 3, 20, 400.

3. Slide 3 green unit beads 3 times to the right, i.e. total 9 green unit beads.

4. Slide 2 blue ten beads 3 times to the right, i.e. total 6 blue ten beads (rep. 60).

5. Slide 4 red hundred beads 3 times to the right, you will find that at the 3rd time, you will be short of 2 red hundred beads to move to the right.

6. Exchange by sliding all the red hundred beads to the left and sliding 1 green thousand bead to the right as well as the remaining 2 red hundred beads back to the right i.e. total 1 green thousand bead and 2 red hundred beads (rep. 1200)

7. Count the beads on the right and record the answer on the worksheet, i.e. 1,269.

VIDEO DEMONSTRATION:

https://youtu.be/U4y7Wl94nmE

PRESENTATION X (MULTIPLICATION – TWO DIGIT MULTIPLIER WITH EXCHANGE):

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

       8437
x         34
-------------
   286,858

2. Expand the multiplicand 8437 on notation paper, i.e. 7, 30, 400 and 8000 for multiplying by 4.

3. Expand again the multiplicand 8437 on notation paper for multiplying 3 tens, i.e. 7, 30, 400 and 8000.

4. It is easier to do 7 x 10 x 3, instead of 7 x 30. So re-write the expanded multiplicand on the notation paper as 70 (i.e. 7x10), 300 (i.e. 30 x 10), 4000 (i.e. 400 x 10) and 80000 (i.e. 8000 x 10).

5. Start by multiplying the unit multiplier with the multiplicand 7 x 4 = 28 on the bead frame, i.e. slide 8 green unit beads and 2 blue ten beads to the right.

6. Build 30 x 4 = 120 on the bead frame, i.e. slide 2 blue ten beads and 1 red hundred bead to the right.

7. Build 400 x 4 = 1600 on the bead frame, i.e. slide 6 red hundred beads and 1 green thousand bead to the right.

8. Build 8000 x 4 = 32000 on the bead frame, i.e. slide 2 green thousand beads and 3 blue ten thousand beads to the right.

9. Multiply the ten multiplier with the multiplicand, i.e. 70 x 3 = 210 and slide 1 blue ten beads and 2 red hundred beads to the right.

8. Build 300 x 3 = 900 and slide 9 red hundred beads to the right. You will find that after sliding 1 red hundred beads to the right, you will be short of 8 red hundred beads.

9. Exchange by bringing all the 10 red hundred beads to the left and slide 1 green thousand unit to the right. Then continue to slide 8 red hundred beads back to the right.

10. Build 4000 x 3 = 12000 and slide 2 green thousand beads and 1 blue ten thousand beads to the right.

11. Build 80000 x 3 = 240000 (8 ten thousands taken 4 times is 24 ten thousands) and slide 4 blue ten thousand and 2 red hundred thousand to the right.

10. Count the beads on the right from the lowest bead wire and record the answer on the worksheet i.e. 286,858.

VIDEO DEMONSTRATION:


PRESENTATION X (MULTIPLICATION – THREE DIGIT MULTIPLIER WITH EXCHANGE):

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

      384
x    245
----------

2. Expand the multiplicand 384 on notation paper, i.e. 4, 80 and 300 for multiplying by 5.

3. Expand again the multiplicand 8437 on notation paper for multiplying 4 tens. As it is easier to do 4 x 10 x 4, instead of 4 x 40. So re-write the expanded multiplicand on the notation paper as 40 (i.e. 4x10), 800 (i.e. 80 x 10) and 3000 (i.e. 300 x 10).

4. Expand the multiplicand the 3rd time on the notation paper for multiplying 2 hundreds. As it is easier to do 4 x 100, instead of 4 x 200, re-write the expanded multiplicand as 400 (i.e. 4 x 100), 8000 (i.e. 80 x 100) and 30000 (i.e. 300 x 100)
--
5. Start by multiplying the unit multiplier with the multiplicand 4 x 5 = 20 on the bead frame, i.e. slide 2 blue ten beads to the right.

6. Build 80 x 5 = 400 on the bead frame, i.e. slide 4 red hundred beads to the right.

7. Build 300 x 5 = 1500 on the bead frame, i.e. slide 5 red hundred beads and 1 green thousand bead to the right.

8. Build 8000 x 4 = 32000 on the bead frame, i.e. slide 2 green thousand beads and 3 blue ten thousand beads to the right.

9. You will arrive at the partial product of 1,920 and record it on the notation paper. (Remember to read the answer from the large bead frame from the bottom up.)
------
10. Clear the bead frame by moving all the beads to the left for multiplying by the 10 multiplier, i.e. 40 x 4 = 160 and slide 6 blue ten beads and 1 red hundred bead to the right.

11. Build 800 x 4 = 3200 and slide 2 red hundred beads and 3 green thousand beads to the right.

12. Build 3000 x 4 = 12000 and slide 2 green thousand beads and 1 blue ten thousand bead to the right.

13. You will arrive at the 2nd partial product of 15,360 and record it on the notation paper.
------
14. Clear the bead frame by moving all the beads to the left for multiplying by the 100 multiplier, i.e. 400 x 2 = 800 and slide 8 red hundred beads to the right.

15. Build 8000 x 2 = 16000 and slide 6 green thousand beads and 1 blue ten thousand bead to the right.

16. Build 30000 x 2 = 60000 and slide 6 ten thousand beads to the right.

17. You will arrive at the 3rd partial product of 76,800 and record it on the notation paper.

18. Add up all the three partial product to get the final answer. (Add first on paper and then add on the bead frame, and if they match, you get the correct answer, i.e. 1,920 + 15,360 + 76,800 = 94,080.
------
19. On the bead frame, build the 1st partial product 1,920 by sliding 2 blue ten beads, 9 red hundred beads and 1 green thousand bead to the right.

20. Add the 2nd partial product on the bead frame 15,360 by sliding 6 blue ten beads to the right, (slide 1 red hundred bead, do an exchange by sliding back all the red beads and slide 1 green thousand bead to the right, and then slide the remaining 2 red hundred beads to the right, slide 5 green thousand beads and 1 blue ten thousand bead to the right.

21. Add the 3rd partial product on the bead frame 76,800 by sliding 8 red hundred beads and slide all red hundred beads back and exchange for 1 green thousand bead to the right, slide 2 green thousand beads to the right, and you have insufficient, and thus you would need to exchange by moving all the green thousand beads back, slide 1 blue ten thousand bead to the right and slide the remaining 4 green thousand beads to the right and lastly 7 ten thousand beads to the right.

22. Build 80000 x 3 = 240000 (8 ten thousands taken 4 times is 24 ten thousands) and slide 4 blue ten thousand and 2 red hundred thousand to the right.

23. Count the beads on the right from the lowest bead wire and record the answer on the worksheet i.e. 94,080.

VIDEO DEMONSTRATION:


ADDITIONAL INFORMATION:

REFERENCES:

http://www.montessorialbum.com/montessori/index.php?title=Large_Bead_Frame
http://www.infomontessori.com/mathematics/passage-to-abstraction-large-bead-frame.htm

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