Q: Briefly explain the construction and functionally
of Bead Frames. Explain in your own words the exercise by which:
·
Addition
facts
Or
·
Multiplication
facts
Can be taught with the help of
small bead frame.
Bead Frames
A manual computing device consisting
of a frame holding parallel rods strung with movable counters.
Construction and functionality.
Materials.
A frame with supports to enable it to stand. The frame has
four wires across, each strung with 10 beads. The op wire for units green
beads; the 2nd wire for tens – blue beads; the 3rd wire for thousands – green
beads.
On the left hand side of the frame is a colored strip; white for the group of units and grey for the thousands. On this strip the category of each wire is marked.
Notes
- It is important to take each step, slowly and carefully to understand the use of this material.
- It is also important to give many examples of numbers (in each step) with zeros in it, such as: 1069, 4301, and 8140.
Presentation 1
Introduction
On the left hand side of the frame is a colored strip; white for the group of units and grey for the thousands. On this strip the category of each wire is marked.
Notes
- It is important to take each step, slowly and carefully to understand the use of this material.
- It is also important to give many examples of numbers (in each step) with zeros in it, such as: 1069, 4301, and 8140.
Presentation 1
Introduction
1.
Have the child bring the material to the table.
2.
Tell him that before we begin, we are going to need the
Introductory Tray of beads.
3.
Have the child bring this over.
4.
Show the child the unit bead and then tell him that all
of the beads on the first wire also represent unit beads.
5.
Show his one green bead and say, “So this is one unit.”
6.
Repeat in this way for the ten bar and the blue beads.
7.
Repeat for the hundred square and the red beads.
8.
Repeat for the thousand cube and the 4th wire of greed
beads.
9.
Do a Three Period Lesson with the new beads.
10. Show
the child the numbers written on the side of the frame.
11. Have
the child but back the Introductory Tray and have him bring the stamp game.
12. Take
out one of each. See below for placement.
13. Bring
attention to the similarity of the colors from the tiles to the beads on the
frame.
14. Also
bring attention to the numbers written on the tiles and the numbers written on
the side of the bead frame.
15. Have
the child but the Stamp Game back.
|
1000
|
100
|
10
|
1
|
Counting without a
zero
1.
Tell the child that you are going to make 5 units.
2.
Gently slide one unit at a time from the first wire to
the right side of the frame. Count each unit as you do so.
3.
Show the child how to replace the units to the left
once done.
4.
Repeat for the tens.
5.
Give the child an amount of hundreds and have him push
the red beads to the right of the frame.
6.
Ask him to show you what to do once done. (Replace the
beads to the left side of the frame.)
7.
Repeat for the thousands.
8.
Move the frame off to the side and introduce the paper.
9.
Explain the marks and lines on the paper.
10. Fold
the paper in half.
11. Tell
the child that we will now count the unit beads.
12. Push
one unit bead to the right and count: “one unit”.
13. Write
a 1 on the line for the units on the paper.
14. Push
another unit bead to the right and count: “two units”.
15. Write
2 on the line under the 1.
16. Repeat
this way unit 5.
17. Then
have the child move the bead, count as he does so and then write it on the
paper.
18. When
he gets to ten units, he should remember that ten units is one ten.
19. Move
one of the ten beads halfway to the right and say, “So ten units is one ten”.
20. Have
the child mark 1 ten on the ten line
21. Then
gently push all of the unit beads to the left.
22. Record
how many tens there are as you had done with the units.
23. Repeat
for the hundreds.
When you have ten hundreds, move the thousand bead halfway
and record 1 thousand. Tell the child that we no longer have any room of the
paper so that is all we have to do.
Counting with a zero
1.
Have the child count the units as above but this time
after he counts each unit, ask him if there are any other beads.
2.
When he gets to ten units, move a ten bead halfway to
the right as you had done before and move all of the units to the left.
3.
Slide the ten bead all the way to the right and count:
“one ten”.
4.
Have the child record this and ask if there are any
other beads. Because there are none, have him write a zero in the units column.
5.
Repeat in this way for all the tens, hundreds and
thousand.
Making large numbers
1.
Tell the child that you are going to show him how to
make large numbers.
2.
Move a few units, tens, hundreds, and thousands to the
right.
3.
Count the units, tens, and hundreds, recording after
each count. (As you count each bead, move them slightly to the left with your
finger to separate it from the beads you have not yet counted.)
4.
Read the final number with the child. For example: five
thousand, two hundred and eighty-four.
5.
Repeat a few times and have the child count and record.
6.
Once the child understands, write a large number: 2596
7.
Have the child read it and show him how to create it
with the beads by moving first the 6 units, then the 9 tens, then the 5
hundreds, and finally the two thousands to the right.
8.
Repeat this a few times until the child understand how
to make a large number with the beads from a written number.
9.
Then make a number with a zero in the tens with the
beads.
10. Have
the child count and record.
11. Have
him leave the tens blank.
12. Once
he has recorded everything else, come back to the fact that there are no tens
and discuss that we can but a zero in the tens to show us that there are no
tens.
13. Repeat
this a few times.
14. Tell
the child that you will make 12.
15. Count
the units unit 10.
16. Move
a ten bead to the right and say, “ten”.
17. Then
move two unit beads to the right counting, “eleven, twelve.”
18. Repeat
this a few times.
Making numbers with a
zero
1.
This is done in a similar manner as in the above
presentation. Begin with a simple number such as two ten beads and no unit
beads.
2.
Have the child count the beads and then tell you what
the number is (in this case: 20).
3.
Repeat this a few times unit the child understands the
concept.
4.
Then move on to making large numbers but making the
units, tens, or hundreds a zero.
5.
Once the child understands, make a number, have the
child count the beads and then record the number. Point out that because there
are no units, tens, or hundreds, we need to write a zero in the place.
Example below shows the number 2607:
Example below shows the number 2607:
Presentation 2
Static Addition
1.
Tell the child that today you will show him how to do
addition with the bead frame.
2.
Write an equation on the paper:
3.
Make the first add-in (5 units) with the beads and then
add 3 units. Count the total number of unit beads and record.
4.
Leave the unit beads to the right and repeat for the
tens, hundreds, and thousands.
Dynamic Addition
Dynamic Addition is done in a similar manner as Simple Addition but show the child how to “carry” over the extra beads.
Dynamic Addition is done in a similar manner as Simple Addition but show the child how to “carry” over the extra beads.
For example:
1.
Have the child first count out five units.
2.
Have him add the add-in but once you get to ten unit
beads ask the child how we can get more units.
3.
Move one ten over to the right and the ten units to the
left.
4.
Count out one unit to make 11.
5.
Ask him how many units there are: 1
6.
Have him record the one unit.
7.
Have him add the 3 tens and the 2 tens to the 1 ten you
began with from the ten units.
8.
The rest of the addition problem is done in the same
manner as in Static Addition.
Presentation 3
Static Multiplication
Static Multiplication
1.
Tell the child that today you will show him how to do
multiplication with the small bead frame.
2.
Write an equation on the paper.
3.
Have the child create 1 unit three times.
4.
Record how many units you have all together.
5.
Repeat for the tens and hundreds.
6.
Read the total equation with the answer out loud.
7.
After doing a few examples, remind the child that he
knows his multiplication tables and he can therefore know the answers without
using the beads.
Dynamic Multiplication
1.
Write an equation on the paper.
2.
Ask the child what 2 x 6 is. (12)
3.
“We are going to have 3 tens times 6. So what is 3
times 6?”
4.
Have the child give you the answer.
5.
Place your left thumb over the ten written on the left
side of the frame and say, “So we will have 18 tens.”
6.
Have the child create 18 with one ten bead and eight
unit beads.
7.
Then tell the child, “Now, we will have 3 tens times 6,
so what is 3 times 6?” (18)
8.
Place your thumb over the ten number and repeat to the
child that we are multiplying the tens. So to make 18 (really 180) use one
hundred bead and eight unit beads.
9.
Record how many ten beads there are? (9)
10. Repeat
in this manner for 4 times 6 (really 400 times 6) and 1 times 6 (really 1000
times 6).
11. Record
after each.
Note
This is referred to the piece of material as marking
the
passage to abstraction.
passage to abstraction.
This material allows the child to stop using the material
when he no longer needs it to find the answer to the problem.
Purpose
Direct
- To show the relationship between categories of the decimal
system.
- To clarify position and place value. This helps addition and subtraction.
- To show the relationship between categories of the decimal
system.
- To clarify position and place value. This helps addition and subtraction.
Control of Error
the child’s own ability and the colored lines on the paper.
the child’s own ability and the colored lines on the paper.
Age
5 1/2 - 6 years
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