T. Hester rev. 2014
MECR/2014
Small Bead Frame
Materials:
A rectangular wooden frame eight inches wide and ten inches high strung with four horizontal wires with 10 beads on each. The rows of wire are labeled on the left side from top to bottom: 1, 10, 100, and 1000. The 1000 is on a gray background (= new hierarchy). The beads are color coded in each row: green (units), blue (tens), red (hundreds), and green (thousands). Notation paper with 4 color coded columns. Pencil. Problem cards. Counter for moving the beads. Table.
Preparation:
Stamp Games.
Dot Game.
Age: 6+ years.
Direct Aims:
“The bridge to abstraction.”
To develop greater understanding and fluency in the operations in the decimal system.
To develop a more abstract understanding of positional notation.
To give a visual representation of place value.
Indirect Aims:
To prepare for computation in the abstract.
To develop order, concentration, coordination and independence.
Presentation I – Introduction:
Invite the child to work with the Bead Frame. Bring the Bead Frame to a table, laying it flat with the units on the right. Bring the Stamp Game to the table. Compare the green unit stamp with the green unit bead on the frame and show the child where you will write the units on the prepared paper. Indicate the units and count the beads as you slide them down saying, “1 unit, 2 units, etc.” until you reach 10 units. Compare the blue ten stamp with the blue ten bead on the frame and show where you will write the tens on the prepared paper. Count the ten beads. Continue with the 100s, and 1000s.
Presentation I (con.) – Writing Numerals on Prepared Paper
Note: May do this presentation following previous presentation or wait until another time.
Starting with all the beads on the left side of the frame, count the first green unit bead with the counter, moving it over to the right end of the frame. Write 1 on the green unit line on the prepared paper. Count the remaining unit beads and record the numbers to 9. When you count the tenth bead remind the child that we can’t have ten units. Simultaneously push the 10 unit beads to the left as you push the first blue ten bead over to the left end of the frame. Write 1 on the blue ten line on the prepared paper and a 0 on the green unit line on the prepared paper. Continue counting and recording the 10’s, 100’s, and 1000’s.
Presentation II – Formation of Numbers:
1. Invite the child to work with the Bead Frame.
2. Stand the Bead Frame up making sure that all the beads are on the left.
3. On the prepared paper, write a 4 digit numeral. Say, “Let’s make this number on the Bead Frame.”
4. Starting with the units, count the beads in each category, sliding them one by one to the right.
5. When finished, move all the beads to the left.
6. Invite the child to (enter) make new numbers.
7. Show the child how to replace the materials properly.
Extensions:
- Make a number on the Bead Frame with the beads. Have the child count the beads and record the number on the prepared paper.
Note – May switch to a regular pencil and drop the color coded pencils.
- Give the child a number orally. The child writes the number on the prepared paper and makes it with the beads on the frame.
Presentation III – Addition with the Bead Frame:
- Invite the child to work with the Bead Frame. Have the child bring the Bead Frame, prepared paper, and a pencil to the table. Show the child a static problem card.
- Have the child record the first addend on the prepared paper. Have the child make that number on the Bead Frame. (Remember to start with the units first.)
- Write the second addend on the prepared paper and make it on the Bead Frame.
- Count the number on the frame and record the sum (the beads on the right side of the frame) on the prepared paper.
- Repeat the exercise this time with a dynamic problem. Remember to start with the units and when all 10 beads have been moved to the right, they must be moved back to the left and at the same time move one bead from the next category to the right.
- Encourage the child to repeat the exercise.
- Show the child how to return the materials properly.
Variation:
- Enter the units from both numerals first, then the 10s, 100s, and 1000s. Exchange when necessary.
Presentation IV – Multiplication with the Bead Frame:
1. Same process as addition just adding the same number as many times as indicated by the multiplier.
Extensions:
1. Multiply and record times tables using the Bead Frame and prepared paper.
Presentation V – Subtraction with the Bead Frame:
1. Invite the child to work with the Bead Frame. Show the child a static subtraction problem.
2. Have the child to enter the minuend on the prepared paper and with the beads on the frame. Remind the child that in subtraction we take away.
3. Indicate the number of units in the subtrahend. Record this number on the prepared paper and slide that many unit beads back to the left of the frame.
4. Write and subtract the tens, hundreds, and thousands in the same manner.
5. Count and record the beads on the right side of the frame which represent the answer (difference).
6. Select a dynamic subtraction problem and use the same procedure, exchanging as needed. Regrouping example: Move a 10 bead to the left of the frame, then 10 unit beads to the right of the frame.
7. Encourage the child to repeat the process.
8. Show the child how to replace the materials properly.
Vocabulary: Bead Frame.
Points of Interest:
Moving the color beads – especially if a counter or pointer is used.
Exchanging to the next row.
The new method of recording on the prepared paper.
Control of Error:
The color coding of the beads.
There are 10 beads in each row.
The vertical lines on the prepared paper that indicate place value.
The child’s ability to count and exchange the beads carefully.
A control chart to match the problem cards.
Variations:
Extensions:
1. Use a pointer or counter to slide the beads over as you count.
2. For multiplication problems, the Large Bead Frame is better.
3. Multiply by 10, then 100, then 1000. Notice the passage to higher categories and that only zeroes are added in the notation.
4. Chinese or Japanese abacus.
5. Research the history of calculating devices and methods for recording quantities.
Notes: