Small Bead Frame

Materials:

The Small Bead Frame: four horizontal wires have 10 beads each - green for units, blue for tens, red for hundreds and green again for units of thousands
Numerals for 1 unit (1), 1 ten (10), and 1 hundred (100) are printed on a white background to the left of their respective wires
Numeral for 1 thousand (1000) is printed on a gray background to the left of its respective wire
Printed paper for the Small Bead Frame
Pencil

Purposes:

To provide the opportunity to work in a more symbolic way with addition and subtraction while gradually moving away from using the material.
To allow the child to apply previously learned and memorized essential combinations.

Age: about 6 ½

Preparation:

The child is comfortable with dynamic addition and dynamic subtraction of the Stamp Game.
The child has worked or is working through the progression of the Memorization exercises.

Presentation 1: Introduction to the Materials

Part A: Introduction to the Frame

Invite the child to take the frame to the table, bring the decimal bead introduction tray.
Show the child the unit bead and the unit on the frame by sliding to the right and back
Repeat for the rest of the categories
Indicate the white painted section with unit, 10 and 100. The white space represents the simple family. The gray portion represents the thousands family
Return the demonstration tray

Part B: Counting the Frame

Count the units by naming the unit (one unit, two units) and sliding the bead to the right. When you get to 10 remind of what we do with ten units. And show the child to exchange by sliding the whole row back to the left.
Repeat with the other categories. Don’t mention an exchange for the thousands
Let the child count it start to finish.

Note: Reinforce with the child that they say the name of the category as they count

Part C: Recording with No Zeros

Introduce the paper. Point out the colored lines and link them to the frame. Explain why there are two columns of units-the simple family and the thousands.
Tell the child that you will count the frame and record it on the paper.
Slide the first unit bead to the right, “One unit,” and write 1ontop of the green line. Continue for a couple and transfer to the child.
At nine, model how to exchange by sliding the beads back left and slide the first ten to the right say, “One ten,” and write a 1 on the next row on the blue line.
Turn it over to the child through nine and repeat the modeling of the exchange process.
Continue for the rest, move a bead and write the number, of the categories up to 1000 (not beyond 1000)

Part D: Recording with Zeros

Use the other side of the paper.
Have the child record the units as before up to nine.
At ten units, exchange. Slide one ten to the right, “One ten,” touch the unit wire, “Zero units.” record 1 on the ten line and zero on the unit line.
Let the child continue to 90.
Model the exchange. Slide one bead, “One hundred,” touch the ten wire, “Zero tens,” touch unit wire, “Zero units.” record 100
Come back for 900 to show the 1000 in the same manner.

Presentation 2: Composing Numbers (another day)

Presentation 3: Addition

Part A: Static Addition

Bring bead frame, paper, and writing tray
Write an addend on the paper for the child to read and build on the frame.
Add the plus sign, the next addend, and the equal line.
The guide says they will build the second addend.
To add: slide the quantity of the second addend starting with units to the center of the wire.
Then slide all over to the right.
Child counts the total units and records.
Child repeats for the rest
Tip the frame to clear it. Child reads the whole equation.

Note: As long as the child is working at the static level, they are dependent on the teacher for equations

Part B: Dynamic

Set up as in static
Write a number on the paper for the child to read and build on the frame.
Add the plus, next addend, and line. Child to reads.
To make the first exchange, the guide counts over beads until they run out, repeat the number you were last counting on then push all to the left, then slide one exchange from the next category over to the right and continue counting the original category moving them to the center until the desired number is counted and then slide over to the right.
Guide continues for the rest of the problem. Child can record and the problem is read together.
Clear the frame and have the child work the problem independently.
Invite the child to write their own problem.

Part C: Passage to Abstraction

Note: The child has been doing memorization work in addition and they will use those memorized math facts now.

Write a dynamic problem for the child to read. Explain you want to show some shortcuts. Example:
2736
+3528

Direct child’s attention to the units and read them both. Ask if they remember what they add up to. Example: 14= 1 ten 4 units
Guide builds it in the center of the wires, slides to the right then clears it and child builds it on the frame.
Have them read the tens in the problem and ask if they remember what they add up to.
Guide build, clears, and then the child builds it using the tens.
Repeat for the hundreds (you have to build on the hundreds wire because that is where the numbers are that you are adding) Example: total 12= 1thousand and 2 hundreds
Repeat for thousands
When moving the beads, look at the paper and slide as they would appear on the line
Child records the answer and reads the equation.

Presentation 4: Subtraction

Part A: Static

Invite the child as before
Write a large minuend. The child reads it and builds it on the frame.
Write the subtrahend, the minus symbol, and have the child read it.
Guide builds all categories from the minuend on the right side of the frame.
Slide to the left the beads for each category of the subtrahend, stopping in the middle before final slide.
Clear the frame and have child build minuend.
Ask how many units will be taken away and the child will slide them to the left. Repeat for all categories.
Child records at the end and reads the entire equation.
Tip frame to clear it.
Write more for the child to practice.

Part B: Dynamic

Write minuend, the child reads and builds.
- Write subtrahend and child reads. Example:
  8394
  -5737

Show the child how to take seven away by counting and sliding to the left stopping in the middle before sliding the group. When there are no beads left, tell them you need more so an exchange is needed. Repeat the last number counted as you slide to the left one ten and slide all the units to the right and slide left the rest needed.
Finish the equation read the answer off the frame with the child, clear the frame and let the child do.
When the child is finished, they read the answer off the frame and write it
Tip the frame to clear it. Do one more
Invite the child to write their own equations being sure there is a large number in the thousands.

Control of Error: None

Pedagogical Notes:

The passage to abstraction materials are what the elementary classrooms typically begin with.
You can do multiplication on the frame, but because of its size, it is limiting. The Large Bead Frame is much better designed for multiplication.
Passage to abstraction is where the decimal system and the memorization meet
The Addition Part C: Passage to Abstraction lesson is where the child gets to use the facts they have memorized. Being able to use this knowledge, means they are much less reliant on the materials.

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