The Large Bead Frame

Materials

• Large bead frame (or the virtual bead frame on this site, set to Large)
• Paper and pencil
• Homemade notation paper: seven columns labeled 1, 10, 100, 1,000, 10,000, 100,000, 1,000,000
• The small bead frame for a side-by-side comparison, if you have one

No materials at home? Use the virtual Bead Frames (Small & Large).

Before this lesson

• Small Bead Frame Addition

Aims

Presentation

1. 1 Set the large frame beside the small one (or switch the virtual frame to Large) and compare them top to bottom.Same frame, more wires. Everything you know still works here.
2. 2 Point out the bands along the edge: white behind units, tens, hundreds; gray behind the thousands wires; black behind the millions wire.White is the units family, gray is the thousands family, and black begins the millions family. Green, blue, red — then green, blue, red again.
3. 3 Slide one bead on each wire from top to bottom, reading each value: one, ten, one hundred, one thousand, ten thousand, one hundred thousand …One bead here is one million.
4. 4 Reset, then build 1,000,000 with a single bead. Ask how long it would take to count a million by ones — this single quiet bead holds all of that.
5. 5 Build a large number such as 2,435,061 wire by wire and read it together. Point out that the empty hundreds wire is the zero.Two million, four hundred thirty-five thousand, sixty-one.
6. 6 Write the number on paper and show that the commas fall exactly where the bands change — after the millions family and after the thousands family.The commas on paper are the bands on the frame.
7. 7 Work an addition with exchanges reaching into the new wires, for example 456,789 + 543,211, exchanging wire by wire and reading the sum: 1,000,000.

Points of interest

• A single bead standing for one million
• The bands showing exactly where the commas belong in a written number
• Carries that ripple all the way up the frame, wire after wire, from one small addition
• Zeros inside big numbers — wires that never move

Control of error

• Each wire still holds only ten beads, so every needed exchange announces itself
• Reading a number aloud family by family exposes a wire built wrong
• The written problem on paper and the frame must agree; the virtual frame’s Make-a-number check marks each wire

Vocabulary

• ten-thousands
• hundred-thousands
• million
• family
• period
• comma
• magnitude

Variations

• Dictate seven-digit numbers, including ones with several zeros, for your child to build and write
• Subtraction with borrowing across empty wires — watch a borrow travel down through a zero
• Build 25, then 250, then 2,500, then 25,000: watch the same two digits step down the frame, wire by wire, as the number grows tenfold

Extensions

• Multiply on the frame by repeated addition: 3 × 2,314 is 2,314 added three times, exchanges and all
• Find numbers in the newspaper or an atlas (city populations, distances in miles) and build them on the frame

Follow-up work (pencil & paper)

• Print a place-value worksheet with large numbers. Your child writes each number in expanded form (2,435,061 = 2,000,000 + 400,000 + …), then builds a few on the frame to verify.Printable: Place Value & Expanded Form
• Print multi-digit addition and subtraction problems with five- and six-digit numbers. Your child computes in pencil, then proves one or two answers on the large frame.Printable: Multi-Digit Operations
• Million hunt: together, list five real quantities near a thousand, a hundred thousand, and a million (people, miles, dollars), write them with commas, and read them aloud family by family.

What comes next

With big numbers tamed, your child is ready for the checkerboard: Introduction to the Checkerboard presents long multiplication, where these same place-value families become rows and columns of bead bars.

Next in this strand: Introduction to the Checkerboard