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The Digi-Block Team
Digi-Block is a base-ten model that kids BUILD BY THEMSELVES.
Kids use specially-designed boxes (“holders”) to assemble single blocks into blocks-of-10; then they assemble these blocks-of-10 to make blocks-of-100, and they assemble block-of-100 to make blocks-of-1000.
“Ten ones is one ten.”
The key to PLACE-VALUE is to think of “ten” in two different ways – as one thing and as ten things. With Digi-Block, this potentially confusing duality becomes physically obvious: a block-of-ten looks like one thing, but when it’s open, it looks like ten things! Children who work with Digi-Block develop a natural, intuitive understanding of place value.
The blocks pack and unpack, NO TRADING involved.
Since the blocks pack and unpack, regrouping becomes child’s play: “Carrying” amounts to closing a box, and “borrowing” to opening a box. NO TRADING is required!
The structure of "BLOCKS-WITHIN-BLOCKS" makes long-division physically obvious.
Mistake-proof and designed for self-discovery.
A holder clicks shut only when there are ten blocks inside. This feature allows kids to focus on physically performing the operations by packing and unpacking blocks, with the full confidence that the physical outcome will show the correct result of the mathematical operation. (E.g., they can be sure that every block-of-100 that they created contains 100 single blocks, even though they cannot see inside.)
Smooth transition to written numbers.
The “Counter” is a device that organizes the blocks in places, one for each size, with a digit (0 to 9) underneath each place. It provides a physical demonstration of how a collection of blocks is represented by a written number. A key feature is that inserting a tenth block into a hanging holder causes the holder to eject! This feature fascinates children, who love to add blocks one at a time and observe how the digits progress from 000 to 999.
Seamless transition to decimal fractions.
The pattern is always the same – inside a block-of-1,000 there are ten blocks-of-100, inside a block-of-100 there are ten blocks-of-10, and inside a block-of-10 there are ten single blocks. A child who has worked with the blocks for some time, finds it natural to extend this pattern downwards – inside a single block there should be ten smaller blocks (tenths) and inside each of these there should be ten even smaller blocks (hundredths).
Note: Due to limitations of plastics technology, we are unable to build the single blocks so they actually contain ten smaller blocks inside. Instead, we provide loose tenths blocks, ten of which - when aligned next to one another - are exactly the size of a single block. Our experience shows that kids who are familiar with packing and unpacking blocks of 10 and blocks of 100, have no trouble dealing with the single blocks as if they truly packed and unpacked.
Digi-Block come in three different styles.
The classic blocks are opaque and they all have the same (green) color. This means that all the blocks (one, ten, hundred, etc) look identical except for their size. Multiplication by ten then amounts to an enlargement of the picture, and therefore to a shift of the digits!
For young children, who are not yet ready for the idea of shifting orders of magnitude, it may be advantageous not to start with the classical blocks. Multi-colored blocks (“Power Blocks”) provide a gentle introduction. The different colors allow children to add and subtract sets of blocks representing two or even three-digit numbers, without having to address potentially confusing expressions such as “three tens and five ones” – instead, they can think about “three blues and five greens.”
Transparent blocks have the advantage that you can see inside. This makes things simpler, and therefore appropriate for very young children or special-needs students. However, the advantage turns into a disadvantage when moving on to the abstraction that “ten ones is one ten”, which is at the heart of the base-ten system. To grasp this abstraction, it is preferable that the blocks be opaque.
Digi-Trains help very young children make the first steps in learning the base-10 system.
Digi Trains help very young children learn to confidently count, add, and subtract numbers up to one hundred, without first having to learn the symbols for the digits 1, 2, …, 9, let alone the abstraction of zero! The idea is to only speak the numbers, not write them, and to rely on the trains to emphasize the rhythm of the spoken count.
Single blocks are loaded into open holders (“cars”) that are placed behind an engine. There is only one rule for making a good train: “Move the blocks as far forward as possible!” Counting the blocks on a train, with a beat on the last block in each car, naturally leads kids to discover the advantage of counting by tens. Kids love putting trains together and taking them apart. In doing so, they see for themselves how addition and subtraction work!
Note: For ease of presentation, the animations below include digits; but as you can see, everything can be done with just the spoken numbers. (Digits are introduced later, as follows: The first digit is the number of full cars; the second digit is the number of remaining blocks in the caboose.)