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Dienes Base 10 Blocks

Number · Year 2–Year 5

Thousands, hundreds, tens and ones. Build numbers and read the total.

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About the dienes

Dienes blocks show what a number is made of. Drag a hundred flat, a ten rod or a unit out of the tray, and the total at the top adds up as you build.

The blocks are drawn in the conventional classroom colours and to scale with each other, so a hundred flat really does look like ten rods and a rod really does look like ten units. That proportion is the whole teaching point and is the thing most on-screen versions get wrong.

Use them for partitioning, for column addition and subtraction, and for the step before place value counters. Blocks show why ten ones become a ten; counters ask children to take it on trust.

Tidy up groups the blocks into rows by size, which turns a busy mat back into a readable number.

SET A NUMBER TO MAKE and the board turns into a question. Press New for a fresh one the same size, or Set to dial one in a digit at a time: the steppers are a place value chart, so a press changes the hundreds or the tens and never carries into the digit beside it. What the board compares is the TOTAL and not which blocks made it, so a class who built a hundred out of ten rods has built a hundred.

Only a finished build is marked. Part way there the board shows the two numbers side by side and says nothing else, because how far off they are is the very thing they are working out.

How to use it on your whiteboard

  1. 1Drag a block from the tray onto the mat, or tap it to drop one on.
  2. 2Build a number from thousands, hundreds, tens and ones. The total reads out at the top.
  3. 3Press New under Make for a number to build, or Set to choose one digit by digit.
  4. 4Drag blocks around to group them, or to show an exchange.
  5. 5Tap Tidy up to sort everything into rows by size.
  6. 6Undo steps back one action at a time, and Clear takes everything off the mat.

Questions

Are the blocks to scale?
Yes. A ten rod is ten units long and a hundred flat is ten rods, drawn in the same proportion. A version that is not to scale cannot show why exchanging works.
Can I show exchanging?
Yes. Put ten units next to a rod and the class can see they are the same. For the abstract step afterwards, our place value counters have an Exchange button.
How high does it go?
Thousand cubes, hundred flats, ten rods and ones, and nothing caps how many go on the mat. A number to make can be set as high as 9,999,999, though a million is a thousand thousand cubes: past about twelve of them a new cube lands on top of an earlier one rather than being turned away, so a big number is a long build rather than an impossible one.
Can I set a number for the class to make?
Yes. Press New under Make for one, or Set to choose it digit by digit. The board shows the number to make beside the running total and says so when they match. Nothing is ever marked wrong: part way there it just shows both numbers, because how far off they are is the thing the class is working out.