Math Playground

Numbers › Number blocks

Number blocks

Cubes, rods and flats — the classic base-ten manipulatives, now in your browser. Build any number; see why 'place value' is the only idea that really matters.

Number blocks

Tap + or − to add and remove blocks. Each rod is ten cubes, each flat is a hundred.

= 124

hundreds

1 × 100 = 100

tens

2 × 10 = 20

ones

4 × 1 = 4

Place value reads

124

1 hundred, 2 tens, 4 ones = 124

What are they?

The three shapes encode the structure of our base-ten system:

  • Cube (1) — the smallest unit, the "one".
  • Rod (10) — ten cubes glued together. One rod = one ten.
  • Flat (100) — ten rods side by side. One flat = one hundred.

The blocks make place value physical: 263 isn't an abstract string of three digits, it's 2 flats, 6 rods, 3 cubes. Add or take away blocks and the number changes accordingly.

Building any number

To represent the number 347, grab 3 hundreds, 4 tens and 7 ones. To get from 347 to 348, add one more ones-cube. To get from 347 to 357, add one more tens-rod. To get from 347 to 447, add one more hundreds-flat. The blocks make those moves feel as small as they really are.

Why this matters later

Every algorithm you ever learn — column addition, long subtraction, long multiplication — is really just shuffling these blocks. When you "carry the 1" in 28 + 14, you're saying "the 10 ones make a ten — swap them for a rod, leave 2 cubes." When you "borrow" in long subtraction, you're breaking a rod into 10 cubes.

The trade game

A key idea: 10 ones = 1 ten and 10 tens = 1 hundred. The blocks let you "trade" between sizes:

  • 13 ones → trade 10 of them for one rod → 1 ten + 3 ones. Same total: 13.
  • 16 tens → trade 10 of them for one flat → 1 hundred + 6 tens. Same total: 160.

That trade is the heart of "carrying" in addition. Try it: add 17 + 8 with the blocks. You'll have 1 ten and 15 ones. Trade 10 ones for a ten — now you have 2 tens and 5 ones, which is 25.

Try it

  1. Build the number 105 with the blocks. How many of each kind do you need?
  2. Build 99. Now add one — what trade do you have to make?
  3. If you have 4 flats, 12 rods, and 8 cubes, what number is that?
  4. The number 200 needs how many blocks (minimum)?

Answers: 1) 1 flat, 0 rods, 5 cubes. 2) 1 ten swaps for 10 ones, so you'd need to add a ten then trade 10 ones for a ten then 10 tens for a flat — ending at 1 flat, 0 rods, 0 cubes. 3) 12 rods = 1 flat + 2 rods, so 4 + 1 = 5 flats, 2 rods, 8 cubes = 528. 4) 2 flats.