Base Ten Blocks

• Number: Place value, Operations (+, -, x, ÷)

Originally these blocks came in different bases, hence the name Multibase Arithmetic Blocks (MAB). They are sometimes referred to as Deinnes Blocks, after Z.P. Deinnes who popularized them.


Technical Note:

Base Ten Materials are pre-bundled. Prior to using Base Ten Blocks students should bundle sticks.

Mathematical Language

Block, cube, flat, place value, rod, tens, hundreds, thousands, tens of thousands, hundreds of thousands, millions.

Using Base Ten Blocks

Base ten blocks are pre-bundled proportionally sized materials that illustrate the place value relationship that 10 ones make 1 ten and 1 ten = 10 ones. Each piece is ten times the size of the previous piece. Ten small cubes fit along the length of one long piece. Ten longs fit along a flat. Ten flats may be piled to make one large cube.
These relationships are designed to show the multiplicative nature of our base-ten system.

Base Ten Blocks are designed to help students understand place value. 

This relationship helps students understand that 10 ones is 1 ten, 10 tens is 1 hundred and 10 hundreds is 1 thousand.

Rather than refer to the pieces as 1, 10, 100 and 1000, the terms unit (cube), rod, flat and cubes are used. Later, when students move from whole numbers to decimal fractions the values of the pieces may be renamed. If the flat is given a value of 1, then the rod would represent one-tenth or 0.1 and the unit cube would represent one-hundredth or 0.01. 

Representing numbers

Students need to be taught to represent numbers using the blocks. Thirty-seven is shown by setting out 3 rods and 7 units.

Adding numbers

Students need to be taught to represent numbers using the blocks. Thirty-seven is shown by setting out 3 rods and 7 units.

Subtracting numbers

Subtraction involves setting out the correct number of blocks and then removing some.
Fifty-seven take 23 would involve setting out blocks to represent 57 and then taking 23 blocks away. This would leave an answer of 34.

Typical Classroom Requirements

Class sets:

  500 unit, 50 rods, 50 flats, 4 cubes

  1000 units, 100 rods, 100 flats, 6 cubes.

Support and Complementary Materials

Place Value Dice will generate four-digit numbers that may be
represented using Base Ten Blocks.

Dr Paul Swan Base Ten Blocks Book

Place Value Spinners will emphasise the ‘Hundreds Tens Ones’ pattern for naming numbers.

A Place Value Mat helps students to keep track of their blocks when performing calculations. Placing materials on to a Place Value Mat will help to emphasise the positional move nature of our place value system.