# Counters

Counters are a versatile manipulative that have many uses in the maths classroom. I have demonstrated a selection in this section.

MathsBot has a great selection of interactive counters.

The examples below demonstrate the connections that can be made between number and algebra using counters.

## Four operations with base 10 and base x counters

### Multiplication

152

152 x 2

exchange ten 10’s for 1 hundred

x2 + 5x + 2

2(x2 + 5x + 2) = 2x2 + 10x + 4

152

152 x 10

Each counter moves one place to the left (10 times bigger)

x2 + 5x + 2

x(x2 + 5x + 2) = x3 + 5x2 + 2x

Each counter moves one place to the left (x times bigger)

13 x 12 = 13x2 + 13x10

(x + 3)(x + 2) ≡ 2(x+3) + x(x+3) ≡ x2 + 5x + 6

Each "counter" moves one place to the left (x times bigger)

### Division

### Algebraic division

## Standard Index Form

Standard index form is all about base 10.

### Making sense of standard form misconceptions.

### Non-standard standard form problems

Write 23 x 102 in standard index form.

Write 0.23 x 10-2 in standard index form.