# 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**

**Four operations with base 10 and base x counters**

**Multiplication**

**Multiplication**

152

152 x 2

exchange ten 10’s for 1 hundred

x^{2} + 5x + 2

2(x^{2} + 5x + 2) = 2x^{2} + 10x + 4

152

152 x 10

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

x^{2} + 5x + 2

x(x^{2} + 5x + 2) = x^{3} + 5x^{2} + 2x

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

** (x + 3)(x + 2) ≡ x**^{2}** + 5x + 6 **

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

**Division**

**Division**

### Algebraic division

**Standard Index Form**

**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 10^{2} in standard index form.

Write 0.23 x 10^{-2} in standard index form.