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.
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)
Standard index form is all about base 10.
Write 23 x 102 in standard index form.
Write 0.23 x 10-2 in standard index form.