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.
