# Numbered Counters

- Author:
- Tom Carpenter

- Topic:
- Equations, Linear Equations, Numbers

## Instructions

1. Click and drag the counters down across the line onto the main work board. You must click on the triangular part of the counter in order to move it.
2. If you wish to label your own counter, type in you label into the "Input" box provided and it will appear on the purple token.
3. The "Re-set" button will restack your dragged counters.

## Ideas for use

**1. Place value**: Click on the "place value grid" to reveal a column structure and use the green, yellow, orange and pink counters as appropriate.

**2. Calculating with negatives**: Using the green and red counters, positive and negative columns can be stacked up with one '+1' counter matching up with one '-1" counter where possible. For example, the sum '5+(-3) can be represented by a column of five '+1' counters next to a column of three '-1' counters with each '-1' counter next to a '+1' counter. With these three pairs of counters essentially cancelling each other out, two '+1' counters remain. Substitution can be done similarly.

**3. Collecting like terms**: All counters can be used to use to create an unsimplified expression string, which can then be simplified by organising the like terms together.

**4. Solving simple equations**: Click on the 'balancing scales' to reveal a tool for equating two sides of an equation. Drag counters onto both sides of the scales to create an equation that can be solved by removing (or adding) counters to both sides. For example, the equation '2x+3=7' can be set up by placing two 'x' counters and three '1' counters on the left scale and seven '1' counters on the right scale. It can then be solved by removing three '1' counters on both sides, and then removing half the counters on both sides to leave 'x=2'.