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Complete Mathematics/Teaching with Two-Colour Counters
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Teaching with Two-Colour Counters


Two-colour counters are an incredibly versatile manipulative, which is great as they are also one of the cheapest!

In this course you will learn how to start getting the most out of this powerful and versatile manipulative, with tried and tested ‘low floor, high ceiling’ activities to use in the classroom, covering topics such as number, algebra, proof and probability.
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Contents

Introduction

Two-Colour counters are an incredibly versatile manipulative, which is great as they are also one of the cheapest! In this course you will learn how to start getting the most out of this powerful manipulative, with tried and tested ‘low floor, high ceiling’ activities to use in the classroom, covering topics such as number, algebra, proof and probability.
Course Introduction
  • 2 mins
  • 21.8 MB
Preview

Mathematical Modelling

This section of the course looks at how Two-Colour counters can be used to model a mathematical situation
Hotel Doors Problem
  • 4 mins
  • 59.6 MB
Preview
Hotel Doors - Solution up to 12th door
  • 3 mins
  • 41.9 MB
Hotel Doors - Generalising to n doors
  • 5 mins
  • 80.6 MB
Task - Hotel Doors
  • 112 KB
Preview
Task - Hotel Doors - Solutions
  • 181 KB

Sequences

This section of the course looks at how Two-Colour counters can be used to model sequences.
Linear nth Term
  • 3 mins
  • 52.4 MB
Quadratic nth Term
  • 5 mins
  • 83.6 MB
nth term rule for a triangular number
  • 3 mins
  • 52.9 MB
Task - Sequences
  • 145 KB
Task - Sequences - Solutions
  • 189 KB

Directed Number

This section of the course looks at how Two-Colour counters can be used to model calculations involving directed number.
Zero Pairs
  • 2 mins
  • 37.4 MB
Addition with directed number
  • 3 mins
  • 50 MB
Additions - Moving from the counters
  • 3 mins
  • 50 MB
Subtraction with directed number
  • 5 mins
  • 78 MB
Task - Directed Number
  • 819 KB
Task - Directed Number - Solutions
  • 829 KB

Visual Proofs

This section of the course looks at how Two-Colour counters can be used to demonstrate visual proofs of mathematical statements.
Fibonacci - 1st + 5th = 3(3rd)
  • 5 mins
  • 85.4 MB
Sum of odd integers 1 to n is a square
  • 3 mins
  • 43.7 MB
Consecutive triangular numbers sums to a square
  • 2 mins
  • 26.9 MB

Probability

This section of the course looks at how Two-Colour counters can be used to model problems involving probability.
Venn Diagrams
  • 5 mins
  • 89.9 MB
Replace or not replace
  • 5 mins
  • 90.1 MB
Simpson's Paradox
  • 3 mins
  • 39.5 MB

Average and Range

This section of the course looks at how Two-Colour counters can be used to model problems involving averages and range.
The concept of the mean
  • 2 mins
  • 35.3 MB
Fixing towers - mean 4, mode 3
  • 2 mins
  • 25.5 MB
Fixing towers - mean 3, range 4
  • 2 mins
  • 27.8 MB
Fixing towers - mean 3, range 4, median 3
  • 3 mins
  • 56.3 MB

A Final Investigation

This section of the course looks at how Two-Colour counters can be used to model situations.
Frogs and Toads
  • 4 mins
  • 65.4 MB
Task - Frogs and Toads
  • 113 KB
Task - Frogs and Toads - Solutions
  • 125 KB
Course Summary
  • 1 min
  • 9.44 MB

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