Teaching with Algebra Tiles: Mastering Proof

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Teaching with Algebra Tiles: Mastering Proof

Algebraic proof is often found as one of the most challenging ideas within the school curricula. Using algebra tiles this becomes more intuitive for pupils and offers teachers a far better way of communicating these ideas that build upon models used in directed number, simplifying, equality, distribution and factoring.

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Recap

In this section of the course, we will recap using algebra tiles and explore the link between base 10 and base x.

A recap of algebra tiles

Long division

Preview

Recap Practise

Think of a Number

In this section we will look at how simple number problems can be modelled, and communicated, effectively using algebra tiles.

Think of a number

Preview

Think of a number practise

Odd and Even Numbers

In this section, the focus will be on the modelling of odd and even numbers using algebra tiles and moving towards generality.

Odd and even numbers

The square of an odd number

Algebraic Proofs

In this section, we will explore algebraic proofs using algebra tiles.

Algebraic Proof Problems

Consecutive numbers and divisibility

Sum of two consecutive numbers

Consecutive even numbers

Consecutive numbers and multiples of five

Products of consecutive numbers

Products and square numbers

Squaring odd numbers

Divisibility of (n+2)² – (n-2)²

Proving that (n + 1)² + (n + 3)² − (n + 5)² = (n + 3)(n − 5)

Primes

In this section, we will work with algebra tiles to examine proofs with prime numbers and show how intuitive this becomes with a physical model.

Sieve of Eratosthenes

Primes and multiples of 6

Primes greater than 3