Combining Operations

These lessons on number are intended to introduce some of the key ideas needed to work with algebraic expressions later on. I currently plan to teach these mostly in year 7, followed by equivalent lessons involving algebra.

In the long term, I hope that they will help students to understand why 5x +3y – 2x ≡  5x – 2x + 3y and why  .

Aims Lesson Plan Resources Mentioned in Lesson Plan Notes
To apply the order of operations with the four main operations and brackets operations A – plan (down the page layout) operations A
To apply the order of operations with powers operations B – plan (order of ops with powers) operations B
To apply the order operations with negative numbers operations C – plan (order of ops with negatives) operations C
To understand and use the commutative and associative properties operations D – plan (commutative, associative) operations D – notes
To know that you can think of subtraction as adding a negative.
To use this to move constant terms around an expression
operations E – plan (rearranging sums)
To know that you can think of division as multiplication by a fraction
To use this to move numbers around within a term
operations F – plan (rearranging multiplications)
To know the terminology inverse pair
To know that +a-a is equivalent to +0 and that  is equivalent to multiplying by 1
operations G – plan (inverse pairs) operations G
To understand the distributive property of operations.
To know which operations distribute over others, including powers and roots.
operations H – plan (distributive) operations H – notes