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 |