The ‘Why’: Why does multiplication work the way it does? This lesson starts with an exercise designed to get students to recognize that multiplication is a way of simplifying repeated addition. It is then followed by a refresher of the commutative and associative laws and why they work. Similar to the addition and subtraction lessons, this is then split into mental and written techniques. Mental techniques covered include; doubles, using 10’s, hand tricks and partitioning. Students should be reminded that, whilst they may be able to answer quickly and another way, these are good techniques for them to have in their back pockets. The aim is to give a technique for as many time tables as possible. Each slide features an “I do, you do” example, followed by a time trail to see how many students can complete in one minute. Following this is the written techniques that includes: bar models, grid method, lattice method and lines. Some of these descriptions are slight rewording of popular techniques. Grid method is the method by which the place value of each number is split and put in a table. The lattice method, is similar but features diagonal lines to give two digit answers followed by diagonal addition to give each place value. Lastly, line is the Japanese method of drawing a single line to represent each place value, followed by another line across is and then counting the points at which they cross. The deliberate decision was made to not include column method as it will likely have been covered in primary and often leads students to an incorrect answer. Towards the end of the lesson, there are some techniques for decimal multiplication including using similar sums and estimating followed by practice using any method. At the end is a mix of problem solving tasks including worded and spot the mistake problems. Activities included: Repeated addition starter Commutative and associative law refresher Mental multiplication methods Written multiplication methods Decimal Multiplication Estimating and Using Similar Sums Mixed Problem solving

Topic Intro designed to introduce Year 7 students to careers and real life uses of maths plus its place in their learning journey and other skills that they will be building on.

Topic Intro designed to introduce Year 7 students to careers and real life uses of maths plus its place in their learning journey and other skills that they will be building on.

Topic Intro designed to introduce Year 7 students to careers and real life uses of maths plus its place in their learning journey and other skills that they will be building on.

Topic Intro designed to introduce Year 7 students to careers and real life uses of maths plus its place in their learning journey and other skills that they will be building on.

Topic Intro designed to introduce Year 7 students to careers and real life uses of maths plus its place in their learning journey and other skills that they will be building on.

Topic Intro designed to introduce Year 7 students to careers and real life uses of maths plus its place in their learning journey and other skills that they will be building on.

Topic Intro designed to introduce Year 7 students to careers and real life uses of maths plus its place in their learning journey and other skills that they will be building on.

Topic Intro designed to introduce Year 7 students to careers and real life uses of maths plus its place in their learning journey and other skills that they will be building on.

Topic Intro designed to introduce Year 7 students to careers and real life uses of maths plus it’s place in their learning journey and other skills that they will be building on

The ‘Why’: Why do we use the current number system? Because Place value is taught to Primary students, many come in to lessons with a working understanding of ‘what’ place value is and ‘how’ it works. What is often not made clear, is the motivations behind it. The early part of this lesson gets students to understand that numbers (as we think of them today) are in fact symbols that represent a value and that many other systems existed before this. It then gets students to understand why it would be inconvenient to have a new symbol for every single number and how handy the positional notation system is. Some students will go on to ask “Why do we count in tens?” This leads nicely into talking about different bases and binary as extension. Activities included: Number Symbols from the past Counting systems throughout history Representing Number activity Design your own Number system Where our symbols came from The History of 10 Positional Notation activity Problem Solving Questions Different Bases Counting in Binary

Topic Intro designed to introduce Year 7 students to careers and real life uses of maths plus its place in their learning journey and other skills that they will be building on.

Topic Intro designed to introduce Year 7 students to careers and real life uses of maths plus its place in their learning journey and other skills that they will be building on.

Topic Intro designed to introduce Year 7 students to careers and real life uses of maths plus its place in their learning journey and other skills that they will be building on.

Topic Intro designed to introduce Year 7 students to careers and real life uses of maths plus its place in their learning journey and other skills that they will be building on.

Topic Intro designed to introduce Year 7 students to careers and real life uses of maths plus its place in their learning journey and other skills that they will be building on.

Topic Intro designed to introduce Year 7 students to careers and real life uses of maths plus its place in their learning journey and other skills that they will be building on.

Topic Intro designed to introduce Year 7 students to careers and real life uses of maths plus its place in their learning journey and other skills that they will be building on.

Topic Intro designed to introduce Year 8 students to careers and real life uses of maths plus its place in their learning journey and other skills that they will be building on.

The ‘Why’: Why does subtraction work the way it does? This lesson starts with a worded problem about people’s heights. This is to introduce the idea of a real world application of subtraction as well as unit conversion and problem solving skills. Next is an introduction to inverse operations. This explained as being one of the most beautiful and simplistic ideas in all of mathematics; that anything that can be done one way can also be done in reverse. This is shown through bar models and fact families. As an extension of the work on addition, mental subtraction techniques such as partitioning and compensating are covered as an ‘I do, you do’ followed by some practice questions of each. Then, move on to written subtraction. This is one of very few slides where the answers haven’t been provided. However, a place value grid has been provided to talk through the answers and techniques. There is then some practice (with grids) that does include the answers and some problem solving questions as extension. There is then a slide addressing a misconception that is often built in by teachers; that you “can’t take 3 from 2”. This isn’t strictly speaking true. If you take 3 from 2, you get negative 1. There is then an example of how, if you are secure in your understanding of place value, you can subtract using these numbers. There is then explanation and practice for subtracting decimals. Although this will have been modelled earlier, this will be the students first chance to practice. Again, the first screen is an “I do, you do” (without answers) and then practice (with answers). There is then an example of how bar models and fact families can be used to solve algebraic expressions and lastly, some problem solving tasks using algebraic skills. Activities included: Worded height starter The beauty of inverse functions Partitioning and compensating mental subtraction Written subtraction practice Problem solving Place value subtraction Subtracting decimals practice Using bar models for algebra Algebra problem solving