The ‘Why’: Why do we need to be able to add? This lesson starts with students creating a spider diagram on what they think numbers are. Encourage them to think about what you can do with numbers? Some suggestions are included which could be revealed if students are struggling and prompt thoughts in other directions. The term “Gut, data, gut” is used and is taken from a concept used in Marketing. It suggests that whenever money needs to be spent, you will have a rough idea (a gut instinct if you will) about how much something should cost. You then go seeking data to prove that and then realign this with your gut decision making. The example included is a simple scenario involving a shop. Students will have some instincts about how to do mental addition. It is still important for them to understand the different techniques. There is a prompt to encourage this in students. The final activity shows a total bill for four friends who went to lunch and ask them to check their gut feeling about how much they are being asked to pay. Activities included: What are numbers? Gut, Data, Gut example Commutative law Activity Mental Addition Techniques Associative law activity Written Method Practice Problem Solving Estimating Lunch at a café Cryptarithms

The ‘Why’: Why do we count a value of less than zero? This lesson starts by introducing the idea of a bank statement with money going and out of an account in different ways. At one point, a standing order for £100 comes out when only £99 exists in the account. It may be worth explaining what a standing order is although some will understand this implicitly. Debt is in fact the origin of negative numbers which is why the lesson starts here. It then goes on to use other real life examples including temperature and moods. Some mastery tasks are included in this from the White rose SOW including the number line and problem solving activities. Activities included: Bank Statement Starter Temperature Explanation Number Lines Activity Temperature around the world Adding & Subtracting Negative numbers Mini Whiteboard Activity Moods Walking in a line to Multiply

The ‘Why’: Why do we count in 10’s? This lesson builds on the understanding of Place value and includes a recap of this if the first place value lesson wasn’t used. When asking students, “Why do we count in tens?” the suggestions around the room are often “Because we do” or “Because that’s the system that makes sense”. Students are often surprised to learn that it is likely due to the convenience of having 10 fingers. Showing the pattern that leads to anything to the power of 1 and 0 also allows students to understand that this pattern goes on in both directions forever. Once there is a good understanding of negative powers of 10, a task framing the usefulness of this to Motorsport lap times is included as extension. There is also a short introduction to standard form which students often see on their calculators. Activities included: Pocket Money Starter The History of Number Systems Place Value Recap Counting in Tens Definition of Powers Multiplying by Powers of 10 Dividing by Powers of 10 Negative Powers Standard Form Motorsport

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