1. Extending Year 6 Key Skills to develop 1.Tackling a multi-stage problem 2.Hypothesising and then checking for accuracy 3.Expressing ideas clearly in written form Key Content for success at level 6 Number: 1.Fraction arithmetic 2.Negative number arithmetic Algebra: Substitution of values into a formula Order of operations Drawing of linear graphs Using algebra to describe patterns Using algebra to generalise a situatio Understanding how to find the ‘n’th term of a sequence Solving Equations Equations with an unknown on both sides

2. Intro Lesson: Two extensive puzzle requiring good problem solving skills Lesson 1: Consecutive Numbers, Common Multiples and Highest Common Factors Lesson 2: Equivalent Fractions and Fractions of an Amount Lessons 3+4: Adding Fractions with different denominators and Egyptian Fractions Lesson 5: Negative Numbers and order of operations in algebra Lessons 6: Describing things using algebra Solving equations with the unknown mainly on one side Lessons 7+8+9: Using the balancing method to solve equations with the unknown on both sides Lesson 10+11 Sequences – finding a rule for a sequence Lesson 12 Scorpios – applications to finding a sequence Lesson 13 Drawing graphs of linear relationships

3. Intro Lesson: Two extensive puzzle requiring good problem solving skills I got both of these puzzles from the TES website. The Murder Mystery puzzle is easier and requires little actual maths knowledge, however the Theatre Problem is quite challenging especially without a calculator and requires good numeracy skills as well as an ability to read and think carefully Pupils enjoy both of these puzzles and they illustrate a purpose to mathematics as well as how important it is to read things carefully, split things into smaller chunks and record working and answers clearly. Able students often struggle with these skills even though they find the content relatively straight forward.

4. Lesson 1: Consecutive Numbers, Common Multiples and Highest Common Factors The starter activity here is excellent as it is accessible to all and provides opportunity for conjecture and testing of hypotheses. Make certain pupils know what we mean by consecutive. You can introduce algebra to demonstrate why three successive numbers must always be divisible by 3 and ideas of proof! n, n + 1, n + 2 add to be 3n + 3 = 3 lots of (n + 1) You can then teach pupils about HCFs and LCMs before having a go at the puzzles at the end. The last one is an NRich Classic and a poster for it is available on the web site.

5. Lesson 2: Equivalent Fractions and Fractions of an Amount I usually ask pupils what they understand by equivalent fractions and get them to establish how you can find equivalent fractions by multiplying (or dividing) the numerator and denominator of a fraction by the same number. It is good to demonstrate this with a drawing and to remind them that when you find equivalent fractions by dividing it is called cancelling. Pupils can then do the number maze and the equivalent fractions sort. The ‘Game discs’ puzzle is again from NRich. With an understanding of factors, LCMs and equivalent fractions this is very accessible but looks confusing and hard to begin with. Before they get started it is important to ensure that they understand the difference between ‘rows’ and ‘columns’. I set the puzzle as a challenge and give them no guidance for about 5-10 mins. What I want them to do is to start drawing a diagram and to begin thinking about how big the booklet is going to be. I then usually talk to them the fact that I would start by drawing a diagram and fixing a booklet size, say 1 by 1 and then see what the question leads me to. I then set them going again. There are two more word puzzles from NRich in the word file.

6. Lessons 3+4: Adding Fractions with different denominators and Egyptian Fractions Pupils need to be able to add and subtract fractions, including those with a different denominator. I usually establish how to do this in one lesson and then lead into the work on Egyptian Fractions. This applies the new knowledge. The worksheets are fairly self explanatory and offer opportunities for conjecture and pattern spotting.

7. Lesson 5: Negative Numbers and order of operations in algebra The starter is a great example to show pupils how you can use algebra to prove a result I use the coded puzzle as a check to ensure that the pupils can add, subtract, multiply and divide with negative numbers. I then get them to evaluate some algebraic expressions – remembering the laws of BIDMAS The pupils can use page 3 and 4 of the word file To finish summarise the laws of BIDMAS and perhaps you can do this puzzle Eg if a = 3 and b = -4 I can make 1 by doing a + ½b 2 by having 2a + b 3 by having a 4 by having 2a etc. How can I make the other numbers less than 20? Can I make all numbers less than 100?

8. Lessons 6: Describing things using algebra Solving equations with the unknown mainly on one side For level 5 SATs pupils need to be able to solve linear equations with the variable on one side of the equation. I usually do a lesson focusing on what it means to solve an equation and looking at the relationship between an equation and a think of a number problem. I establish with pupils how they can solve equations by using inverses and by rearranging the equation. If they are ready I might introduce the idea of balancing scales, but the slides at the start of the next lesson focus on this method.

9. Lessons 7+8+9: Using the balancing method to solve equations with the unknown on both sides For level 5 SATs pupils need to be able to solve linear equations with the variable on one side of the equation. I usually do a lesson focusing on what it means to solve an equation and looking at the relationship between an equation and a ‘think of a number problem”. I establish with pupils how they can solve equations by using inverses and by rearranging the equation. If they are ready, I might introduce the idea of balancing scales, but the slides at the start of the second lesson focus on this method. For the second lesson on this topic, start by showing the class the first three scales pictures and get them to work out how many stars a ‘face’ is worth. I show the pupils how you can represent each set of scales with an equation. The pupils then practise this with slides 5 to 16 – writing down the algebra as they go. They can then do the questions without scales. Often more practise of this skill is required. You can easily spend a third lesson practising more difficult equations. Slides are provided.

10. Lesson 10+11 Sequences – finding a rule for a sequence The first lesson focuses on understanding what a sequence is and what types of sequences there are. Pupils will enjoy the first slide where they have to work out the next few numbers in each sequence. Expect many of them to get the value of the 20 th term incorrect because they will believe that the value of the 20 th term is twice the value of the 10 th – a misuse of proportionality. After they have had a go at doing this – I usually run through the answers and ask them what methods they used – I explain that the sequences that merely involved adding on a constant difference are called linear sequences. I then look at ways that they have used to try and work out the value of the 20 th term. This leads to how we can use a linear formula to describe a sequence. I spend the rest of the lesson getting pupils top practise generating a sequence from a formula. In the second lesson pupils start with the matchup activity. I lead the pupils to spot how the sequences with a difference of 2 are all based on the two times table and have a formula with 2n in it, ones with a difference of 3 are based on 3n etc. I show pupils how you can use this to write down a formula for any linear sequence and they can then practise this.

11. Lesson 12 Scorpios This is all about applying how to find a linear formula to describe a ‘real life’ situation. I explain to pupils that a Scorpio is a type of insect. There are many different varieties but they all grow using a linear formula. The number of squares in a Scorpio tells you its age in years. Each year it grows more body parts (circles) according to a simple, linear rule. Pupils need to draw the next two Scorpio’s and then try and write down a formula relating the limbs (circles) to the age (squares). They can then predict how many limbs the Scorpios will have when they are 20 and 100 years old. Pupils can make their own Scorpios using a ‘linear’ pattern.

12. Lesson 13 Plotting linear graphs I usually start this by checking that pupils can plot coordinates in all 4 quadrants of the coordinate axes with a simple coordinate plotting exercise. I then get them to suggest numbers that fit a rule and write them down. I then introduce the idea of a plotting the numbers they have given me as a coordinate on a pair of axes and show them that we get a straight line. They can then practise plotting other graphs where the rule is described firstly in words and then only using an algebraic equation.

13. The last folder contains past papers for level 6 extension paper and some extra level 6 questions from old SATs papers. Some of these I collated myself and some are from the TES web site.