# Dan Walker's Shop

I'm a secondary school maths teacher with a passion for creating high quality resources. All of my complete lesson resources come as single powerpoint files, so everything you need is in one place. Slides have a clean, unfussy layout and I'm not big on plastering learning objectives or acronyms everywhere. My aim is to incorporate interesting, purposeful activities that really make pupils think. I have a website coming soon!

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I'm a secondary school maths teacher with a passion for creating high quality resources. All of my complete lesson resources come as single powerpoint files, so everything you need is in one place. Slides have a clean, unfussy layout and I'm not big on plastering learning objectives or acronyms everywhere. My aim is to incorporate interesting, purposeful activities that really make pupils think. I have a website coming soon!

#### Coordinates rich task

This started as a lesson on plotting coordinates in the 1st quadrant, but morphed into something much deeper and could be used with any class from year 7 to year 11. Pupils will need to know what scalene, isosceles and right-angled triangles are to access this lesson. The first 16 slides are examples of plotting coordinates that could be used to introduce this skill, or as questions to check pupils can do it, or skipped altogether. Then there’s a worksheet where pupils plot sets of three given points and have to identify the type of triangle. I’ve followed this up with a set of questions for pupils to answer, where they justify their answers. This offers an engaging task for pupils to do, whilst practicing the basic of plotting coordinates, but also sets up the next task well. The ‘main’ task involves a grid with two points plotted. Pupils are asked to plot a third point on the grid, so that the resulting triangle is right-angled. This has 9 possible solutions for pupils to try to find. Then a second variant of making an isosceles triangle using the same two points, with 5 solutions. These are real low floor high ceiling tasks, with the scope to look at constructions, circle theorems and trig ratios for older pupils. Younger pupils could simply try with 2 new points and get some useful practice of thinking about coordinates and triangle types, in an engaging way. I have included a page of suggested next steps and animated solutions that could be shown to pupils. Please review if you buy as any feedback is appreciated!

#### Perimeter

A complete lesson on perimeter, with a strong problem solving element. Incorporate a set of on-trend-minimally-different questions and several opportunities for pupils to generate their own questions. Also incorporates area elements, to deliberately challenge the misconception of confusing the two properties of area and perimeter. Activities included: Starter: A few basic perimeter questions, to check pupils know what perimeter is. Main: Pupils come up with a variety of shapes with the same perimeter, then discuss answers with partners. Designed to get pupils thinking about which answers could be different, and which must be the same. A slight variation for the next activity - pupils are given diagrams of pentominoes (ie same area) and work out their perimeters. Raises some interesting questions about when perimeter varies, and when it doesn’t. A third activity based on diagrams a bit like the cover image. Using shapes made from different arrangements of identical rectangles, pupils work out the perimeters of increasingly elaborate shapes, some of which can’t be done. Questions have been designed so that only slight alterations have been made from one diagram to the next, but the resulting perimeter calculations are varied, interesting and sometimes surprising (IMO!). Has the potential to be extended by pupils creating their own shapes and trying to work out when it is possible to calculate the perimeter. Plenary: A closer look at the impossible questions, using a couple of different methods. Printable worksheets and answers included, where appropriate. Please review if you buy as any feedback is appreciated!

#### Fibonacci sequences

A complete lesson with the 9-1 GCSE Maths specification in mind. Activities included: Starter: Some recap questions on solving two-step linear equations (needed later in the lesson). Main: An introduction to Fibonacci sequences, followed by a quick activity where pupils extend Fibonacci sequences. A challenging, rich task, inspired by one of TES user scottyknowles18’s excellent sequences rich tasks. Pupils try to come up with Fibonacci sequences that fit different criteria (eg that the 4th term is 10). Great for encouraging creativity and discussion. A related follow up activity where pupils try to find missing numbers in given Fibonacci sequences, initially by trial and error, but then following some explanation, by forming and solving linear equations. Extension - a slightly harder version of the follow up activity. Plenary: A look at an alternative algebraic method for finding missing numbers. Some slides could be printed as worksheets, although it’s not strictly necessary. Answers to most tasks included, but not the open-ended rich task. Please review if you buy as any feedback is appreciated!

#### Equation of a circle

A complete lesson on the equation of a circle with centre the origin. The intention is to get pupils familiar with not only the format of the equation of a circle, and a derivation of the equation, but also problems involving coordinates on a circle. Activities included: Starter: A related question where pupils try to identify which of three given points are closer to the origin, before considering what must be true if points are a given distance from the origin. Main: The starter leads directly into a clear definition of the equation of a circle, followed by a set of quick diagnostic whole-class questions to check for understanding. Example-question pairs of increasingly difficult problems involving coordinates on circles, followed by a set of three worksheets. The last one is more of a mini-investigation, with opportunities for pupils to conjecture and generalise. Plenary: Three final puzzles to check for understanding. Printable worksheets and answers included. Please review if you buy as any feedback is appreciated!

#### Equations of tangents of circles

A complete lesson or two on finding equations of tangents to circles with centre the origin. Aimed at the new GCSE specification, although it could also be used with an A-level group. Activities included: Starter: Two recap questions on necessary prerequisites, the first on equations of circles, the second on equations of perpendicular lines. If pupils really struggled with this I would stop and address these issues, rather than persist with the rest of the lesson. Main: A set of questions on finding the gradient of OP, given some point P on a circle, followed by a related worksheet for pupils to practice. A follow-up ‘reverse’ task where pupils find points P such that the gradient of OP takes certain values. The intention is that pupils can do this task by logic and geometric reasoning, rather than by forming and solving formal equations, although the task could be further extended to look at this. The focus then shifts to gradients of tangents, and finally equations of tangents, with examples and a related set of questions for pupils to practice. An extension task where pupils find the equation of the circle given the tangent. Plenary: A spot the mistake question. Printable worksheets and answers included. Please review if you buy as any feedback is appreciated!

#### Drawing in 2D and 3D

A powerpoint including examples, worksheets and solutions on 3D sketching of prisms and other solids, nets of 3D solids, drawing on isometric paper and plans/elevations. Worksheets at bottom of presentation for printing.

#### Tangrams

Two sets of tangrams, the first making mathematical shapes, the second making more creative pictures. Includes outlines drawn to scale to assist weaker pupils.

#### Pythagoras puzzle

Basically colouring by numbers, but with questions on Pythagoras' theorem. Actually created by one of my pupils!

#### A* GCSE maths paper

A truly 'mock&' paper I put together of ONLY A* questions (each on a different A* skill), complete with model answers Can&';t remember where I got the list of A* skills from. I give this out at the start of the course and dip into it when we can - it really motivates the pupils to know they are reaching A* standard. Mistakes from earlier version now corrected.

#### Ratio robberies

A fun 'investigation&' using ratio and problem solving skills. Slightly dark theme of thieves sharing the profits of different robberies. Made by another TES user &';taylorda01' (thanks for the resource!) but I wanted to add answers to it.

#### Quadratic sequences rich tasks

At least a lesson’s worth of activities on the theme of quadratic sequences. Designed to come after pupils have learnt the basics (how to use and find an nth term rule of a quadratic sequence). Gives pupils a chance to create their own examples and think mathematically. There are four activities included: Activity 1 - given sets of four numbers, pupils have to order them so that they form quadratic sequences. Designed to deepen pupils understanding that the terms in a quadratic sequences don’t necessarily always go up or down. Activities 2 and 3 - on the same theme of looking at the sequences you get when you pick and order three numbers of choice. Can you always create a quadratic sequence in this way? What if you had four numbers? Could be used to link to quadratic functions. Activity 4 - inverting the last activity, can pupils find possible values for the first three terms and a rule, given the fourth term? A chance for pupils to generate their own examples and possibly do some solving of equations in more than one variable. Where applicable, worked answers provided.

#### Standard form collect a joke

Non-calculator sums with standard form is a boring topic, so what better than a rubbish joke to go with it? Pupils answer questions and use the code to reveal a feeble gag.

#### Quadratic shape sequences

A complete lesson on patterns of growing shapes that lead to quadratic sequences. See the cover image to get an idea of what I mean by this. Activities included: Starter: A matching activity relating to representation of linear sequences, to set the scene for considering similar representations of quadratic sequences, but also to pay close attention to the common sequences given by the nth term rules 2n and 2n-1 (ie even and odd numbers), as these feature heavily in the lesson. Main: A prompt to give pupils a sense of the intended outcomes of the lesson (see cover image). An extended set of examples of shape sequences with increasingly tricky nth term rules. The intention is that pupils would derive an nth term rule for the number of squares in each shape using the geometry of each shape rather than counting squares and finding an nth term rule from a list of numbers. A worksheet with a set of six different shape sequences, for pupils to consider/discuss. The nth term rules have been given, so the task is to justify these rules by considering the geometry of each shape sequence. Each rule can be justified in a number of ways, so this should lead to some good discussion of methods. Plenary: Ideally, pupils would share their differing methods, but I’ve shown a few methods to one of the sequences to stimulate discussion. Printable worksheets (2) included. Please review if you buy as any feedback is appreciated!

#### Gauss's formula

A complete lesson on the theme of the formula for 1+2+3+…+n, looking at how the rule emerges in different scenarios. Activities included: Starter: A classic related puzzle - counting how many lines in a complete graph. After the initial prompt showing a decagon, two differing approaches to a solution are shown. These will help pupils make connections later in the lesson. This is followed by a prompt relating to the handshaking lemma, which is the same thing in a different guise. Pupils could investigate this in small groups. Main: A prompt for pupils to consider the question supposedly put to Gauss as a child - to work out 1+2+3+…+100. Gauss’s method is then shown, at which point pupils could try the same method to sum to a different total. The method is then generalised to obtain Gauss’s rule of n(n+1)/2, followed by a worksheet of related questions. These include some challenging questions requiring pupils to adapt Gauss’s method (eg to work out 2+4+6+…+100). Plenary: A final look at the sequence Gauss’s rule generates (the triangle numbers). Please review if you buy as any feedback is appreciated!

#### Generating quadratic sequences

A complete lesson on using an nth term rule of a quadratic sequence. Starter: A quick quiz on linear sequences, to set the scene for doing similar techniques with quadratic sequences. Main: A recap on using an nth term rule to generate terms in a linear sequence, by substituting. An example of doing the same for a quadratic sequence, followed by a short worksheet for pupils to practice and an extension task for quick finishers. A slide showing how pupils can check their answers by looking at the differences between terms. A mini-competition to check understanding so far. A set of open questions for pupils to explore, where they try to find nth term rules that fit simple criteria. The intention is that this will develop their sense of how the coefficients of the rule affect the sequence. Plenary: A final question with a slightly different perspective on generating sequences - given an initial sequence and its rule, pupils state the sequences given by related rules. No printing needed, although I’ve included something that could be printed off as a worksheet. Please review if you buy, as any feedback is appreciated!

#### Finding the nth term rule of a quadratic sequence

A complete lesson on finding the nth term rule of a quadratic sequence. This primarily focuses on one method (see cover slide), although I’ve thrown in a different method as an extension. I always cover linear sequences in a similar way and incorporate a recap on this within the lesson. Starter: To prepare for the main part of the lesson, pupils try to solve a system of three equations with three unknowns. Main: A recap on finding the nth term rule of a linear sequence, to prepare pupils for a similar method with quadratic sequences. Examples on the core method, followed by a worksheet with a progression in difficulty for pupils to practice. I’ve included two versions of the worksheet - a simple list of questions that could be projected, or a much more structured worksheet that could be printed. Worked solutions are included. A worked example of an alternative method, that could be given as a handout for pupils who finish early to try on the questions they’ve already done. Plenary: A proof of why the method works. I’d much rather show this at the start of the lesson, but in my experience this usually overloads students and puts them off if used too soon! Please review if you buy as any feedback is appreciated!

#### Recognising and extending quadratic sequences

A complete lesson for introducing quadratic sequences. Rather than go straight into using or finding nth term rules, the focus is on looking at differences between terms to identify and extend given sequences. Activities included: Starter: A related number puzzle Main: Slides/examples to define quadratic sequences A set of sequences, some quadratic, for pupils to determine whether they are quadratic or not. A more challenging, open-ended task, where, given the first, second and fourth terms of a quadratic sequence, pupils form and solve an equation to find the third term. Having solved once for given numbers, pupils can create their own examples. Plenary: A comparison between linear and quadratic sequences. No printing required, please review if you buy as any feedback is appreciated!

#### Algebra Cluedo

Pupils eliminate suspects/weapons/rooms by completing worksheets on a range of algebra topics including substitution, expanding, factorising, linear & quadratic equations, algebraic fractions and simultaneous linear equations. Works well as revision or as a competition. Also includes answers and a worksheet to remind pupils of techniques required.

#### Volume of spheres

A complete lesson on the theme of volumes of spheres, best suited for more able students. Given that this can be a very dull, restricted topic if pupils just calculate volumes of spheres, hemispheres, etc given the volume formula, the focus is more on deriving a formula. I would teach this after pupils have met all other volume rules (cuboids, cylinders, cones, pyramids) - the derivations and activities require a knowledge of these other rules. Activities included: Starter: A question to get pupils thinking about the different volume rules they’ve already met (cube, pyramid, cylinder, cone). Main: Starting from an image of a square within a circle within a square, pupils are prompted to come up with an inequality for the area of the circle (ie use the inner square as a lower bound and outer square as an upper bound). This ‘leads’ to an estimate of pi=3, but the real purpose is to prepare pupils to do a similar process in 3D, to come with an estimate for the volume of a sphere… Starting from an image of a cone and a sphere within a cylinder (see cover image), pupils are prompted to come up with an inequality for the volume of the circle (using the cone as a lower bound and cylinder as an upper bound). This ‘leads’ to a conjecture for the volume rule of a sphere! Some simple examples using the rule. At this point, you could supplement with extra ‘basic’ questions if necessary. Some questions on the theme of the solar system, looking at volumes of planets and reverse problems (finding radius or diameter given the volume). This also involves standard form as the volumes involved are huge, and could be followed up with some questions about scale and volume factor. I’ve also thrown in a formal proof for the volume rule, that could be looked at with very able students. Plenary: A link to a short video showing a completely different (and fairly accessible) proof, that could be recreated using an orange, knife, and some messy cutting… Please review if you buy as any feedback is appreciated!