Drawing in 2D and 3D
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danwalker

Drawing in 2D and 3D

(139)
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.
The tangent function from 0 to 360 degrees
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danwalker

The tangent function from 0 to 360 degrees

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A complete lesson on the graph of tangent from 0 to 360 degrees. I’ve also made complete lessons on sine and cosine from 0 to 360 degrees and all three functions outside the range 0 to 360 degrees. Designed to come after pupils have been taught about the ratios sine, cosine and tangent in the context of right-angled triangle trigonometry, and have met the unit circle definitions of sine and cosine. Activities included: Starter: A quick set of questions on finding the gradient of a line. This is a prerequisite to understanding how tan varies for different angles. Main: An example to remind pupils how to find an unknown angle in a right-angled triangle using the tangent ratio, followed by a set of similar questions. The intention is that pupils estimate using the graph of tangent rather than using the inverse tan key on a calculator, to refamiliarise them with the graph from 0 to 90 degrees. Slides to define tan as sin/cos and hence as gradient when using the unit circle definition. A worksheet where pupils construct the graph of tan from 0 to 360 degrees (see cover image). A set of related questions, where pupils use graph and unit circle representations to explain why pairs of angles have the same tan. Pupils can be extended further by making and proving conjectures about pairs of angles whose tans are equal. Plenary: An image to prompt discussion about the “usual” definition of tangent (using the terminology opposite, adjacent and hypotenuse) and the fuller definition (using the unit circle) Printable worksheets and answers included. Please review if you buy as any feedback is appreciated!
Solving basic trigonometric equations beyond the range 0 to 360 degrees
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danwalker

Solving basic trigonometric equations beyond the range 0 to 360 degrees

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A complete lesson on solving equations of the form sinx = a, asinx = b and asinx + b = 0 (or using cos or tan) for any range. Designed to come after pupils have spent time solving equations in the range 0 to 360 degrees, and are also familiar with the cyclic nature of the trigonometric functions. See my other resources for lessons on these topics. I made this to use with my further maths gcse group, but could also be used with an A-level class. Activities included: Stater: A set of 4 questions to test if pupils can solve trigonometric equations in the range 0 to 360 degrees. Main: A visual prompt to consider solutions beyond 360 degrees. followed by a second example (see cover image) that will lead to a “dead-end” for pupils. Slides to define principal values for sine, cosine and tangent, followed by a summary of how to solve equations for any range. Three example problem pairs to model methods and then get pupils trying. Includes graphical representations to help pupils understand. A worksheet with a progression in difficulty and a challenging extension to create equations with a required number of solutions. Plenary: A prompt to discuss solutions to the extension task.
The functions sine and cosine from 0 to 360 degrees
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danwalker

The functions sine and cosine from 0 to 360 degrees

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A complete lesson on the graphs of sine and cosine from 0 to 360 degrees. I’ve also made complete lessons on tangent from 0 to 360 degrees and all three functions outside the range 0 to 360 degrees. Designed to come after pupils have been taught about the ratios sine, cosine and tangent in the context of right-angled triangle trigonometry. Activities included: Starter: Examples to remind pupils how to find unknown angles in a right-angled triangle (see cover slide), followed by two sets of questions; the first using sine the second using cosine. The intention is that pupils estimate using the graphs of sine and cosine rather than with calculators, to refamiliarise them with the graphs from 0 to 90 degrees. Although I’ve called this a starter, this part is key and would take a decent amount of time. I would print off the question sets and accompanying graphs as a 2-on-1 double sided worksheet. Main: Slide to define sine and cosine using the unit circle, with a hyperlink to a nice geogebra to show the graphs dynamically. Or you could get pupils to try to construct the graphs themselves by visualising. A set of related questions that I would do using mini-whiteboards, where pupils consider symmetry properties of the graphs. A mini-investigation where pupils look at angles with the same sine or cosine and look for a pattern. Plenary: An image to prompt discussion about the “usual” definition of sine and cosine (using the terminology opposite, adjacent and hypotenuse) and the fuller definition (using the unit circle) Printable worksheets and answers included. Please review if you buy as any feedback is appreciated!
Solving basic trigonometric equations
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danwalker

Solving basic trigonometric equations

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A complete lesson on solving equations of the form sinx = a, asinx = b and asinx+b=0 (or with cos or tan) in the range 0 to 360 degrees. Designed to come after pupils have spent time looking at the functions of sine, cosine and tangent, so that they are familiar with the symmetry properties of these functions. See my other resources for lessons on these precursors. I made this to use with my further maths gcse group, but could be used with A-level classes too. Activities included: Starter: A set of four questions, effectively equations but presented as visual graph problems, to remind pupils of the symmetry properties of sine and cosine and the fact that tangent repeats every 180 degrees. Main: An example to transition from a visual problem to a formal, worded problem, and a reminder of the symmetry properties of sine and cosine. Five examples of solving trigonometric equations of increasing difficulty, including graphical representations to help pupils understand. A set of similar questions for pupils to do independently. I’ve made this into a worksheet where the graphs are included, to scaffold the work. Includes an extension task where pupils create equations with a required number of solutions. Plenary: A “spot the mistake” that addresses a few common misconceptions. Printable worksheets and answers provided. Please review f you buy as any feedback is appreciated!
The graphs of sine, cosine and tangent outside the range 0 to 360 degrees
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danwalker

The graphs of sine, cosine and tangent outside the range 0 to 360 degrees

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A complete lesson on the graphs of sine, cosine and tangent outside the range 0 to 360 degrees. I’ve also made complete lessons on these functions in the range 0 to 360 degrees. Designed to come after pupils have been taught about the ratios sine, cosine and tangent in the context of right-angled triangle trigonometry, and looked at the graphs of sine cosine and tangent in the range 0 to 360 degrees. This could also be used as a precursor to solving trigonometric equations in the further maths gcse or A-level. Activities included: Starter: A worksheet where pupils identify key coordinates on the graphs of sine and cosine from 0 to 360 degrees. Main: A reminder of the definitions of sine, cosine and tangent using the unit circle, with a prompt for pupils to discuss what happens outside the range 0 to 360 and a slide to make this clear. Three examples of using knowledge of the graphs to effectively solve a trigonometric equation. This isn’t formalised, but done more as a visual puzzle that pupils can answer using symmetry and the fact that the functions are periodic (see cover image). A worksheet with a set of similar questions, followed by a related extension task. Plenary: A brief summary about sound waves and how pitch and volume is determined. Printable worksheets and answers included. Please review if you buy as any feedback is appreciated!
Tangrams
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danwalker

Tangrams

(34)
Two sets of tangrams, the first making mathematical shapes, the second making more creative pictures. Includes outlines drawn to scale to assist weaker pupils.
Vectors
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danwalker

Vectors

(32)
A powerpoint with a series of lessons on GCSE vectors, with examples, activities and finally exam questions. Includes a few resources adapted from TES user payphone and another from jensilvermath.com.
A* GCSE maths paper
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danwalker

A* GCSE maths paper

(95)
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
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danwalker

Ratio robberies

(47)
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.
Pythagoras puzzle
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danwalker

Pythagoras puzzle

(46)
Basically colouring by numbers, but with questions on Pythagoras' theorem. Actually created by one of my pupils!
Standard form collect a joke
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danwalker

Standard form collect a joke

(25)
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.
Algebra Cluedo
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danwalker

Algebra Cluedo

(32)
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.
Percentage problems lock game
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danwalker

Percentage problems lock game

(21)
Worksheet where answers to questions are used to obtain a 3-digit code (which I set as the combination to a lockable money box containing a prize). Questions on a mixture of all the GCSE-standard percentage skills.
Percentage of amount maze
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danwalker

Percentage of amount maze

(26)
Maze consists of squares containing questions with answers, some of which are wrong. Pupils are only allowed to pass through squares containing correct answers. Extension - pupils design their own maze. I like to discuss how to make the maze harder by including classic misconceptions like divide by 5 to get 5%