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Circle theorem and algebra

Circle theorem and algebra

Few questions I wrote where students have to set up and solve equations, using their knowledge of circle theorems. Please note on the handwritten sheet, I made a mistake. One of the cyclic quadrilaterals and simultaneous equations does not work, the equations are parallel. I usually sell it as “I have made one deliberate mistake”
steele1989
Maths A Level New Spec Coordinate Geometry Notes and Examples

Maths A Level New Spec Coordinate Geometry Notes and Examples

These notes and examples are designed for the delivery of the new A Level Maths specification. You will receive an editable Word document that can be issued to students with gaps for them to fill in the solutions to the examples and make further notes. Full solutions to the examples are provided for the teacher in the form of a PDF document. This could be made available to students if they miss a lesson, reducing teacher workload. Each topic is available as a separate purchase, or you can download the entire set covering all the the Year 1 pure maths content.
Omega
Fully resourced lesson on geometric patterns is Islamic Art

Fully resourced lesson on geometric patterns is Islamic Art

Most suitable for key stage 3. Looks at geometry in Islamic Art. Students then create their designs using either compasses (higher groups) or isometric/square grids (may be better with lower groups). Probably good for end of module/term lesson Resources in the lesson gathered from all over the place, but thought it would be useful to have in one place as a single lesson.
alicecreswick
GCSE 9-1 Geometry Questions (Bundle)

GCSE 9-1 Geometry Questions (Bundle)

These carefully selected compilations of exam questions have fully-worked solutions designed for students to go through at home, saving valuable time in class. Click 👉 tes.com/…/Exam Question Bundles… to download the other four bundles.<hr>I usually print these questions as an A5 booklet and issue them in class or give them out as a homework. I also make them available for a student who wants to do focused independent study on a topic.<hr>👍If you like this resource, then please rate it and/or leave a comment💬. If the rate-resource button on this page doesn’t work, then go to your ratings page by clicking 👉 www.tes.com/…/rate-resources…
Maths4Everyone
Circlies

Circlies

Lesson 1 - Drawing circles with a compass. Radius and diameter Lesson 2 - Circumference and discovering Pi Lesson 3 - Estimating the area and using Pi to find the area Perfect for an intro to circles as it gets the students to discover and discuss their findings.
tomprotheroe92
Radius diameter and drawing a circle

Radius diameter and drawing a circle

Good intro lesson for circles. Introducing the concepts of radius and diameter and allowing them to see other things such as chords and segments. Lesson also goes through how to draw a circle using a compass.
tomprotheroe92
5 Worksheets on the Circle Theorems

5 Worksheets on the Circle Theorems

5 Worksheets covering all the circle theorems - around 50 questions in total including answers Circle Theorems 1 is 10 questions on the angle at the centre and also the same segment Circle Theorems 2 is 10 questions on angles in a semicircle and a cyclic quadrilateral Circle Theorems 3 is 6 questions on radius / tangent and 2 tangents from one point Circle Theorems 4 is 6 questions on the Alternate Segment Theorem Circle Theorems 5 is 20 questions on all the theorems None of these questions are ridiculously complex as you get in textbooks and they are extremely well drawn though not to scale.
happymathematician
Roll-a-topic GCSE foundation Geometry Revision

Roll-a-topic GCSE foundation Geometry Revision

A revision activity that can be used for KS3 or foundation GCSE pupils. Can be implemented in lots of ways. I ask pupils to get into pairs, take turns rolling two dice to form a co-ordinate and attempt to solve the corresponding question. Pupil put their initials on problems they have solved and after 30-45 minutes stop and count who has solved the most. Very engaging for year 10 and 11 foundation GCSE pupils. If you use this resource please leave a review! :)
prescott72
Areas of Sectors and Segments

Areas of Sectors and Segments

A worksheet with plenty of areas of sectors and segments questions for students to try. Numerical answers are at the bottom. Let me know if you like it.
RAGMaths
Circle theorems lesson 8

Circle theorems lesson 8

A complete lesson on the theorem that a perpendicular bisector of a chord passes through the centre of a circle. Assumes pupils can already use the theorems that: The angle at the centre is twice the angle at the circumference The angle in a semicircle is 90 degrees Angles in the same same segment are equal .Opposite angles in a cyclic quadrilateral sum to 180 degrees A tangent is perpendicular to a radius Angles in alternate segments are equal Tangents from a point are equal so that more varied questions can be asked. Please see my other resources for lessons on these theorems. Activities included: Starter: An animation reminding pupils about perpendicular bisectors, with the intention being that they would then practice this a few times with ruler and compass. Main: Instructions for pupils to investigate the theorem, by drawing a circle, chord and then bisecting the chord. Slides to clarify the ‘two-directional’ nature of the theorem. Examples of missing angle or length problems using the theorem (plus another theorem, usually) A similar set of eight questions for pupils to consolidate. An extension prompt for pupils to use the theorem to locate the exact centre of a given circle. Plenary: An animation of the proof without words, the intention being that pupils try to describe the steps. Printable worksheets and answers included. Please review if you buy, as any feedback is appreciated!
danwalker
Circle theorems lesson 7

Circle theorems lesson 7

A complete lesson on the theorem that tangents from a point are equal. Assumes pupils can already use the theorems that: The angle at the centre is twice the angle at the circumference The angle in a semicircle is 90 degrees Angles in the same same segment are equal .Opposite angles in a cyclic quadrilateral sum to 180 degrees A tangent is perpendicular to a radius Angles in alternate segments are equal so that more varied questions can be asked. Please see my other resources for lessons on these theorems. Activities included: Starter: Instructions for pupils to discover the theorem, by drawing tangents and measuring. Main: Slides to clarify why this theorem usually involves isosceles triangles. Related examples, finding missing angles. A set of eight questions using the theorem (and usually another theorem or angle fact). Two very sneaky extension questions. Plenary: An animation of the proof without words, the intention being that pupils try to describe the steps. Printable worksheets and answers included. Please review if you buy, as any feedback is appreciated!
danwalker
Circle theorems lesson 6

Circle theorems lesson 6

A complete lesson on the alternate segment theorem. Assumes pupils can already use the theorems that: The angle at the centre is twice the angle at the circumference The angle in a semicircle is 90 degrees Angles in the same same segment are equal .Opposite angles in a cyclic quadrilateral sum to 180 degrees A tangent is perpendicular to a radius so that more varied questions can be asked. Please see my other resources for lessons on these theorems. Activities included: Starter: Some basic questions to check pupils know what the word subtend means. Main: Animated slides to define what an alternate segment is. An example where the angle in the alternate segment is found without reference to the theorem (see cover image), followed by three similar questions for pupils to try. I’ve done this because if pupils can follow these steps, they can prove the theorem. However this element of the lesson could be bypassed or used later, depending on the class. Multiple choice questions where pupils simply have to identify which angles match as a result of the theorem. In my experience, they always struggle to identify the correct angle, so these questions really help. Seven examples of finding missing angles using the theorem (plus a second theorem for most of them). A set of eight similar problems for pupils to consolidate. An extension with two variations -an angle chase of sorts. Plenary: An animation of the proof without words, the intention being that pupils try to describe the steps. Printable worksheets and answers included. Please review if you buy, as any feedback is appreciated.
danwalker
Circle theorems lesson 5

Circle theorems lesson 5

A complete lesson on the theorem that a tangent is perpendicular to a radius. Assumes pupils can already use the theorems that: The angle at the centre is twice the angle at the circumference The angle in a semicircle is 90 degrees Angles in the same same segment are equal .Opposite angles in a cyclic quadrilateral sum to 180 degrees so that more varied questions can be asked. Please see my other resources for lessons on these theorems. Activities included: Starter: Some basic recap questions on theorems 1 to 4 Main: Instructions for pupils to discover the rule, by drawing tangents and measuring the angle to the centre. A set of six examples, mostly using more than one theorem. A set of eight similar questions for pupils to consolidate. A prompt for pupils to create their own questions, as an extension. Plenary: A proof by contradiction of the theorem. Printable worksheets and answers included. Please do review if you buy, as any feedback is greatly appreciated!
danwalker
Circle theorems lesson 4

Circle theorems lesson 4

A complete lesson on the theorem that opposite angles in a cyclic quadrilateral sum to 180 degrees. Assumes that pupils have already met the theorems that the angle at the centre is twice the angle at the circumference, the angle in a semicircle is 90, and angles in the same segment are equal. See my other resources for lessons on these theorems. Activities included: Starter: Some basics recap questions on the theorems already covered. Main: An animation to define a cyclic quadrilateral, followed by a quick question for pupils, where they decide whether or not diagrams contain cyclic quadrilaterals. An example where the angle at the centre theorem is used to find an opposite angle in a cyclic quadrilateral, followed by a set of three similar questions for pupils to do. They are then guided to observe that the opposite angles sum to 180 degrees. A quick proof using a very similar method to the one pupils have just used. A set of 8 examples that could be used as questions for pupils to try and discuss. These have a progression in difficulty, with the later ones incorporating other angle rules. I’ve also thrown in a few non-examples. A worksheet of similar questions for pupils to consolidate, followed by a second worksheet with a slightly different style of question, where pupils work out if given quadrilaterals are cyclic. A related extension task, where pupils try to decide if certain shapes are always, sometimes or never cyclic. Plenary: A slide showing all four theorems so far, and a chance for pupils to reflect on these and see how the angle at the centre theorem can be used to prove all of the rest. Printable worksheets and answers included. Please review if you buy as any feedback is appreciated!
danwalker
Circle theorems lesson 3

Circle theorems lesson 3

A complete lesson on the theorem that angles in the same segment are equal. I always teach the theorem that the angle at the centre is twice the angle at the circumference first (see my other resources for a lesson on that theorem), as it can be used to easily prove the same segment theorem. Activities included: Starter: Some basic questions on the theorems that the angle at the centre is twice the angle at the circumference, and that the angle in a semi-circle is 90 degrees, to check pupils remember them. Main: Slides to show what a chord, major segment and minor segment are, and to show what it means to say that two angles are in the same segment. This is followed up by instructions for pupils to construct the usual diagram for this theorem, to further consolidate their understanding of the terminology and get them to investigate what happens to the angle. A ‘no words’ proof of the theorem, using the theorem that the angle at the centre is twice the angle at the circumference. Missing angle examples of the theorem, that could be used as questions for pupils to try. These include more interesting variations that incorporate other angle rules. A set of similar questions with a progression in difficulty, for pupils to consolidate. Two extension questions. Plenary: A final set of six diagrams, where pupils have to decide if two angles match, either because of the theorem learnt in the lesson or because of another angle rule. Printable worksheets and answers included. Please do review if you buy as any feedback is greatly appreciated!
danwalker
Circle theorems lesson 2

Circle theorems lesson 2

A complete lesson on the theorem that the angle in a semicircle is 90 degrees. I always teach the theorem that the angle at the centre is twice the angle at the circumference first (see my other resources for a lesson on that theorem), as it can be used to easily prove the semicircle theorem. Activities included: Starter: Some basic questions on the theorem that the angle at the centre is twice the angle at the circumference, to check pupils remember it. Main: Examples and non-examples of the semicircle theorem, that could be used as questions for pupils to try. These include more interesting variations like using Pythagoras’ theorem or incorporating other angle rules. A set of questions with a progression in difficulty. These deliberately include a few questions that can’t be done, to focus pupils’ attention on the key features of diagrams. An extension task prompt for pupils to create their own questions using the two theorems already encountered. Plenary: Three discussion questions to promote deeper thinking, the first looking at alternative methods for one of the questions from the worksheet, the next considering whether a given line is a diameter, the third considering whether given diagrams show an acute, 90 degree or obtuse angle. Printable worksheets and answers included. Please do review if you buy as any feedback is greatly appreciated!
danwalker
Year 6 Circles Summer Block 3 Lesson Pack

Year 6 Circles Summer Block 3 Lesson Pack

This Year 6 Circles lesson pack includes a teaching PowerPoint and differentiated varied fluency, and reasoning problem solving questions. The varied fluency resource is differentiated in three ways and includes a selection of different questions types. The reasoning and problem solving resource is differentiated in three ways and includes one reasoning and two problem solving question types. You can find more resources which follow the same small steps White Rose Maths Guidance here.
ClassroomSecrets
Geometry Project

Geometry Project

This is a geometry project for you to teach your students. This really fits in with when you are studying geometry. This project is best used as homework as this is how the booklet has been structured. Feel free to edit in any way you want to. Also as some of instructions in the booklet might not fit your teaching schedule you may wish to edit out those parts. This project is designed for Ks3 students in about a middle set. It is a great homework activity and can last for up to 4/5 weeks if extended.Also i have called it a Term 5 Booklet but please edit this so that it fits what term you are doing it in. Please leave any comments in the comments box so i know how it was or how to improve it.
joggold46
Area and Circumference of Circle - (very) Simple, Scaffolded, Mixed Exercise + ANSWERS

Area and Circumference of Circle - (very) Simple, Scaffolded, Mixed Exercise + ANSWERS

Students have to show their working out for both the area and circumference of a circle from either the radius or the diameter. As an extension, put a circle, give the area or circumference and get students to work backwards. This is supposed to be an extremely simple exercise for pupils to have some practice with. My bottom set year 9s really struggled with the difference between being given the radius or the diameter. Feel free to adapt in any way. Let me know how it goes.
jamesclegg
Carl Gauss Birthday Challenge

Carl Gauss Birthday Challenge

The activity contains 10 sections of questions based around life of one of the greatest mathematicians. Students will get an opportunity to perform calculations on numbers linked to Gauss’s life, spot patterns with numbers and make connections as well as broaden their horizons by answering questions from other academic disciplines.
mathstakeoff
Circle theorems lesson 1

Circle theorems lesson 1

A complete lesson on the theorem that the angle at the centre is twice the angle at the circumference. For me, this is definitely the first theorem to teach as it can be derived using ideas pupils have already covered. and then used to derive some of the other theorems. I will shortly be uploading lessons for the other theorems. Activities included: Starter: A few basic questions to check pupils can find missing angles in triangles. Main: A short discovery activity where pupils split the classic diagram for this theorem into isosceles triangles (see cover image). If you think this could overload pupils, it could be skipped, although I think if they can’t cope with this activity, they’re not ready for circle theorems! A link to the mathspad free tool for this topic. I hope mathspad don’t mind me putting this link - I will remove it if they do. A large set of mini-whiteboard questions for pupils to try. These have been designed with a variation element as well as non-examples, to really make sure pupils think about the features of the diagrams. A worksheet for pupils to consolidate independently, with two possible extension tasks: (1) pupils creating their own examples and non-examples, (2) pupils attempting a proof of the theorem. Plenary: A final set of six diagrams, where pupils have to decide if the theorem applies. Printable worksheets and answers included. Please review if you buy as any feedback is appreciated!
danwalker
Maths: Lexicology Across the Curriculum - Bingo.

Maths: Lexicology Across the Curriculum - Bingo.

There are eight different bingo cards in this resource. I do not call out the affixes (prefixes and suffixes), I elicit the name of the affix through a series of concept questions. This is a great resource to improve knowledge and understanding of prefixes and suffixes which will ultimately develop a Mathematical Lexicon. Bingo as a ten minute starter creates a fantastic learning environment. For more resources visit my website www.lexicologyforreading.co.uk
lexicologyforreading
Compound Area with Circles - Problem Solving

Compound Area with Circles - Problem Solving

This is a lesson developing on from area and circumference of circles, allowing students to apply the skills onto more complex shapes and incorporate into a problem solving question. Answers are on slides, as well as some examples and the complex problem at the end has a step by step. This is aimed at upper middle/higher ability students
AcingMaths
Cluedo - Shape

Cluedo - Shape

Adapted resource from @danwalker (https://www.tes.com/teaching-resource/algebra-cluedo-6339269) Revision of Foundation topics based on shape - Perimeter, area, volume, surface area, circles, plans and elevations along with some function skills questions
lj9g08
Formula Revision Foundation

Formula Revision Foundation

A set of 6 simple formula recall tests. Foundation level. With answer slides. Along with these I made sets of cards with 4 questions on to practice using the formulae. I laminated these and let the pupils choose which one to do. Answers to these are also on the Formula Test and Answers files. The Formula Test And Answers notebook file has links to the various answer slides along with links to the original question cards. Question cards A to F are a mix of stuff. Question cards G to J are my first attempt at making some SSDD questions. I’ve been adding to it as I go along, so there may be more to come. I’ve exported the main Formula Test And Answers to pdf for those who don’t have access to Smart notebook - links don’t work on that though. If you see any errors please feel free to say in the comments.
simonfa
NEW AS Quadratics,Circles & Discriminant

NEW AS Quadratics,Circles & Discriminant

A resource of questions which could be used as an assessment, HW or revision covering the topics; quadratic inequalities, finding and using the equations of circles, finding points intersection of lines with quadratics/circles and solving problems involving the use of the discriminant. Also contains a problem-solving challenge and has worked solutions attached. Perfectly suited for the New AS specification.
karloprimo
Four fantastic investigations for higher end thinking.

Four fantastic investigations for higher end thinking.

This was done on my trip to the Science Museum. We took four key shots and have come up with four investigations in relation to these photos. They start very easy and become rather tricky. These are brilliant for those students who really need to be pushed at the higher end!
DaysCount
Volume and surface area homework

Volume and surface area homework

Homework includes: Title, name, due date Questions Challenge questions Problem solver Exam style questions -Solutions for all Please review and follow For more resources: https://www.tes.com/teaching-resources/shop/osmith25
osmith25
Geometry Skills Color By Number Bundle 1: 10 Essential Skills

Geometry Skills Color By Number Bundle 1: 10 Essential Skills

With these activities, students will enjoy practicing their geometry skills as they have fun creating beautiful, colorful mandalas! These activities are an excellent choice for sub plans, enrichment/reinforcement, early finishers, and extra practice with some fun. These engaging activities are especially useful for end-of-year practice, spiral review, and motivated practice when students are exhausted from standardized testing or mentally “checked out” before a long break! Teachers and students alike enjoy motivating activities, so engage your students today with these fun activities! These 10 activities include: Circumference and Areas of Circles Classifying Angles Classifying Quadrilaterals Inequalities in One Triangle Inverse Trigonometric Ratios Isosceles and Equilateral Triangles Properties of Trapezoids Similar Triangles Triangle Inequality Theorem Trigonometric Ratios Coloring is a great way to get your students motivated and interested in practicing and reviewing their geometry skills! In addition, these activities are great for emergency sub plans, enrichment, early finishers, skills reinforcement, and extra credit. As an added bonus, the final products make fabulous classroom decor! With a savings of over 40% if the activities were purchased separately, this bundle is a win-win for everyone! Thanks and enjoy your new product!
charlotte_james615
Geometry bundle! (Circles, angles, perimeter, area, Pythagoras, similar shapes, transformations, volume and surface area)

Geometry bundle! (Circles, angles, perimeter, area, Pythagoras, similar shapes, transformations, volume and surface area)

All my geometry resources in one handy place! £20 when sold separately, but only £16 when bought as a bundle! 20% saving! Please feel to browse the individual resources in my shop for more info on each. The bundle includes ready to go lessons, with: Starters, Animated examples and Differentiated questions with answers! Bundle includes lessons on: Circumference of circles, Area of circles, Finding arc length, Area of sectors, Calculating angles, Angles in triangles, Angles in quadrilaterals, Angles on parallel lines, Converting between units of measure, Perimeter and area, Area and perimeter of triangles, Area of parallelograms and trapeziums, Introduction into Pythagoras - finding t length of a hypotenuse, Finding the length of a shorter side in a right angled triangle using Pythagoras, To use Pythagoras in 3D shapes, Recognising similar shapes, Finding the area of similar shapes, Finding volume of similar shapes, Reflection, Translation, Rotation, Consolidation of transformations, Volume and surface area of cuboids, Volume of cones, pyramids and spheres, Volume of other shapes, Surface area of prisms, Surface area of cylinders, Surface area of cones and spheres, Surface area of cones using Pythagoras! All these lessons will keep you going for weeks! I really hope this bundle helps your planning and work/life balance. Thanks =]
stephigittins
Area, perimeter and circumference homework

Area, perimeter and circumference homework

Homework includes: Title, name, due date Questions Challenge questions Problem solver Exam style questions -Solutions for all Please review and follow For more resources: https://www.tes.com/teaching-resources/shop/osmith25
osmith25
Circles Matching Task - Area, Perimeter, Circumference

Circles Matching Task - Area, Perimeter, Circumference

A matching task designed to develop fluency in finding the area and perimeter of circles. There are three cards that do not match the rest of the cards. An extension is to make the cards that fit these distracters; in some cases this will require starting with the circumference or the area and working backwards. Answers are provided for the matching pairs. The print out for the matching task is pre-jumbled so you do not need to worry about cutting them out prior to the lesson.
scottyknowles18
7th Grade Math Circle Circumference and Area Guided Notes

7th Grade Math Circle Circumference and Area Guided Notes

These circle circumference and area guided notes focus on calculating and making sense of circumference and area of circles. Students will calculate in both exact and approximate form. They will informally derive the area formula from the circumference. Students writing sloppy notes? Improve their engagement and understanding of circle circumference and area with these guided notes. No prep, just print and go. These guided notes work great as an introduction, reinforcement or review of the material. Formatted for back-to-back printing with page numbers. Teacher can create a packet for student organization. Contents • 1 title page • 5 pages of guided notes • 1 page of practice (9 problems) • 1 lined page for extra notes • Complete answer key
micsigaran