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Enriching mathematics for all learners

A free-to-use collection of mathematics activities, lessons and problems designed to nurture curious, resourceful and confident learners of mathematics. Produced by The University of Cambridge.

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The Nrich Maths Project Cambridge,England. Mathematics resources for children,parents and teachers to enrich learning. Problems,children's solutions,interactivities,games,articles.

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Unleash learning with LbQ maths resources

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LbQ maths is a teaching app that harnesses the power of continuous formative assessment and immediate feedback in maths classrooms.

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I'm Sarah Carter, a high school math teacher who passionately believes math equals love. Through this blog, I'm on a mission to equip other teachers to create inviting and engaging classrooms where learning mathematics is fun.

I currently teach AP Calculus AB, Pre-Calculus, and Statistics at Coweta High School in Coweta, OK. Over my eleven-year teaching career, I have taught both math and science at the secondary level. If you want to know more about my career in education, check out my About Me page.

THANKSGIVING MATH ACTIVITIES

MOST POPULAR ACTIVITIES

MOST RECENT BLOG POSTS

If you're looking for a traditional blog reading experience, I recommend checking out my BLOG page. You can find it by following the previous link or by clicking on the Blog Tab at the top of the page. This page will list all of my blog posts (over 1300 of them!) in chronological order with the most recent blog post first.

This blog started as a way for me to make sense of my student teaching experiences in the middle school and high school math classroom. It's evolved over the past decade to become a way to share free resources for engaging and fun math activities with teachers around the world.

Looking for resources for a specific math teaching topic? I recommend navigating the blog using the tabs at the top of the page or by using the search box. You can easily find and read all of my posts about polynomials, puzzles, or posters this way.

FREE PRINTABLE MATH RESOURCES

PRINTABLE MATH PUZZLES

I am a passionate proponent of incorporating puzzles into the mathematics classroom. Over the past five years, I have compiled a collection of hundreds of free printable puzzles that have been used in math classrooms around the world with students ranging from elementary school to high school as well as adults! You can find out more about how to access these free puzzles on my puzzles page!

FREE PRINTABLE MATH POSTERS AND CLASSROOM DECORATIONS

My high school math classroom is my happy place, and I love decorating it to display my love of math to my students. I have created many math posters over the years that I am sharing here on my blog. I recommend checking out my entire math poster collection - ten years' worth of math posters!

FUN AND CREATIVE MATH PRACTICE ACTIVITIES

I love creating fun, interactive, and hands-on activities. Be sure to check out some of these activities while you are here!

GAMES

Looking to infuse some fun into your math classroom? Check out these free printable games! You and your students are sure to have a ton of fun!

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I'm Sarah Carter, a high school math teacher who passionately believes math equals love. Through this blog, I'm on a mission to equip other teachers to create

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Try one of our mathematical crafts!

Below you will find all the Maths Craft handouts from our events, and more. You are free to use our resources so long as you don't change anything or commercialise them. For more details, please see our licence.

Menger Sponge

Fractals are mathematical objects built from repeated copies of themselves. Create a fractal sculpture from business cards. Start by making single cubes, and then assemble them into a sculpture representing a Menger Sponge. Then use our cladding to make it look like a higher-level Menger Sponge. Maths Craft have also made some instructional videos on building a Menger sponge.

Are you a New Zealand maths teacher?

Want to build a Menger sponge in your maths class? Order your own Maths Craft in a Box, an entirely free, self-contained box dedicated to exploring the fascinating world of fractals in the classroom.

Möbius Strips

A Möbius strip is a surprising object; it's a surface with only one edge and one side. Start with our instructions for making and investigating paper Möbius strips. You can even make entwined Möbius hearts.

Licence

All Maths Craft New Zealand handouts are available under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International Licence. The Maths Craft New Zealand handouts are free to be used at home or in a classroom. By using these handouts, you agree not to use the Maths Craft New Zealand branding for your own products or events, nor to package or distribute our material in any format, even if you do so for free. If you're not sure what the license and agreement allows, please get in touch; we'd love to hear from you.

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Below you will find all the Maths Craft handouts from our events, and more. You are free to use our resources so long as you don't change anything or commercialise them. For more details, please see our licence. Fractals are mathematical objects built from repeated copies of themselves.

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TeacherMatic is your personal assistant helping you to be more efficient and productive. The AI engine takes care of all the mundane tasks, allowing you to focus on what really matters - teaching and learning, and building positive meaningful relationships with your learners

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During the power hour, you will engage in a revision plan specifically designed to address all tiered skills in preparation for the final exam.

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A collection of GCSE Statistics and KS3 Maths Resources.

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Here you will find resources that are a mix of topics that can support all areas of pupils knowledge and understanding.

AQA Practice set 4 Foundation Goal Free problems - The AQA practice set 4 Foundation papers for the 9-1 GCSE adapted by @MrODonovan

Edexcel Specimen Papers 1 Goal Free - The complete set of the Edexcel Specimen paper set 1 adapted to be goal free (as best as is possible!)

Mixed Foundation Problems - A set of 33 Foundation problems adapted to be goal free. Thanks to Mark Greenaway (@suffolkmaths)

Mixed Higher Problems - A set of 43 Higher problems adapted to be goal free. Thanks to Mark Greenaway (@suffolkmaths)

Mixed Exam style questions - A set of 65 questions, some targeted specifically at Higher topics. The space for pupils to create questions and answers has the choice of being structured (space for 4 questions and answers) or unstructured (completely open space). Thanks to Miss A Banks (@MissBanksMaths)

EMaths Adapted KS2 Reasoning Paper 1 - A Key Stage 2 reasoning paper adapted to be goal free. With thanks to Mark McCourt (@Emaths) for allowing me to use his papers.

KS2 Adapted problems - A selection of 20 Key Stage 2 problems created by Keegan Toshack @Keobrien100

KS1 Adapted problems - A selection of Key Stage 1 problems created by Keegan Toshack @Keobrien100

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Welcome to Goal Free Problems, a place to find and share goal free problems for use with pupils in class and revision

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Mathematics resources and support for teachers along with revision resources for students. Covers all of GCSE and A-Level maths.

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What's the Point of Maths? - with Nira Chamberlain

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Welcome to Tips for Teachers - the site that helps you supercharge your teaching one idea at a time.

There are over 100 tips below, each available in audio and video.

But the fun does not stop there. You can also:

1. Order my Tips for Teachers book

2. Access on-demand or face-to-face Tips for Teachers CPD

3. Sign up for the free Tips for Teachers newsletter

4. Become a Patreon to get lots of lovely goodies

I really hope you find this site useful

Tips for Teachers - Top 5s

These collections of tips are all taken from my Tips for Teachers book

Habits and routines

1. Build habits, not one-off things - Harry Fletcher-Wood - audio - video

2. Willpower is overrated - Peps McCrea - video

3. Consistency before challenge - Peps McCrea - video

4. Be aware of the Valley of Latent Potential - Craig Barton - video

5. Don't just describe a routine, justify it - Craig Barton - video

6. Don't just introduce a routine, retrieve it - Craig Barton - video

7. Teach students what to do when they are stuck - Tom Bennett - audio - video

8. Beware the distraction addiction - Jamie Thom - audio - video

9. Interruptions leave a wake - Peps McCrea - video

Behaviour and relationships

1. Validate introverts - Jamie Thom - audio - video

2. Three reflections on behaviour in schools - Ollie Lovell and Craig Barton - video

3. Teach behaviour lesson one - Femi Adeniran - audio - video

4. Use the school behaviour policy - Tom Bennett - audio - video

5. Use non-verbal gestures for better behaviour management - Mark Roberts - audio - video

6. Students need to know you are in charge of the classroom - Tom Bennett - audio - video

7. Be clear and follow through - Charlie Burkitt - audio - video

8. Think creatively when attempting to improve engagement/performance of boys - Jon Mumford - audio - video

9. Enjoy the kids' company - Charlie Burkitt - audio - video

10. To develop resilience you need both high challenge and high support - Bradley Busch - audio - video

11. Teach students how to behave in a supply or cover lesson - Tom Bennett - audio - video

12. Teach students how to have the right equipment - Tom Bennett - audio - video

13. Make detention work fit the crime - Dylan Wiliam - audio - video

14. Ban mobile phones - Bradley Busch - audio - video

15. Some behaviours are more important than others - Kieran Mackle - audio - video

The means of participation

Checking for understanding

1. Be aware of student bias - Sarah Donarski - audio - video

2. Three reasons students don't know the answer - Ollie Lovell and Craig Barton - video

3. Check for understanding - Ollie Lovell - audio - video

4. Always build from what they know - Sarah Cottingham - audio - video

5. Always check for understanding - Clare Sealy - audio - video

6. No hints before a check for understanding - Ollie Lovell + Craig Barton - video

7. Planning the checks for understanding - Craig Latimir - video

8. Ask a question at the end of every lesson that every student should be able to get right - Daisy Christodoulou - audio - video

9. Planning the end of a lesson - Craig Latimir - video

10. Consider lengthening wait times to maximise retrieval - Bradley Busch - audio - video

11. How to ensure questioning involves all pupils - Jade Pearce - audio - video

12. The Tick Trick - Ollie Lovell and Craig Barton - video

13. Ask students to make a pre-topic mind map - Alex Quigley - audio - video

14. Use talk cubes to encourage students to contribute - Emma Turner - audio - video

15. Start with whoever got 8 out of 10 - Tom Sherrington - audio - video

16. Use Post-it notes to find out what they don't understand - Mark Roberts - audio - video

17. Play "Just a minute!" - Alex Quigley - audio - video

18. Provide explicit scaffolds for verbal responses - Tom Sherrington - audio - video

19. Pick the student least likely to know - Sammy Kempner - audio - video

20. Foster cross-class accountability - Tom Sherrington - audio - video

21. Trick your students to test if they really understand - Sammy Kempner - audio - video

22. Depressurise learning - Chris Such - audio - video

Responsive teaching

1. Don't forget the "respond" part of responsive teaching - Jo Morgan - audio - video

2. Planning responsive teaching - Craig Latimir - video

3. Modify your lessons as you go - Jake Gordon - audio - video

4. Responsive teaching: what to do when some students understand, and some don't - Craig Barton - video

5. Don't let "Don't know" be the end of the conversation - Dylan Wiliam - audio - video

6. End every conversation with the student saying something smart - Michael Pershan - audio - video

7. Rephrase to amaze - Mark Roberts - audio - video

8. Diagnostic Questions - the perfect exit ticket? - Craig Barton - video

9. How to design good multiple-choice questions - Kate Jones - audio - video

10. Share photos of students' work - Jake Gordon - audio - video

Planning lessons

1. The crucial role of curriculum - Ollie Lovell + Craig Barton - video

2. Lesson planning mistakes - Craig Latimir - video

3. Lesson planning principles - Craig Latimir - video

4. The first thing to think about - Craig Latimir - video

5. Make question planning part of lesson planning - Dylan Wiliam - audio - video

6. Focus on explanations, not resources - Femi Adeniran - audio - video

7. Plan sequences not lessons - Jemma Sherwood - audio - video

8. Backwards plan. ALWAYS backwards plan! - Ollie Lovell - audio - video

9. Be super clear about what you want children to learn - Clare Sealy - audio - video

10. Do less, but better - Harry Fletcher-Wood - audio - video

11. We should all be focussing on doing fewer things and greater depth - Mary Myatt - audio - video

12. Review every lesson plan in terms of what the student is thinking about - Daisy Christodoulou - audio - video

13. Plan for error - Emma Turner - audio - video

14. Take a low effort, high impact approach to task and question design - Kate Jones - audio - video

15. Teach what you mean to teach - Jemma Sherwood - audio - video

16. Focus on the concepts and the Big Ideas in our curriculum - Mary Myatt - audio - video

17. Learning doesn't start in Year 7 - Craig Latimir - audio - video

Examples and modelling

1. Beware the curse of knowledge - Sarah Cottingham - audio - video

2. Set out the big picture - Tom Sherrington - audio - video

3. We know more and remember more when we've heard it in a story - Mary Myatt - audio - video

4. Planning the exposition - Craig Latimir - video

5. Planning the modelling - Craig Latimir - video

6. Mind your modes - Peps McCrea - video

7. Question, don't tell - Sammy Kempner - audio - video

8. Use explicit instruction for novice learners - Jade Pearce - audio - video

9. Model techniques live - Jo Morgan - audio - video

10. Try teaching from anywhere in the room - Jake Gordon - audio - video

11. Begin your explanations as a series of questions that everyone can answer - Michael Pershan - audio - video

12. Use, where possible, dialogic teaching - Sarah Donarski - audio - video

13. Encourage students to say "stop!" if they are confused during an explanation - Emma Turner - audio - video

14. Avoid the Split-Attention Effect during worked examples - Craig Barton - video

15. What you say matters - Jemma Sherwood - audio - video

16. What you don't say matters - Jemma Sherwood - audio - video

17. Don't ask students to listen and read simultaneously - Craig Barton - video

18. Explicitly teach the skills an expert in your domain uses - Craig Latimir - audio - video

19. Use visual aids, including props and online tools to bring explanations alive - Jo Morgan - audio - video

20. Reduce clutter from everything students see and hear - Jake Gordon - audio - video

21. Beware of seductive details - Craig Barton - video

22. Use examples, not definitions, when teaching & assessing - Daisy Christodoulou - audio - video

23. Get used to asking "what if" after explaining something - Michael Pershan - audio - video

24. Provoke curiosity in our students - Mary Myatt - audio - video

25. Use related examples and non-examples to explain a concept - Craig Barton - video

26. Further thoughts on the Myth of Copying Things Down - Ollie Lovell and Craig Barton - video

27. Hone your public speaking - Jamie Thom - audio - video

28. Feign enthusiasm when necessary - Chris Such - audio - video

Student practice

1. Planning the practice phase - Craig Latimir - video

2. Teach in small chunks and fool kids into doing lots of work initially - Femi Adeniran - audio - video

3. Make sure students know whether they are right or wrong, and don't wait until it's too late - Jo Morgan - audio - video

4. Provide answers so pupils can check their work in real-time - Femi Adeniran - audio - video

5. Set occasional open-response tasks - Tom Sherrington - audio - video

6. Two frameworks for learner-generated examples - Craig Barton - video

7. Use SSDD Problems to improve students' practice - Craig Barton - video

8. How to help students avoid "silly" mistakes - Craig Barton - video

Memory and retrieval

Data and assessment

1. To make good use of data, compare to other subjects - Adam Boxer - audio - video

2. Know how to effectively assess - Sarah Donarski - audio - video

3. Stop talking about grades - Mark Roberts - audio - video

Homework

1. To make homework more effective, integrate it with classwork - Adam Boxer - audio - video

2. My favourite homework activity - Craig Barton - video

3. Rebrand homework as practice - David Goodwin - audio - video

Marking and feedback

Improving as a teacher

Observations and coaching

1. How to observe a lesson - Adam Boxer - audio - video

2. How to give a colleague feedback - Adam Boxer - audio - video

3. Diagnosis in coaching - Ollie Lovell and Craig Barton - video

4. Develop competing hypotheses when observing teaching and learning - Ollie Lovell and Craig Barton - video

Leadership and culture

Health and well-being

1. Maintain perspective - Harry Fletcher-Wood - audio - video

2. Remember the tortoise and the hare - Jamie Thom - audio - video

3. Tackle the negativity radio - Jamie Thom - audio - video

4. How to get better sleep - Ollie Lovell and Craig Barton - video

5. The secret to a happy life - Craig Latimir - audio - video

6. End the day on a positive - Ollie Lovell and Craig Barton - video

Maths, Maths, Maths!

1. Use the same questions, with different numbers - Sammy Kempner - audio - video

2. Use calculators with students from the earliest opportunity - Jo Morgan - audio - video

3. The power of a slideshow for teaching mathematics - Ollie Lovell and Craig Barton - video

4. Doing maths is not the same as teaching maths - Jemma Sherwood - audio - video

5. Practice, practice, practice...not until you can get it right but until you cannot get it wrong - Julia Smith - audio - video

6. It ain't what you do, it's the way that you do it...and that's what gets results - Julia Smith - audio - video

7. Fluency in the four operations is a cornerstone of developing mathematical understanding - Julia Smith - audio - video

8. How to deal with students who say they hate maths or are no good at maths - Julia Smith - audio - video

Reading, literacy and oracy

Micro-tips

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All the Tips for Teachers from the videos and podcasts in one place. Click on a tip to hear the podcast / watch the video!

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The EEF is an independent charity dedicated to breaking the link between family income and educational achievement.

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We believe in the power of maths to transform lives and nations. Access to that power should not depend on a child’s background.

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Maths, Why Bother? | MYPATH Careers Resources

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The ‘Maths, Why Bother?’ resource aims to help Maths teaching staff to show students the explicit links between the maths curriculum and the world of work.

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World's First Accelerated Learning Platform

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Trigonometry Revision

Trigonometry

Trigonometry is the study of triangles. In this topic, we're going to focus on three trigonometric functions that specifically concern right-angled triangles. They are: sine, cosine, and tangent, which get shortened to sin, cos, and tan in trigonometry questions.

Make sure you are happy with the following topics before moving onto trigonometry revision.

MME Premium Membership

Learn an entire GCSE course for maths, English and science on the most comprehensive online learning platform. With revision explainer videos & notes, practice questions, topic tests and full mock exams for each topic on every course, it's easy to Learn and Revise with the MME Learning Portal.

SOHCAHTOA

First we need to be able to label each side of a right angled triangle:

The hypotenuse is always the longest side; it is the one opposite the right-angle.

The opposite side is the side that is opposite to the angle.

The adjacent side is the side that is adjacent (next to) the angle.

\textcolor{purple}{\sin(x)}=\dfrac{\textcolor{red}{\text{opposite}}}{\textcolor{blue}{\text{hypotenuse}}}

\textcolor{purple}{\cos(x)}=\dfrac{\textcolor{limegreen}{\text{adjacent}}}{\textcolor{blue}{\text{hypotenuse}}}

\textcolor{purple}{\tan(x)}=\dfrac{\textcolor{red}{\text{opposite}}}{\textcolor{limegreen}{\text{adjacent}}}

If we let O be the opposite, A be the adjacent and H be the hypotenuse, then these are shortened to:

As a result, the acronym: SOHCAHTOA is helpful for remembering which sides go with which function.

Angles of Elevation and Depression

If you look towards something that is not at eye level, the angle your eyes make with the object is an angle of elevation / depression.

An angle of elevation is when you look upwards towards something.

An angle of depression is when you look downwards towards something.

These angles can be used to calculate the height and distance of objects.

Example: Bill is 30\text{ m} away from a church. The angle of elevation when he looks at the top of the church's spire is 45\degree. If Bill's 1.5\text{ m} above the ground, how tall is the church spire? eye level is

The side we want to work out is opposite from the angle we have. We also have the length of the adjacent side. This means that we want to use TOA, or \tan=\dfrac{\text{opposite}}{\text{adjacent}}

\tan(45)=\dfrac{h}{30} where h is the height we wish to calculate.

h=30\tan(45)

Now, we can use \tan(45)=1 to find that h=30\text{ m}

However, this is not the height of the spire, as this was calculated from Bill's eye level. So we have to add Bill's eye level to this to get the real height of the spire.

\text{Height}=30+1.5=31.5\text{ m}

Level 4-5 GCSE AQA Edexcel OCR WJEC

Example 1: Missing Length

Find the length of the side marked y to 1 dp.
[2 marks]
First of all we need to find which equation we need to use.

We have the hypotenuse \textcolor{blue}{H} = \textcolor{blue}{12} cm

We also have the adjacent side \textcolor{limegreen}{A} = \textcolor{limegreen}{y}

So, if \textcolor{limegreen}{A} and \textcolor{blue}{H} are the two sides we are working with, then it's the

'\textcolor{purple}{C}\textcolor{limegreen}{A}\textcolor{blue}{H}' part of SOHCAHTOA we need to use.

\textcolor{purple}{\cos(x)}=\dfrac{\textcolor{limegreen}{A}}{\textcolor{blue}{H}}

Substituting in the two sides and one angle, we get:

\textcolor{purple}{\cos(38°)} =\dfrac{\textcolor{limegreen}{y}}{\textcolor{blue}{12}}

Next, we need to solve the equation. Multiplying both sides by 12 gives us:

\textcolor{limegreen}{y}=\textcolor{blue}{12} \textcolor{purple}{\cos(38°)}

Putting this into our calculator we get:

\textcolor{limegreen}{y}=9.456129043...

\textcolor{limegreen}{y}=9.5 cm (1 dp)

Example 2: Missing Angle

Find the size of angle z to 2 sf.
[2 marks]
First of all we need to find which equation we need to use.

We have the opposite side = \textcolor{red}{5} mm

We also have the adjacent side = \textcolor{limegreen}{8} mm

As we are working with \textcolor{red}{O} and \textcolor{limegreen}{A}, then '\textcolor{purple}{T}\textcolor{red}{O}\textcolor{limegreen}{A}' is the part of SOHCAHTOA we will use:

\textcolor{purple}{\tan(z)}=\dfrac{\textcolor{red}{O}}{\textcolor{limegreen}{A}}

Substituting in the two known sides gives us:

\textcolor{purple}{\tan(z)}=\dfrac{\textcolor{red}{5}}{\textcolor{limegreen}{8}}

Now, like before we want to solve the equation to find our missing angle, z.

To solve this we need to use the inverse tan function \tan^{-1}.

What this means is that if we apply '\tan^{-1}' to both sides of the equation above, it will cancel out the tan. We get:

\textcolor{purple}{\tan(z)}=\dfrac{\textcolor{red}{5}}{\textcolor{limegreen}{8}}

z=\textcolor{purple}{\tan}^{-1}\left(\dfrac{\textcolor{red}{5}}{\textcolor{limegreen}{8}}\right)

z=32.00538321...

z=32\degree (2 sf)

This works the same way with \sin and \cos; you will need to use the \sin^{-1} and \cos^{-1}.

Example 3: Angles of Elevation and Depression

Jess looks downwards at a frisbee that has landed 4\text{ m} away from her feet. If Jess' eye level is 1.7\text{ m} above the ground, find the angle of depression.

Give your answer to one decimal place.
[2 marks]

We have the opposite and adjacent side lengths of the angle we want to find, so we need to use TOA or \tan=\dfrac{\text{opposite}}{\text{adjacent}}

\tan(x)=\dfrac{1.7}{4}

x=\tan^{-1}\left(\dfrac{1.7}{4}\right)

x=23.0\degree

Level 4-5 GCSE AQA Edexcel OCR WJEC

Trigonometry Example Questions

In this case, the two sides we're concerned with are the hypotenuse and the side adjacent to the angle given. Therefore, we want the 'CAH' part of 'SOH CAH TOA' where A=35,H=p, and the angle is 43\degree:

\cos(43°)=\dfrac{35}{p}

Next we need to solve for p. Multiplying both side by p to get:

p\times\cos(43°)=35

Then, as \cos(43°) is just a number, we can we can divide both sides by \cos(43°):

p=\dfrac{35}{\cos(43°)}

Finally, putting this into the calculator we get:

p=47.85646...

p=47.9 m (3 sf)

The two sides we're working with are the hypotenuse and the opposite side, therefore, we want the 'SOH' part of 'SOH CAH TOA', where O=13,H=15, and the angle is q°:

\sin(q)=\dfrac{13}{15}

To find q, we have to apply the inverse sine function to both sides. It cancels out the sin on the left-hand side and we get:

q=\sin^{-1}\left(\dfrac{13}{15}\right)

q=60.073565...

q=60.1\degree (1 dp).

According to SOH CAH TOA, the sin of w must be equal to the opposite side divided by the hypotenuse. The opposite side is given to us: 2, but the hypotenuse is not. Since we have a right-angled triangle, we can use Pythagoras to find the hypotenuse. If the hypotenuse is c, then a and b are both 2, so the equation a^2+b^2=c^2 becomes:

c^2=2^2+2^2=4+4=8

Square rooting both sides, we get:

c=\sqrt{8}=2\sqrt{2}

Now we have the hypotenuse, we can use 'SOH':

\sin(w)=\dfrac{2}{2\sqrt{2}}

Notice that there is a 2 on the top and bottom that can cancel:

\sin(w)=\dfrac{2}{2\sqrt{2}}=\dfrac{1}{\sqrt{2}}

In this case, the two sides we're working with are the hypotenuse, and the side opposite to the angle given. Therefore, we want the 'SOH' part of 'SOH CAH TOA' where O=CB,H=12, and the angle is 30\degree:

\sin(30°)=\dfrac{CB}{12}

Next we can solve this by multiplying both side by 12 to get:

12\sin(30°)=CB

Finally, putting this into the calculator we get:

CB=6.00 cm (3 sf)

The two sides we're working with are the adjacent and the opposite. Therefore, we want the 'TOA' part of 'SOH CAH TOA', where O=4,A=7, and the angle is x:

\tan(x)=\dfrac{4}{7}

To find x, we have to apply the inverse tangent function to both sides. It cancels out the tan on the left-hand side and we get:

x=\tan^{-1}\left(\dfrac{4}{7}\right)=29.7448813...

x=29.7° (1 dp).

We have an angle of 87\degree, its adjacent of 4\text{ m} and want to find the opposite, so we need to use TOA.

\tan(87\degree)=\dfrac{h}{4} where h is the height of the building.

h=\tan(87)\times4

Doing this on a calculator gives:

h=76.3\text{ m}

Trigonometry Worksheet and Example Questions

Trigonometry Drill Questions

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Trigonometry Worksheets, Questions and Revision

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Trigonometry questions and Soh Cah Toa revision worksheets can be found on this MME Maths Trigonometry revision page.

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Symbolab Math Calculator - Step by Step calculator

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Symbolab: equation search and math solver - solves algebra, trigonometry and calculus problems step by step

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Maths Games for KS2: designed by a teacher for teachers - Mathsframe

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Mathsframe has more than 200 interactive maths games and 300 maths worksheets and assessments linked to the new curriculum. All resources are designed by an experienced KS2 teacher. New games and worksheets are added regularly.

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Solving Linear Equations with Fractions Solving Linear Equations with Decimals Solving Linear Equations with Standard Form Solving Linear Equations

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Bring Your Notes to Life with the
AI Quiz Generator

Simply reading textbooks often isn't enough to solidify knowledge. Instead of just taking notes, transform your textbooks into interactive quizzes. Engage with your material, test your understanding, and retain information in a smarter, more effective way.

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A-Level questions by topic, videos, notes, past papers and more. For students studying Maths, Biology, Chemistry, Physics, Psychology or Law.

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This investigation explores using different shapes as the hands of the clock. What things occur as the the hands move.

On a clock the three hands - the second, minute and hour hands - are on the same axis. How often in a 24 hour day will the second hand be parallel to either of the two other hands?

During the third hour after midnight the hands on a clock point in the same direction (so one hand is over the top of the other). At what time, to the nearest second, does this happen?

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md angles polygons and geom proof - stage 3

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Angles Alien Attack

Defend the Earth from an alien invasion using your knowledge of angles. Choose to read them from the protractor or estimate them without a protractor.

Scan to open this game on a mobile device. Right-click to copy and paste it onto a homework sheet.

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Form Time Ideas - Tutor group activities

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Ideas and activities to keep your tutor group engaged during form time. A fresh set of activities is generated each time you visit.

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Flippity.net: Flashcards and Other Resources for Educators and Learners

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Create an interactive virtual breakout activity.

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NOLEJ is a decentralized skills platform powered by an AI engine, that automatically generates interactive courseware & global knowledge graph

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Flippity.net: Flashcards and Other Resources for Educators and Learners

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Create an interactive virtual breakout activity.

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Applets for illustrating concepts visually, generating backwards fading worked examples, and creating an unlimited amount of practice questions

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Simultaneous Equations | AQA GCSE Maths Questions & Answers 2022 (Medium)

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Revision notes on 'Multiplication (non-Calc)' for the AQA GCSE Maths exam. Designed by the expert teachers at Save My Exams.

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Numerous pages and resources in this blog relate to Algebra, additionally you can find any post including Algebra resources here.

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City Guesser - Can you guess what city you're in?

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City Guesser is a game that plops you into a random city and forces you to guess where you are at!

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Free resources so you can leverage AI in education with effective strategies, polices and ethical guidelines. Helping you create the future today in your school. AI for Education is yours to take and run with.

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Technology is changing the world, and it’s changing our schools and classrooms.It feels impossible to keep up with everything.You’re looking for

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Maths for Primary and Secondary

Resources for students and teachers

Access hundreds of quizzes and other interactive activities that will help you enjoy and improve your maths whether you are at school or at home. There are thousands of carefully designed questions to improve maths knowledge and help develop fluency in important maths skills. These activities, developed for ks1 up to GCSE, have been helping students to better their target grades for more than ten years.

You can access the activities for free, but if you sign up for an account activities will be grouped together by topic and your scores for the interactive games and quizzes will be saved so that you can keep track of your progress.

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Popular with both teachers and students, the questions in these free maths resources are carefully crafted and include the answers. They are designed to help students to take the first steps in each topic, then strengthen and extend their knowledge and skills. The resources include revision questions for KS2 SATs and GCSE.

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Generador de Crucigramas
Créateur de mots croisé

1. Enter your crossword words and clues in the form below OR choose a premade word list (just below the instructions box) OR use the Quick Add Box to create your crossword clues and answers with Artificial Intelligence (AI).

2. Click the large green "Make Crossword Puzzle" button near the bottom of the form to make your free custom puzzle quickly.

3. You can now create online NEW!PLAYABLE and NEW!SHAREABLE crossword puzzles! Or make PDF's, Images, or just print them.

These Crosswords were created here!

Quick Start Tools

You enter any subject and we will generate all of your words and clues for you! TIPS Video

Generate Clues/Words with A.I.

Import a word/clue list into the form that is already made

Quick Add (Import Word List)

We have some pre-made lists that you can use:

Pre-Made Word Lists

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Crossword Puzzle Maker | Print, Play Online & Easily Share using our custom crossword maker

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Free crossword maker w/no registration needed! Free A.I. Generation. Play Online & Share! Add images, change colors and fonts to create professional looking printable crossword puzzles. Our A.I. crossword maker can create the entire puzzle with just a subject!

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Changes from old GCSE to 2017 at a glance

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Changes from old GCSE to 2017 at a glance

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03/09/17

Changes to Maths GCSE Curriculum Explained:
A guide for pupils and parents
Share:

June 2017 saw the first cohort of pupils sitting the new GCSE maths curriculum. These pupils have been studying the revised specification since September 2015, but due to the rapidity of changes, you may not yet be fully abreast of the reforms. We've done the hard work for you and condensed a wealth of technical information to the following brief guide.
The changes in a nutshell...
GCSE Mathematics is set to contain more content at a higher level (cue groans from teenagers everywhere!). Beyond this, the nature of the examinations is changing also, with pupils required to memorise additional formulae (that were previously provided on a cheat-sheet at the front of the exam) and a greater emphasis on application of mathematics / solving non-routine problems , potentially putting an end to those who pass maths exams by cramming numerous practice papers at the last minute, and simply repeating the techniques on exam day, with little real understanding of what they are doing.

In order to examine this new larger-harder-meaner GCSE, pupils will now sit 4.5 hours of exams (up from 3.5 hours previously). This is being split by most exam boards as three papers of 1.5 hours each; two with a calculator and one without.

There are still two tiers of papers being offered for maths GCSE. Pupils sitting foundation tier will be able to achieve a maximum grade of 5, while the higher tier paper will cover grades 4-9. As you've likely already spotted, questions targeting grade 4/5 pupils will appear on both papers.

There are several reasons for these changes. The first is to bring the UK GCSE in line with standards internationally. The second is to ensure that pupils are better prepared for post-16 study, be that A Levels (which are reforming) or Universities, which are now having a larger say on the content of KS4/KS5 exams.
I'm following so far, got any more details?
As you might imagine, there's going to be a fairly thorough reshuffle of topics in order to deliver this new syllabus. Here's the lowdown:

Topics moving from AS Level to 9-1
GCSE Higher Tier

Expand the products of more than two binomials

Interpret the reverse process as the 'inverse function'; interpret the succession of two functions as a 'composite function' (using formal function notation)

Deduce turning points by completing the square

Calculate or estimate gradients of graphs and areas under graphs, and interpret results in real-life cases (not including calculus)

Simple geometric progressions including surds, and other sequences

Deduce expressions to calculate the nth term of quadratic sequences

Calculate and interpret conditional probabilities through Venn diagrams

Topics moving from old Higher Tier to 9-1
GCSE Foundation Tier

Index laws: zero and negative powers (numeric and algebraic)

Standard form

Compound interest and reverse percentages

Direct and indirect proportion (numeric and algebraic)

Expand the product of two linear expressions

Factorise quadratic expressions in the form x2 + bx + c Solve linear/linear simultaneous equations

Solve quadratic equations by factorisation

Plot cubic and reciprocal graphs, recognise quadratic and cubic graphs

Trigonometric ratios in 2D right-angled triangles

Fractional scale enlargements in transformations

Lengths of arcs and areas of sectors of circles

Mensuration problems Vectors (except geometric problems/proofs)

Density Tree diagrams

Topics new to both tiers

Use inequality notation to specify simple error intervals

Identify and interpret roots, intercepts, turning points of quadratic functions graphically; deduce roots algebraically

Fibonacci type sequences, quadratic sequences, geometric progressions

Relate ratios to linear functions Interpret the gradient of a straight line graph as a rate of change

Know the exact values of sin θ and cos θ and tan θ for θ = 0°, 30°, 45°, 60° and 90°

Topics now omitted from GCSE maths

Trial and improvement

Tessellations

Isometric grids

Imperial units of measure

Questionnaires

3D coordinates

Rotation and enlargement of functions

Will there still be resists?
Resit opportunities will still exist in both November, and in the following May/June exam series. In fact, anyone continuing in post-16 education will be required a 'good' pass in GCSE maths and English, and will have a compulsory resit if they have not yet achieved this (whether this will be a grade 4 or 5 is still up for debate!)
What about the change-haters, what are they saying?
Here at Manning's Tutors, we love maths, and believe that these changes will bring about a positive engagement with the subject. However, we also believe in pupils benefiting from a varied and engaging school curriculum, encompassing diverse subjects in both academic and creative fields.

There are concerns that the additional pressures on schools to deliver this bigger-badder-GCSE might lead to other subjects falling by the wayside. Not to mention the fact that there is a shortage of qualified maths teachers in the UK capable of teaching the material (1 in 5 UK schools currently has a maths teacher vacancy).

This is where Manning's Tutors can help. In addition to our individual tuition options, we also support schools and academies to deliver course content and support pupils through their examinations.
Wow, sounds like I need to get practicing
Indeed you do. Here's some handy links to the sample papers published by the exam boards
Edexcel GCSE Maths 9-1 Sample Papers (3 x 1.5 hour papers) AQA GCSE Maths 9-1 Sample Papers (3 x 1.5 hour papers) OCR GCSE Maths 9-1 Sample Papers

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Changes to Maths GCSE Curriculum Explained: A guide for pupils and parents - Manning's

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Modern tuition for all levels taught by engaging and contemporary tutors.

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Key word countdown is a game to practise maths skills needed for your GCSE maths exam. Earn up to 50 StudyPoints for a top score!

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Frequently Asked Questions

What is Bingo?

Since its invention in the 1920's, bingo has been and continues to be one of the oldest and most loved games that you can find all over the world. Bingo is a game of chance where numbers are drawn between 1 and 75 or 90 (depending on where in the world you are).

All of the players all have a bingo card with at least 16 different numbers on it. Depending on where you are located, the game may have slightly different rules or structure because different jurisdictions have evolved their own version of the game.

The basic premise is that players will mark off each number that they can match on their bingo card. How bingo works is, when a player has a row, column, or diagonal completely covered, they will call out "bingo!"

Who can play Bingo?

If you're wondering who bingo is good for, the answer is everyone! People of all generations love bingo, and the teachers who use WordMint to create their bingo templates find that their students love it.

Bingo can be played with numbers or with words, so there are literally countless combinations that you can create for templates, and it is easy to customise the template to the age or learning level of your students.

How do I create a bingo template?

A bingo card template in word can be a bit difficult to work with. For the easiest bingo card templates, WordMint is the way to go! With over 1000 existing bingo card templates to choose from you could find the perfect card already existing, or you can create your own!

Simply log in to your account and use our template builders to create your own custom bingo templates.

What is WordMint?

WordMint is your go to website for creating quick and easy templates for word searches, crosswords, bingo and countless other puzzles. With over 500,000 pre-made puzzles, you can select one of our existing templates, or create your own.

Do you have printable bingo templates?

Absolutely! All of our templates can be easily print, or you can save your work as a PDF to print for the entire class. Your cards get saved into your account for easy access and printing in the future, so you don't need to worry about saving them at work or at home!

Do you have bingo templates in other languages?

Yes! We have full support for bingo templates in Spanish, French and Japanese with diacritics. You can use other languages just for your titles and instructions, or create a bingo puzzle completely with words instead of numbers.

Can I convert my bingo template into other puzzles?

With WordMint you can create a template and then use it to convert into a variety of other executions - word searches, word scramble, crosswords or many more.

Is Bingo good for kids?

The teachers that use WordMint love that they are able to create bingo templates that challenge their students cognitive abilities, and bring them together in a fun social environment.

You can theme your bingo games, and the ability to use different languages means that you can work language learning into your lessons as well. Because WordMint templates are totally custom, you can create a bingo template for kids that suits their age and education level.

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Printable and customizable Math vocabulary bingo cards. Add your own words.

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Generador de Crucigramas
Créateur de mots croisé

1. Enter your crossword words and clues in the form below OR choose a premade word list (just below the instructions box) OR use the Quick Add Box to create your crossword clues and answers with Artificial Intelligence (AI).

2. Click the large green "Make Crossword Puzzle" button near the bottom of the form to make your free custom puzzle quickly.

3. You can now create online NEW!PLAYABLE and NEW!SHAREABLE crossword puzzles! Or make PDF's, Images, or just print them.

These Crosswords were created here!

Quick Start Tools

You enter any subject and we will generate all of your words and clues for you! TIPS Video

Generate Clues/Words with A.I.

Import a word/clue list into the form that is already made

Quick Add (Import Word List)

We have some pre-made lists that you can use:

Pre-Made Word Lists

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Crossword Puzzle Maker | Print, Play Online & Easily Share using our custom crossword maker

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Free crossword maker w/no registration needed! Free A.I. Generation. Play Online & Share! Add images, change colors and fonts to create professional looking printable crossword puzzles. Our A.I. crossword maker can create the entire puzzle with just a subject!

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Tutorial for Casio CG50 graphics calculator

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Tutorial for Casio CG50 graphics calculator

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First Look - New Casio FX-CG50 Colour Graphic Calculator - Key features & Modes Graphing CG50

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First Look : Casio Classwiz fx-991CW | New Classwiz Review

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Familiarisation Training for New Casio ClassWiz range (fx-83GT CW fx-85GT CW, fx-991CW)

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The only assessment preparation platform I would ever recommend because it develops the deep reading skills essential to building knowledge, critical thinking and problem-solving.

Patrick Derham Former Headmaster, Westminster

Senior Advisor to Study Hall

Patrick Derham Former Headmaster, Westminster

Senior Advisor to Study Hall

ISEB Pretest

CAT4

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ISEB Pretest

CAT4

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Year 6 SATs

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ISEB Pretest

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Consortium 11+

GL 11+

Year 6 SATs

CEM

AI Literacy

You don't have to choose between great content and exam preparation.

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Say goodbye to endless question bank treadmills. We are the first to statistically map what is on the exams and personalise a plan for your individual school choice. We know what's going to improve your results in the time you have. We accurately map exams including the new ISEB. Read more.

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Addressing misconceptions in real-time is critical to learning. If you get stuck on a question, our AI Study Guide will provide child-friendly explanations. What's more, our AI Study Guide is the first-ever to provide animated explanations for non-verbal reasoning, embedded dictionary for vocabulary and grammar hints.

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Study Hall's AI Literacy cleverly improves reading comprehension, reasoning and grammar just as we would at Eton. A**

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Study Hall is the high-quality, evidenced-based 11+ preparation platform we've all been waiting for. It has the potential to transform student outcomes and make your lives easier.

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Study Hall's emphasis on reading, explicit grammar and vocabulary is not just prepping Year 5-7 (middle school) exams, but expertly laying the foundation for the ACT and College Board SAT tests.

Jim Larimore

Former Chief Equity Officer ACT.Org,

Dean of Dartmouth, Vice Dean of Stanford.

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The only assessment preparation platform I would ever recommend because it develops the deep reading skills essential to building knowledge, critical thinking and problem-solving.

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Finish your reports in record time with our AI-powered report writing tool.

Easily write unique, personalised reports that parents and students will love.

Your school has subscribed to Real Fast Reports to help you write school reports faster.

Check out the demo video below, then create an account to get started.

Create Account

Note: you must use your school email address when creating your account.

What teachers say

"I have used your website to write my Year 7 and 8 maths reports and it has been brilliant.

It has saved me time wording the reports and also helped make them more personal."

"Your site has been a game-changer for me.

I've got over 200 students to write reports for and this is saving me so much time."

"It has totally transformed our experience of report writing!"

Why you'll love it

Smart

Write your reports as a series of brief bullet points.

Our innovative AI transforms them into perfect reports, typo-free.

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Write a class set of reports for the price of a chocolate bar. The time you'll save is priceless.

Examples

End of year Physics report for Josh in Year 10

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good progress

enjoys the subject

has found some topics hard

missed numerous homework deadlines - must improve

achieved a good result in the end of year exam, but could do much better

needs to practise calculations and rearranging equations

Real Fast Reports output:
Josh has made good progress in Physics this year. He has enjoyed the subject and has found some topics harder than others, but has persevered and achieved a good result in the end of year exam. However, he must improve his homework punctuality and practise calculations and rearranging equations if he is to achieve his full potential in the subject.

End of term report for Anna in Year 2

Teacher input:

wonderful start to Year 2

great progress socially, academically, and in behaviour

listens carefully in lessons

applies learning well when working independently

shows creative thinking when choosing own learning

have a great Christmas break

Real Fast Reports output:
Anna has had a wonderful start to Year 2. She has made great progress socially, academically, and in behaviour. She listens carefully in lessons and applies her learning well when working independently. She also shows creative thinking when choosing her own learning. We wish Anna a great Christmas break and we look forward to seeing more of the same progress next term.

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AI-Powered School Report Writer - Fast, Accurate Report Generation

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Experience the future of report writing with Real Fast Reports, the leading AI school report writer. Generate personalised, high-quality reports in seconds. Try it for free and transform your report writing today.

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Train a computer to recognize your own images, sounds, & poses. A fast, easy way to create machine learning models for your sites, apps, and more - no expertise or coding required.

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AudioPen — Speak Naturally, Write Clearly. In Any Style.

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AudioPen turns your voice notes into structured, perfectly edited text. Speak naturally, write clearly. In any style.

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It's simple, really.
The 5 Minute Lesson Plan lives up to its name.

Developed alongside Teacher Toolkit, it uses some clever, cognitive science stuff to help you streamline your thought process.

Either fill out the boxes as directed or let the AI do it for you. Then... voila! You'll have a lovely, focused lesson plan, ready to save and share - in just 5 minutes.

Or, as long as it takes you to finish a cup of tea.
(...And maybe a biscuit)

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The 5 Minute Lesson Plan by Angel Solutions with Teacher Toolkit

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Easy Peasy Lesson Squeezy! | Say hello to fast, effective lesson planning with the 5 Minute Lesson Plan

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ThingLink: Create unique experiences with interactive images, videos & 360° media

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Easily create interactive and immersive visual experiences for online communication and learning. Start a free trial!

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Canva is a free-to-use online graphic design tool. Use it to create social media posts, presentations, posters, videos, logos and more.

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Generate lessons with AI

Plan and deliver interactive lessons on any topic - with help from AI

I am teacher of 15 years who, until recently, has delved no more deeply into tech in the classroom, and here I am encouraging colleagues to come on in and see Curipod in action and leading CPD sessions. To top it off, I'm spending my evenings playing on my iPad to see how many new lessons I can create, and what new features have been added that week. The time saved, and the improvement in my lesson materials, is tangible.
- Read the full case study with Aileen Wallace

Curious?

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Join the growing movement of teachers using Curipod to make interactive lessons filled with creativity, reflection and critical thinking

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MagicSchool.ai - AI for teachers - lesson planning and more!

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Join over a million teachers saving hours of time using the #1 AI Platform for Education, MagicSchool, to help lesson plan, differentiate, write assessments, write IEPs, communicate clearly, and more!

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Play millions of free online trivia quizzes. There is a fun quiz about virtually every topic imaginable: Geography, History, Sports, Music, TV and more!

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Maths in a Box

In the UK, every school student has to study maths up to the age of 16. And every maths teacher in the UK at some point will have been asked by their students 'But what is the point of maths?' and 'Why should I carry on studying it?'

Now teachers can get some fresh ideas on how to tackle these questions with Maths in a Box, a collection of resources, including posters, and booklets containing careers profiles and even a book of magic tricks.

The box contains resources which aim to encourage the uptake and further study of maths and are suitable from key stage 3 right up to key stage 5. These materials have been tried and tested in schools around England and Wales as part of the government-funded More Maths Grads project.

Each secondary school in England received a copy of Maths in a Box during the first few months of 2010. A similar box was also distributed to secondary schools in Wales with the same resources in Welsh.

More Maths Grads in a Box HE Edition

This was designed to help universities who want to work with schools to promote interest in mathematics. It contains resources that tackle questions school students ask such as "What is the point of maths?" or "Why should I carry on studying it?"

Together, they show that maths is used in a whole number of ways that school students may never have even thought of - from exploring how quadratic equations and probability are linked to football to understanding why logarithms are so useful in our analysis of earthquakes.

Selected contents from both of these projects are available to download below.

Additional downloads can be found on our Posters, Booklets and Leaflets page.

What's the Point ... index posters

Posters describing the maths inside different photographs

What's the Point ...

20 x A2 posters from that What's the Point booklet

A3 posters 'When will I ever need Maths?'

Posters describing the use of maths in different school subjects

Origami A3 posters

Posters describing the use of maths in different real world areas such as nature or architecture

Cut Through the Numbers A3 poster:

Shows different kinds of careers where doing A-Level Maths would be helpful

Question Mark A3 poster.

Shows the different kinds of careers where doing A-Level Maths would be helpful

FMSP Posters by undergraduates

Detailed posters produced by undergraduates on an interesting mathematical topic. These posters are at quite a high level, but could be used to inspire students.

Age is just a Number posters

Booklets and Activities

From the 'What's the point' DVD

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Posters and Resources from Maths in a Box

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In the UK, every school student has to study maths up to the age of 16. And every maths teacher in the UK at some point will have been asked by their students 'But what is the point of maths?' and 'Why should I carry on studying it?'

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This resource is useful to illustrate the common mistakes students make when multiplying two decimal values. It is suggested that the language used be adjusted so that the term ‘times’ is interchanged with ‘of’, thus one-tenth of one-tenth is equal to one one-hundredth.

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Combine numbers to reach the target. New puzzles are available each day.

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About

Forget knowledge organisers, for the maths classroom it is all about Frayer Models!

Frayer Models are an excellent way to collate key notes and examples for pupils, to support in lesson work or retrieval quizzing.

​

All of the Frayer Models featured on the site download in Microsoft Word ™ and are fully editable to suit your classroom and your pupils.

Contact

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Frayer Models are a great resource for organising information for learners. Find lots of free maths Frayer models here.

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NonExamples.com - Something that is not an example of a rule or definition already shown, used for a clearer explanation.

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Since I started teaching three years ago, I've been well aware of the problems of traditional textbook exercises when introducing a class to a new concept, procedure. More often than not, textbook exercises became far too varied too quickly, with pupils becoming quickly unstuck, and it became difficult to identify the source of their confusion. Alternatively, it felt as though I was presenting students with 'just more practice of the same', which was deeply unsatisfactory (regardless of the prior attainment of the pupils).

Hence (and I am hugely indebted to Mr Barton and his book), creating sequences of intelligent, minimally varied practice questions seemed a reasonable step. When they are used to introduce pupils to a topic, they enable pupils to make connections and really focus on the underlying concept. The ones presented here are very much initial attempts - they are not a perfect model of how to write minimally varied exercises. All the same, I hope you find them of some use!

I am contactable at fortyninecubed (at) gmail . com, or on Twitter at @fortyninecubed.

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Since I started teaching three years ago, I've been well aware of the problems of traditional textbook exercises when introducing a class to a new concept, procedure. More often than not, textbook exercises became far too varied too quickly, with pupils becoming quickly unstuck, and it became difficult to identify the source of their confusion....

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Welcome to the Math Salamanders

Take a look at our massive range of free math worksheets for kids aged Kindergarten and up!

We have a huge bank of free math resources, calculators, puzzles and games for you to use and enjoy with your kids or students.

Is your child struggling with Math and needing help?

Homeschooling your child and looking for some carefully graded free math worksheets?

Do you want some fun printable Math games to play and enjoy with your child?

Looking for some resources to help your child learn their math facts?

Need a fraction or percentage calculator to solve a problem and show you all the working out you need?

Then look no further...the Math Salamanders are here!

Subscribe to Math Salamanders News

Sign up for our newsletter and get free math support delivered to your inbox each month. Free seasonal math grab pack included.

About this website

The Math Salamanders provide you with:

A huge bank of free educational Math worksheets.

Graded sheets so that you can easily select the right level of difficulty.

Fun Math activities, puzzles and games to play.

Practice worksheets to help your child to learn their basic math facts.

The Math Salamanders caters for all Elementary grades, from Kindergarten upwards.

We also have a growing selection of worksheets for middle and high school students.

You can easily find the correct level of our free Math worksheets to suit your needs by clicking on the age category.

Search Our Site

As our site gets larger and larger, it can be hard to find the worksheets and help you are looking for... Just use the search box below!

Alternatively, you can use the search box at the top of each page.

To search our site, just click on the magnifying glass on the right hand side of the screen.

Math Salamanders Shop

We have a range of fun-packed Math games booklets for sale in our store.

There is a booklet for each grade from 1st to 5th with a wide range of math games carefully designed to meet learning skills for each grade.

Meet the Salamanders

If you want to know a little more about the math salamanders and who we are, then use the link below.

Meet the Sallies

Math Salamanders Online Quizzes

We have created online quizzes to complement most of our worksheets.

Practice your skills online and get instant feedback.

There are also some handy hints to explain the correct answer for each question.

Free Math Worksheets By Grade

Online Practice Zone

Try out our online practice zone for testing your math facts and other math skills.

There are zones for practicing addition, subtraction, multiplication, division as well as place value and fractions.

Randomly Generated Worksheets

Most of the worksheets on our site are carefully graded so that you can choose the right level sheet for your child.

However, sometimes - especially when you are practicing math facts - you might want a few randomly generated sheets.

You can choose the values you want and tailor the sheet to the needs of your child.

You can now also write your own title and instructions (in your chosen language) to go with each sheet!

Perfect for homework!

FUN Math Games

Looking for some fun and motivating ways to inspire your kids to learn math?

Why not try one of our free math games - we have a wide selection of printable games for your students to enjoy!

Online Math Calculators

We have a selection of online calculators which are free to use.

Our calculators include fraction, decimal and percentage calculators as well as conversion calculators and age calculators.

Math Sheets By Topic

Here is our huge bank of free Math worksheets, sorted by topic:

Numbers & The Number System

Fractions

4 Operations

Other Math Topics

Materials

All the math worksheets printable and other math resources found on this website are original math materials produced by the Math Salamanders.

We hope you enjoy using this site and find the materials useful.

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Math-Salamanders.com

The Math Salamanders hope you enjoy using these free printable Math worksheets and all our other Math games and resources.

We welcome any comments about our site or worksheets on the Facebook comments box at the bottom of every page.

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Free Math Worksheets for Kids from the Math Salamanders

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Our Math Salamanders website is packed full of free math worksheets as well as math games, math puzzles and interactive math activities.

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In 2016, I attended #MathsConf7 in Leeds. The outcome? A to-do list longer than my arm as I intended to create a textbook of exercises of increasingly difficult questions to improve upon the standard textbook diet that we in the UK feed from. 's 'Best New Resources' ahead of EdExcel's materials to support the new GCSE.
Resourceaholic.com
In February 2020, Craig Barton announced me as 'the master of fluency practice' for these resources.
In April 2017, IDQs was announced as

In between these two times, I've had a promotion at work, a difficult time with a beloved family pet and a new arrival (Elizabeth Taylor, who is now 'not so new'), so time hasn't really been something that I've been accustomed to ...

... but I had turned my attention to randomising the Increasingly Difficult Questions as part of an eTextbook. A sample is available here and any feedback is absolutely welcome.

Anyway... Here are the sets of Increasingly Difficult Questions. I hope they're useful.

LEVEL 2 FURTHER MATHEMATICS

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In 2016, I attended #MathsConf7 in Leeds. The outcome? A to-do list longer than my arm as I intended to create a textbook of exercises of increasingly difficult questions to improve upon the standard...

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GCSE Predicted Maths Papers using Advance Information from exam boards.

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Luna - AI-powered flashcards & smart revision scheduling

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AI-powered flashcard creation and smart scheduling to accelerate your learning.

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The copyright in all of this material belongs to the originators who created it.
trol = Teacher Resources on Line = trol
See for details about these resources, as well as other (general) matters.

All of the resources offered here can only be accessed by
The [size in kilobytes] of each unit is given as a guide to downloading times.

The material is made available here for downloading and dissemination for
NON-PROFIT MAKING PURPOSES ONLY. Go to Cleave Books main Index

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The copyright in all of this material belongs to the originators who created it. trol = Teacher Resources on Line = trol See for details about these resources, as well as other (general) matters. All of the resources offered here can only be accessed by The [size in kilobytes] of each unit is given as a guide to downloading times.

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Applets for illustrating concepts visually, generating backwards fading worked examples, and creating an unlimited amount of practice questions

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Gimkit is a game show for the classroom that requires knowledge, collaboration, and strategy to win. Get started for free!

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FREE DOWNLOAD

Help your students prepare for their Maths GCSE with this free simplifying algebraic fractions worksheet of 30+ questions and answers

Section 1 of the simplifying algebraic fractions worksheet contains 20+ skills-based keyword questions, in 3 groups to support differentiation

Section 2 contains 3 applied simplifying algebraic fractions questions with a mix of worded problems and deeper problem solving questions

Section 3 contains 3 foundation and higher level GCSE exam style simplifying algebraic fractions questions

Answers and a mark scheme for all simplifying algebraic fractions questions are provided

Questions follow variation theory with plenty of opportunities for students to work independently at their own level

All questions created by fully qualified expert secondary maths teachers

Suitable for GCSE maths revision for AQA , OCR and Edexcel exam boards

Unlock access to download your free resource

You can unsubscribe at any time (each email we send will contain an easy way to unsubscribe). To find out more about how we use your data, see our privacy policy.

Raise maths attainment across your school with hundreds of flexible and easy to use GCSE maths worksheets and lessons designed by teachers for teachers.

Simplifying algebraic fractions at a glance

Algebraic fractions are fractions where the numerator, denominator, or both are algebraic expressions. Algebraic fractions can be simplified by finding common factors between the numerator and denominator and cancelling them. These common factors could be integers or algebraic expressions. Algebraic fractions are in their simplest form when there are no more common factors between the numerator and denominator.

Often we will need to factorise the numerator and/or denominator in order to identify common factors. Algebraic fractions can consist of linear expressions, quadratic expressions or other expressions involving larger indices.

As well as simplifying single algebraic fractions, we can simplify expressions involving adding/subtracting/multiplying/dividing algebraic fractions. The same rules apply here as with numeric fractions. For example, to add or subtract algebraic fractions, we first need to write the fractions with a common denominator. We can then add/subtract the numerators giving a single fraction.

Being able to work confidently with algebraic fractions is a skill that will come in useful for A Level maths.

Looking forward, students can then progress to additional simplifying expressions worksheets and other algebra worksheets, for example a sequences worksheet, simultaneous equations worksheet or straight line graphs worksheet.

For more teaching and learning support on Algebra our GCSE maths lessons provide step by step support for all GCSE maths concepts.

Do you have KS4 students who need more focused attention to succeed at GCSE?

There will be students in your class who require individual attention to help them succeed in their maths GCSEs. In a class of 30, it's not always easy to provide.

Help your students feel confident with exam-style questions and the strategies they'll need to answer them correctly with our dedicated GCSE maths revision programme.

Lessons are selected to provide support where each student needs it most, and specially-trained GCSE maths tutors adapt the pitch and pace of each lesson. This ensures a personalised revision programme that raises grades and boosts confidence.

Find out more

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FREE DOWNLOAD Help your students prepare for their Maths GCSE with this free simplifying algebraic fractions worksheet of 30+ questions and answers Section 1 of the simplifying algebraic fractions worksheet contains 20+ skills-based keyword questions, in 3 groups to support differentiation Section 2 contains 3 applied simplifying algebraic fractions questions

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Proven Maths Results - Fun Learning For Kids

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Whiteboards

Whiteboards on which to quickly share photos of students work, annotate, sync between devices, cast a window, give students virtual MWBs and much, much more.

Maths

Resources I'm building to help teach maths.

Computer science

Resources I'm building to help teach computer science.

Random

Resources I'm working on, mostly to help me teach. You may also find them useful, but they may change without warning.

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Maths and computer science resources for students and teachers.

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We recently finished teaching the AS Maths syllabus to Year 12. My colleague and I decided how to split up the start of the second year of the course. I'm starting with the modulus function.

I took one look at the skills needed at thought "Uh-oh". The students are going to be out of practice with this. They are a lovely group, with a wide range of ability, but we've been very focussed on Applied Maths recently.

Option A: Go for it and patch up the vocabulary as we go (getting very frustrated - they knew this last October)

Option B: Break them in gently, recap the skills and vocabulary and extend them further

Option C: Reteach the work from last October.

Yes, you guessed it. I went with Option C. I found a brilliant task on piecewise function graphs on the Underground Maths website.
Image credit: https://undergroundmathematics.org/
There are four graphs given. The basic task is to interpret the functions relating to each graph, through description or function.

I photocopied the graphs onto card and sliced them up. Each group had a set of cards. One person described a graph and the others had to accurately draw it. Some students went straight onto squared paper, others drafted it out on mini whiteboards. They repeated this until all the graphs were drawn and everyone had had a go at describing (the describer stuck in their card, so that they had a complete set). Whilst they were doing this, I moved around and encouraged the use of mathematical vocabulary.

Note: it was interesting to see how many students had forgotten the significance of open and shaded circles to denote boundaries of inequalities.

The second task was to match up the function cards with the graphs. Once again, accuracy was key as not all graphs had functions and not all functions had graphs. There were also some that nearly, but not quite matched. This activity really brought out the key skills relating to domain, range and function notation that I was looking for. The extension task was to complete the missing pairs.

But, did it work? I can confirm that the following lesson the class made very good progress investing the modulus function and it's graph, even going as far to solve equations. They knew what the notation meant, how to plot it and how to interpret the graphs.

I really like the Underground Maths website as it has great resources, good support material and always makes students think. Most of the time it gets teachers thinking too!

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We recently finished teaching the AS Maths syllabus to Year 12. My colleague and I decided how to split up the start of the second year of the course. I'm starting with the modulus function. I took one look at the skills needed at thought "Uh-oh".

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On this page you will find a selection of fully-resourced lessons with a 'mathematical art' theme. The activities in these lessons will help to reinforce many important mathematical skills such as accurate measuring and constructing, visual problem solving and strategic forward planning.

Each resource is accompanied by brief instructions and photos of students' work. If you have any questions about these resources, please do not hesitate to contact me.

I hope you have found something here to try out with your students. I would love to see photos of your students' work if you do. If you post anything on social media, perhaps use the hashtag #mathsart. And do watch this space for new ideas - I have plans for a 'constructing a mandala' lesson, and one on Islamic tiling patterns too... oh, and maybe one on fractals... So much mathematical art, so little time!

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Fully resourced lessons with a mathematical art theme.

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Gcse Statistics Resources | Stats Academy

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Stats Academy - Edexcel GCSE Statistics revision resources

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Series Explorer | ActiveLearn (pearsonactivelearn.com)

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Resources - SketchCPD.com

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Updated for 2021 - Resources Spreadsheet (based on WR)

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Teachit Maths allows teachers to share resources with each other to avoid reinventing the wheel! You'll find varied and interesting approaches to teaching maths at KS3-5 including worksheets, source packs, role-play activities, lesson ideas, quizzes and games, all carefully crafted and edited by maths teachers.

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Hundreds of maths classroom worksheets, lesson activities, quizzes and revision activities, created and edited by teachers for KS3, KS4 and KS5. Free PDFs.

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As a secondary school Maths teacher, I frequently develop resources for use in the classroom. These range from worksheets to interactive demonstrations, and include activities and tasks suitable for both home and classroom use. I'm particularly keen on the use of Excel for developing standalone tools for use by both teachers and students. I index resources as I create them, and my searchable database is available as an Excel spreadsheet. This contains links to over 500 teaching resources hosted on my website. If you prefer, there is anonline pdf page which will be easier if you don't want to download the spreadsheet, but doesn't have the same nifty search functionality.

If you want to report a problem, make a comment, proffer a suggestion or submit a request, please email me: anthony@thechalkface.net

Requirements:
Most files are in Microsoft Excel, PowerPoint or PDF format. For full functionality, some Excel files require you to enable macros (find out how, and why).
There are some video files in .WMV or .MPG format. There are also some dynamic geometry files available, in .GGB format. These require GeoGebra, which is a free piece of dynamic geometry software that can be downloaded from:www.geogebra.org
Update: The latest GeoGebra resources I produce are available on their dedicated sharing site (which has many other great resources too):GeoGebraTube

More A-level resources (past papers, model solutions, Not-Formula Books) at A-level Resources

If you have found my resources particularly helpful, and feel that you can spare a pound or two, I would be very grateful if you would consider making a small donation towards the costs of hosting the website (ad-free).

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As a secondary school Maths teacher, I frequently develop resources for use in the classroom. These range from worksheets to interactive demonstrations, and include activities and tasks suitable for both home and classroom use. I'm particularly keen on the use of Excel for developing standalone tools for use by both teachers and students.

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Emaths - Free Resources for Mathematics Teachers and Students

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Emaths provides free resources for mathematics teachers and students.

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Due to the changes in the National Curriculum, the site is undergoing a major overhaul. At present, everything on the site is free, so please help yourself to any material which will help support your education.

Kind regards to all

David Smith (Creator of Brain- Cells and its resources)

© Brain- Cells E.Resources Ltd All Rights Reserved 01/01/2010
Year 2 Topics Check Book
A book which helps children to identify the the Year 2 topics. To obtain a copy, click on the title .

Tarsia Jigsaw Puzzles

Tarsia puzzles are often useful. To view and obtain our collection of puzzles <Click Here>

KS1 & 2 Mock SAT Tests

These are available for free educational use only and copies may be obtained by clicking on the required paper's icon below.
Year 2 Resources
A set of resources covering the topics specified by the National Curriculum for pupils during Year 2.

Year 1 Topics Check Book
A book which helps children to identify the the Year 1 topics. To obtain a copy, click on the title .

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Due to the changes in the National Curriculum, the site is undergoing a major overhaul. At present, everything on the site is free, so please help yourself to any material which will help support your education.

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**UPDATED with Table of Values section below and mixed to improper conversion

Efficient Calculator Use

The need for pupils to be comfortable and confident with their calculator by the end of their KS4/GCSE studies is not new, but the new 9-1 specification has brought to my attention some new methods (not necessarily functions) that would benefit pupils in being able to perform using and navigating their calculators efficiently. As we follow the AQA 8300 specification many of this appear repeatedly in the practice papers. You might also be interested in our blog Can you Pay my Bills? 9-1 GCSE blog post, which looks at the bank statements, invoices and pay calculations as seen in the AQA practice papers. Any of the calculator methods described are not to replace understanding or written methods, in fact they are based on a mastery of techniques, particularly when considering remainders.

Fractions

The new 9-1 specification AQA calculator papers include questions such as this calculation below. When performed correctly this would result in an improper fraction and pupils would be required to change to a mixed number.

I couldn't understand why so many of my students were getting this wrong. So I asked a pupil to show me how they were entering this in the calculator and it turned out the problem was entering mixed numbers! The pupils were using the primary fraction button (red arrow) and using the 'back' button to insert the whole part before the fraction! The calculator would then interpret this as whole multiplied by the fraction part!!! When in fact they need to use the secondary function (green arrow) in order to insert the mixed number correctly.

These questions will give answers as an improper fraction and pupils may need to convert to mixed numbers (depending on the question requirements). Using the S>D function would give the whole part; instead use the shift button to activate the mixed to improper (orange arrow to left).

FACT Function

Although I have shown pupils this function in the past I have been reluctant to push it's use because pupils need to complete prime factor decomposition for the non-calculator paper. However, increasingly expressing a product as its prime factors or finding the HCF/LCM is present on the new 9-1 calculator papers. To use this function, input the number for example 225, enter, then shift "FACT" and the calculator will express as a product of it's primes. This was Q 24 from paper 2 of the foundation AQA practice set 3 which required pupils to express 225 as a product of it's prime factors, this is awarded two marks. Pupils will save time if they use this function and that time can be used to complete the HCF/LCM part of the question.

This function can also help with questions requiring pupils to identify larger prime numbers as seen in Q3 of the Foundation AQA practice set 4, paper 3. If it is a prime number for e.g 97, after using the FACT function 97 would be displayed; therefore it is prime.

Table of Values

I had totally forgotten about this function, thankfully my Twitter colleagues @MrCarterMaths and @Mathematical_A reminded me!

Select mode (green arrow) which will give the four options seen on the display. Select option 3 : TABLE. You are then prompted by f(x) to enter the function, enter the function using the ALPHA key and the bracket key with the X (red arrows). Ensure pupils check carefully that they have entered this correctly. You are then prompted with "START?" followed by "END?", both referring to the range of values of X in the table, e.g. from -2 to 5 (remember to us (-) for minus two), press enter after each. The final prompt is "STEPS?", i.e. what is X going up in (most often one). Then a table of values is given in a vertical format. @Mathematical_A has mentioned that the new FX991EX has dual tables!!

Here is a video tutorial from @GuideCalculator on this function and you might also be interested in using the table function to complete trial and improvement (although not explicitly on the new specification, it could fall under iteration).

Remainders

Here is one of the treasure hunt cards requiring remainder to be found, again this was originally poorly answered by my pupils despite it being on one of the calculator papers. This style of question is seen in the AQA foundation practice papers, for example Q12 from paper 3 of set 3.

Below is the method we show pupils to tackle this efficiently; this slide is taken from our Walking Talking Mock.

Rounding

Scientific calculators can be used to set a number of decimal places (using shift>set up>6. Fix), however this is not something that I choose to show pupils; they should be able to round correctly and there's too much of chance they don't change it back! So instead it is good 'exam technique' to insist pupils write down the whole answer and then round as required. Again a slide from our walking talking mock on the left demonstrates these calculator paper tips.

To help refine pupils calculator paper skills we have produced some resources for use with a scientific calculator and knowledge of skills such as Pythagoras' Theorem, Trigonometry etc. Therefore this resource is best used once you're confident pupils have the range of skills on the topics listed below.

9-1 Calculator Use Resources

The first new resource is our 9-1 Efficient Calculator Use Treasure Hunt activity differentiated to two levels; amber and green. The amber level covers the following topics; finding remainders, calculating with fractions, improper to mixed, area of fraction of circle, product of primes, Pythagoras, Rounding. The green level covers Trigonometry, remainders, compound interest, density, rounding, area of sector, scales, conversions, using formula. Each of these require pupils to round correctly i.e. decimal places or significant figures.

Check out our Treasure Hunt blog post for different ways to use treasure hunt activities in the classroom and beyond.

The second resource is our 9-1 Efficient Calculator Use Worksheets which includes two worksheets to complement the first resource to make a full lesson or use as homework. Worksheet 1 covers six topics (powers/roots, place value, remainders, primes, fractions and percentages). Worksheet 2 covers three overall topics but each progresses in challenge (use of formula, right angled triangles i.e. Pythagoras' theorem and trigonometry, circles (arcs/sectors).

What calculator tips do you give your pupils? Get in touch @numberloving or NumberLoving's Facebook page.

Photo Credit: Calculator Scientific by Fornax (Own work) is licensed under CC BY-SA 3.0 via Wikimedia Commons

Check out our free and premium resources in our TES NumberLoving Store.

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The need for pupils to be comfortable and confident with their calculator by the end of their KS4/GCSE studies is not new, but the new 9-1 specification has brought to my attention some new methods (not necessarily functions) that would benefit pupils in being able to perform using and navigating their calculators efficiently.

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Interactive Maths - The Interactive Way to Teach Mathematics

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Interactive Maths - The Interactive Way to Teach Mathematics

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Interactive Maths is a site with a mixture of activities for teaching and learning maths, all of which are based around using technology.