KS3 Mathematics (11-14)

A new page for Key Stage 3 (UK 11-14) is now available from the top menu.

Many resources available in posts and pages on this blog are relevant for this age range but I thought it would be useful to have a reference page with links to key documents such as the programme of study for KS3 as well as transition documents from Key Stage 2 to Key Stage 3 and for Key Stage 3 to Key Stage 4.

Included on this page you will find the very valuable Secondary Assessment Materials from NCETM which have been written to support teachers in assessing students at KS3. Examples of questions, tasks and activities are mapped against the key mathematical skills and concepts within the KS3 Programme of Study.

NCETM Secondary Assessment Materials

On Dr Frost Maths choose KS2/3/4 from the resources view or select the White Rose Maths course, this covers Year 5 through to Year 11 and also a one year GCSE resit. See also the secondary resources from White Rose Maths.

White Rose Maths – Secondary Resources

Access is freely available for all the schemes of learning and assessments. Looking at the schemes of learning you will see additional resources to download, for example, the very valuable Complete Secondary Small Steps document. The National Curriculum Progression document shows how the White Rose Maths curriculum links to the Key Stage 3 and 4 National Curriculum.

Both Nrich and Transum have curriculum content maps suggesting resources for KS3 content.

Transum KS3 Statements

Nrich Secondary Curriculum Mapping Document

Also included on the page you will find advice and teaching activities from AQA, Edexcel, and OCR.

AQA Bridging the Gap

Pearson Edexcel-Teaching and-Learning Materials
OCR GCSE 9-1 Check in tests

Transition 2021

OCR, Bridging the Gap – A Student Guide

My post, Transition Time 2021 on Mathematics for Students includes the excellent guide from OCR on the Transition from GCSE to A level and numerous other resources which are aimed at the transition from GCSE to A level and also a collection of resources for students who may be going on to study Maths or a course with mathematical content at university.

Plymouth University – Calculus workbook

From Craig Barton, his podcast, Episode 11: University transition and oral assessments with Paola Iannone looks at the transition to university mathematics and the potential power of oral assessments. I note from Craig that Paola Iannone’s Big 3 includes Kevin Houston’s blog. I have included Kevin Houston in the Transition Time 2021 post, see his ‘How not to get a good mathematics degree‘ and ‘How to get a good mathematics degree‘. He also has provided a pdf file you can download: 10 Ways to Think Like a Mathematician.

See also at the end of that post, The Eleven Commandments for Mathematicians!

The 11 Commandments

For UK Year 12 and 13 students, note these excellent (free) opportunities from AMSP. For current Year 13 students or those taking a gap year the free online Preparation for Higher Education course is designed to help students revise some of the later content of A level Mathematics. It offers the opportunity for an introduction to some topics studied in AS Further Mathematics, such as complex numbers and matrices, which will be helpful to those progressing to degrees in maths, physics, engineering and closely related subjects.

For Year 12 students, see the Problem Solving Matters course, and also information on regular problem solving classes.

At the other end of the school – for younger students, remember that MEI’s Calculator Crunch begins on Monday.

Calculator Crunch 2020

This is aimed at Transition from Year 6 to Year 7 (UK ages 10-11). MEI’s transition resources for this age range include an excellent series of webinars. The webinars explore curriculum and pedagogical continuity across the KS2 to 3 transition and look at the Primary Maths Guidance Document. The guidance for Year 6 is a valuable document for looking at the transition from Year 6 to Year 7 and includes example assessment questions for each of the ready-to-progress criteria.

Primary Guidance – Year 6

NCETM has produced an extensive library of resources offering support with the Primary Guidance documents. This includes 79 PowerPoints, these focus on the ready-to-progress criteria in the DfE maths guidance for KS1 and KS2. These can usefully be viewed by topic or by year.

You can find NCETM guidance videos on YouTube.

Mathematical Miscellany #52

Congratulations to Corbettmaths – 200 million views. 200 million views because it is so good; certainly a go-to site. As well as the brilliant 5-a-day resources the videos and worksheets are also excellent. Do check the ‘More’ menu also, where you will find additional resources including a very comprehensive set of videos and worksheets for level 2 Further Maths.

Corbettmaths – Algebraic Proof, level 2 Further-Maths.
Corbett Maths – A Bit of Everything practice papers

I do like the collection of Practice Papers, note the Revision resources, including A Bit of Everything Papers; the Foundation papers with 116 questions provide very comprehensive syllabus coverage! Each paper includes a contents list with the relevant teaching video.

You can also subscribe to Corbettmaths on YouTube.

Returning on 21st June is Calculator Crunch from MEI. To quote MEI:

On each weekday from 21 June – 1 July we will tweet an engaging question for children to work on – that’s nine questions in total. They all involve using a calculator (basic or scientific) to solve an interesting problem. The problems are designed to deepen children’s mathematical thinking skills in a fun way.

Simply follow @MEIMaths on Twitter and get involved by using the hashtag #CalculatorCrunch.

Calculator Crunch 2020

You can still access all the 2019 and 2020 Calculator Crunch questions.

Matt Woodfine continues to update the brilliant Maths White Board; I see new content added recently, Stem and leaf diagrams and Equation of a circle; I have linked to the recall boards in each case, one of my favourite features of the site is the extensive collection of retrieval practice boards.

Equation of a circle Maths White Board

Also now available is his Term Planner, you can watch the tutorial video to find out more. The planner will allow you to quickly access specific resources from the site.

Maths White Board is easily available from the Use of Technology menu – see tab at the top of the screen.

New KS3 resources are available form Pearson Edexcel. Go to Pearson Edexcel’s Teaching and learning materials and look under key stage 3 support.

Pearson Edexcel-Teaching and-Learning Materials

Multiplication and Division

A look at a selection of resources for multiplication and division – from 2×1 to multiplication and division of polynomials!

The tutorial video is very clear on how this Mathigon resource can be used with spaced repetition, there is also, very usefully a Shuffle mode for simple practice.

Choose the Settings and Instructions icon for a summary of the resource and access shuffle mode to practice with a random subset from all decks at once. You can also jump to a later deck with more difficult questions and different visualisations.


For more practice try Transum for several resources for mastering tables, including, for Mixed Practice, Beat the Clock. Level 6 offers mixed multiplication and Division problems, later levels use all 4 operations.

Also from Transum, try Expedite:


For a challenge, try this Open Middle problem from Steve Phelps, Multiplying Two-Digit Numbers.

Multiplying Two-Digit Numbers – Steve Phelps

For a very clear demonstration of the area model for multiplication, see PhET Sims Area Model – Multiplication. You can enter your own calculations and as always with the PhET Simulations choose what you want displayed. For a look at how multiplication tables help understand multiplication, factoring, and division, see from Phet Sims – Arithmetic.

Following on from the area model, for your older students, try Divide it up from Underground Maths, a resource designed to help students to make links between multiplication and division of polynomials using multiplication grids. The problem is presented in the image here, but also provided is a warm-up activity and further notes

The UK National Curriculum specifies that:
Pupils should be taught to:

Year 6 (UK KS2 age 10-11)

  • multiply multi-digit numbers up to 4 digits by a two-digit whole number using the formal written method of long multiplication
  • divide numbers up to 4 digits by a two-digit whole number using the formal written method of long division, and interpret remainders as whole number remainders, fractions, or by rounding, as appropriate for the context
  • divide numbers up to 4 digits by a two-digit number using the formal written method of short division where appropriate, interpreting remainders according to the context

Appendix 1 of the KS2 document includes the examples below and states that “the examples of formal written methods for all four operations illustrate the range of methods that could be taught. It is not intended to be an exhaustive list, nor is it intended to show progression in formal written methods. For example, the exact position of intermediate calculations (superscript and subscript digits) will vary depending on the method and format used. For multiplication, some pupils may include an addition symbol when adding partial products. For division, some pupils may include a subtraction symbol when subtracting multiples of the divisor.

NC Formal Long Multiplication
NC Formal Long Multiplication
NC Formal Short & Long Division
NC Formal Short & Long Division

And at KS3 (UK age 11-14) we are reminded that students should be able to “use the four operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative”.

The Mathematics documents can all be found on this page.

Mathsonline long multiplication
From MathsOnline, comes a clear step by step demonstration of long multiplication, (uses html). Each step is clearly explained. Long Division is also very clearly illustrated and for your older students we can extend to Algebraic Long Division. Refreshing the page generates a new example each time.
Mathisfun Long Division

Mathisfun explains long division very clearly and additionally offers questions and worksheets. Similar resources are available for Long Multiplication and for Algebraic long division. 

Mathisfun Algebraic Long Division
CIMT Long Multiplication & Division
CIMT Long Multiplication & Division

For examples, exercises and problems try the ever-reliable CIMT’s GCSE chapter 6 on the Number System – see Section 6.4.