I am always asked for Past GCSE and SATS Exam papers and their corresponding mark schemes.

I do not want them readily available for learners to easily download so I have taken the links off from the blog recently. If you need a paper or a mark scheme just mail me at info@magicalmaths.org or tweet me @magicalmaths and I will send you the URL where you can download the files that you need.

EdExcel GCSE Foundation Higher & KS2 KS3 SATS 2001 to 2010 Exam Paper & Mark Scheme Download Page.

A great philosophy to adopt when planning and delivering your lessons. This approach works very well when you are planning a lesson for an observation.

This is a great resource that could be used as a starter to demonstrate encoding and decoding in real life.

The human brain is an amazing organ in the way in which it can decode and encode messages.

Math Percentages Starter

If you are looking for a classic Math percentages problem as a starter to a lesson then you have come to the correct place. This is a great math percentages starter with a little twist of probability to it. The question really forces the learner to think about their percentages and probability in one great question.

Do not forget to check out all the other Magical Math Lesson starters on the website.

Comments are FREE, please leave one below. Leave your answer to the question below!

If you choose an answer to this question at random what is the chance you will be correct?

A) 25%

B) 50%

C) 60%

D) 25%


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What are the 10 principles of Assessment for Learning (AFL)?

For PGCE or GTP students the following principles will be ideas that you have heard in lectures, if you have not than these are concepts that you need to get yourself familiar with;

1. Assessment for learning should be part of effective planning of teaching and learning

A teacher’s planning should provide opportunities for both learner and teacher to obtain and use information about progress towards learning goals. It also has to be flexible to respond to initial and emerging ideas and skills. Planning should include strategies to ensure that learners understand the goals they are pursuing and the criteria that will be applied in assessing their work. How learners will receive feedback, how they will take part in assessing their learning and how they will be helped to make further progress should also be planned.

2. Assessment for learning should focus on how students learn

The process of learning has to be in the minds of both learner and teacher when assessment is planned and when the evidence is interpreted. Learners should become as aware of the ‘how’ of their learning as they are of the ‘what’.

3. Assessment for learning should be recognised as central to classroom practice

Much of what teachers and learners do in classrooms can be described as assessment. That is, tasks and questions prompt learners to demonstrate their knowledge, understanding and skills. What learners say and do is then observed and interpreted, and judgements are made about how learning can be improved. These assessment processes are an essential part of everyday classroom practice and involve both teachers and learners in reflection, dialogue and decision making.

4.Assessment for learning should be regarded as a key professional skill for teachers

Teachers require the professional knowledge and skills to: plan for assessment; observe learning; analyse and interpret evidence of learning; give feedback to learners and support learners in self-assessment. Teachers should be supported in developing these skills through initial and continuing professional development.

5. Assessment for learning should be sensitive and constructive because any assessment has an emotional impact

Teachers should be aware of the impact that comments, marks and grades can have on learners’ confidence and enthusiasm and should be as constructive as possible in the feedback that they give. Comments that focus on the work rather than the person are more constructive for both learning and motivation.

6.Assessment for learning should take account of the importance of learner motivation

Assessment that encourages learning fosters motivation by emphasising progress and achievement rather than failure. Comparison with others who have been more successful is unlikely to motivate learners. It can also lead to their withdrawing from the learning process in areas where they have been made to feel they are ‘no good’. Motivation can be preserved and enhanced by assessment methods which protect the learner’s autonomy, provide some choice and constructive feedback, and create opportunity for self-direction.

7.Assessment for learning should promote commitment to learning goals and a shared understanding of the criteria by which they are assessed

For effective learning to take place learners need to understand what it is they are trying to achieve – and want to achieve it. Understanding and commitment follows when learners have some part in deciding goals and identifying criteria for assessing progress. Communicating assessment criteria involves discussing them with learners using terms that they can understand, providing examples of how the criteria can be met in practice and engaging learners in peer and self-assessment.

8.Learners should receive constructive guidance about how to improve

Learners need information and guidance in order to plan the next steps in their learning. Teachers should:

  • pinpoint the learner’s strengths and advise on how to develop them
  • be clear and constructive about any weaknesses and how they might be addressed
  • provide opportunities for learners to improve upon their work.

9.Assessment for learning develops learners’ capacity for self-assessment so that they can become reflective and self-managing

Independent learners have the ability to seek out and gain new skills, new knowledge and new understandings. They are able to engage in self-reflection and to identify the next steps in their learning. Teachers should equip learners with the desire and the capacity to take charge of their learning through developing the skills of self-assessment.

10.Assessment for learning should recognise the full range of achievements of all learners

Assessment for learning should be used to enhance all learners’ opportunities to learn in all areas of educational activity. It should enable all learners to achieve their best and to have their efforts recognised.

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If your child comes home and says that they got a level 8 in Mathematics than this is something that you and them should be very proud of. This is a tremendous achievement and shows that your child has demonstrated the following abilities in Mathematics;

Solve problems using powers and roots

·       Solve problems involving standard form

·       Solve problems involving repeated proportional change

·       Substitute fractions and decimals into equations and expressions and evaluate them

·       Calculate one variable in a formula when I know the others

·       Understand that a2-b2 = (a+b)(a-b)

·       Solve inequalities in two variables

·       Sketch and interpret graphs of quadratic, cubic and reciprocal functions

·       Interpret graphs that model real life situations


·       Use congruence and mathematical similarity

·       Use sine, cosine and tangent in right angled triangles in 2D

·       Distinguish between formulae for perimeter, area and volume by considering dimensions


·       Interpret and construct cumulative frequency diagrams

·       Estimate the median and interquartile range

·       Calculate the probability of a compound event

Level 7 in Mathematics means that your child has demonstrated that they can can do the majority of the following;

·       Round to one significant figure

·       Understand what happens when we multiply or divide by numbers between 0 and 1

·       Multiply and divide numbers of any size

·       Understand proportional change

·       Describe in symbols the rule for the next term or nth term in a quadratic sequence

·       Multiply things like (a+b)(c+d)

·       Simplify quadratic expressions

·       Solve simultaneous linear equations with two variables using graphs or algebra

·       Solve inequalities


·       Understand and use Pythagoras’ Theorem in 2D

·       Calculate lengths, areas and volumes in right prisms

·       Enlarge a shape by a fractional scale factor

·       Understand similarity

·       Draw the locus of a moving object

·       Find and understand upper and lower bounds

·       Use compound measures like speed, distance, time


·       Give and test a  hypothesis to a situation

·       Understand bias

·       Find the modal class and an estimate for the mean, median and range when using grouped data

·       Compare distributions using frequency polygons

·       Draw a line of best fit on a scatter diagram

·       Understand relative frequency

Formal assessments or observations in lessons would have been made to assess whether a learner has satisfied the criteria to be awarded a level 4. Please share your experiences with this below.

Your child’s target in Mathematics is a level 6, but you ask yourself what does that mean? He or she will be assessed to see if they can do the majority of the following;

·       Use trial and improvement to solve things like x3+5x=38

·       Work out one number as a fraction or percentage of another

·       Understand that fractions, decimals and percentages can be equivalent to each other

·       Calculate using ratio

·       Add and subtract fractions with common denominators

·       Find and describe in words the rule for the next and nth term in a linear sequence

·       Solve linear equations with integer coefficients

·       Plot the graph of y=mx+c

·       Recognise 2D representations of 3D objects

·       Classify quadrilaterals by knowing their properties

·       Find the missing angle when two parallel lines are intersected

·       Solve angle problems in polygons

·       Find the area and circumference of a circle

·       Find the volume of cuboids

·       Enlarge a shape by a positive scale factor


·       Work with continuous data

·       Construct pie charts

·       Say what a scatter diagram tells us

·       Understand correlation

·       Find all the possible outcomes of two experiments

·       Use the fact that the probability of mutually exclusive events add up to 1

You receive your child’s report card and it says that they are working at Level 5 in Mathematics. Brilliant you think, but what does it mean?

Formal assessments or observations in lessons would have been made to assess whether a learner has satisfied the criteria to be awarded a level 5. Some of the things that they need to do is defined below;

·       Multiply and divide whole numbers by 10, 100 and 1000

·       Add and subtract negative numbers

·       Put numbers is order including negative numbers

·       Add, subtract, multiply and divide numbers like 19.75 and 34.21

·       Simplify a fraction

·       Work out a fraction or percentage of a number

·       Multiply or divide a three digit number by a two digit number

·       Use inverse operations of approximation to check my answers

·       Use simple formulae like C=2n+4

·       Use co-ordinates in all four quadrants


·       Measure and draw angles to the nearest degree

·       Remember the metric to imperial conversions

·       Use and understand the formula for the area of a rectangle


·       Find the mean of discrete data

·       Use the range and one of the averages to compare two sets of data

·       Say what diagrams and graphs show

·       Use the probability scale from 0 to 1

·       Understand that experiments don’t always have the same outcome

My child tells me that they are working at level 4 in Mathematics, you ask yourself what does that mean? It means that your child has been assessed and found that they can do the majority of the following in Mathematics lessons;

·       Describe number patterns

·       Find multiples

·       Find factors

·       Work out the square numbers

·       Use word formulae

·       Use co-ordinates in the first quadrant

·       Multiply and divide whole numbers by 10 and 100

·       Say my tables up to 10 x 10

·       Add and subtract numbers like 13.64 and 48.95

·       Write decimal numbers in the correct order

·       Check my own answers


·       Make 3D models

·       Draw 2D shapes

·       Find perimeters of shapes

·       Find the area by counting squares


·       Draw line graphs

·       Present data clearly

·       Read simple pie charts

·       Draw frequency tables

·       Find the mode

·       Find the range


·       Try ideas of their own

Formal assessments or observations in lessons would have been made to assess whether a learner has satisfied the criteria to be awarded a level 4. Please share your experiences with this below.

Your child comes home with their report card or at parents evening you are informed that they are working at level 3 in Mathematics. You are ask yourself, what on earth does that mean? Well it means that in Mathematics lessons they have been assessed to be able to do the majority of the following;

·       Say what each digit stands for in numbers like 725 and 1974

·       Use decimals in money questions

·       Use negative numbers to describe temperature

·       Remember addition facts up to 20

·       Add and take numbers like 18 and 37 in my head

·       Add numbers like 184 and 359 on paper

·       Know my 2, 3, 4, 5, and 10 times tables

·       Draw pictures to represent fractions

·       Know when two fractions are equivalent

·       Find symmetry in 2D shapes

·       Sort 2D and 3D shapes using their properties

·       Measure things using units like centimetres, litres and minutes

·       Find information in tables and lists

·       Draw bar charts

·       Draw pictograms

·       Interpret simple charts and graphs

Parental involvement in education

Many parents ask the question how involved should they get with their child’s learning and the answer is clear and simple, VERY! Parental involvement in education is paramount for any successful learner. Learning does not stop as you leave the classroom, ideas and concepts need to be revised, applied and practised, and this is where Parental involvement in the education process is key.

How to ensure my child makes progress and learns effectively at school?

If you are a parent and you want to get involved in your child’s education the question above is a tough question to answer. However, in a recent study the following ten characteristics were most commonly associated with students who made good or accelerated progress during secondary school, the students;

  1. Were determined and focused in their approach to their work;
  2. Accepted and often enjoyed high levels of challenge presented by their teachers;
  3. Analysed their own strengths and weaknesses;
  4. Were prepared to work independently without direct supervision;
  5. Were resilient and did not become disheartened when faced with disappointments;
  6. Had a clear long-term goal in mind, either in terms of a career or further education, which acted as a significant motivator;
  7. Were good at getting the most out of working in a pair or group;
  8. Displayed other talents and interests (e.g. music, sport, etc) which they developed alongside their school work;
  9. Readily sought and received help from home;
  10. Formed productive and effective ‘learning partnerships’ with their teachers based on mutual respect.

Comments are FREE, If you have any points or advice you want to add, feel free to add a comment below.

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Teaching and effective classroom practice

Effective classroom practice is very important to deliver successful lessons. It is very important that you make the time to investigate your school’s polices and processes. Also it is highly advised to observe your fellow practitioners in the school to learn from good practice.

Having had the opportunity to observe and feedback on hundreds of lessons I have found  that there are number of factors that effect good classroom practice;

Comments are FREE, please feel free to add one below.

  • Have good preparation and planning for each lesson. This includes marking homework and have resources readily available and in working order.
  • Developing personal relationship with class and have good behavioural management.
  • Good lesson structure with objectives and aims clearly defined, i.e. starter main and plenary.
  • Appropriate questions should be given, with clear instructions and explanations delivered throughout lessons.
  • Exercises and activities should be varied and relevant to the subject area.
  • Be dynamic and vigilant in the classroom environment. Prepare for pupils with all abilities and ensure that you are ready for problems arising.
  • Time and effort should be placed on making sure that lessons deal with appropriate topics and activities
  • Lessons should have pace and emphasis should be made on maintenance of momentum.
  • Conclude lessons with good evaluation tasks so that lessons can be measured in terms of successful learning.
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There is no one solution to this and success will depend on school, class, pupil, environment, your mood and a whole host of factors!

It is important that you analyse your school’s behaviour management policy but the following discipline policy sanctions can be highlighted;

  •  Give extra work to be completed after school or at home.
  •  Verbal chastisement after lesson or after school.
  •  Form Tutor’s detention with 24 hours notice.
  • Subject Teacher’s detention/with 24 hours notice.
  • Departmental detention with 24 hours notice.
  • Faculty detention with 24 hours notice.
  • School detention. This can only be issued by the Senior House Tutor/Head of Faculty or by a senior member of staff and must have 24 hours notice.
  • Head Master’s detention. This can only be issued only by the Head Master or a senior member of staff with 24 hours notice.
  • Use of individual daily report sheets issued by Senior House Tutor. This is then overseen by Form Tutor or Senior House Tutor.
  • Use of class report sheets which is issued by Senior House Tutor.
  • Exclusion from a lesson.
  • Fixed term exclusion. In the case of exclusions exceeding 2 days, work should be set.
  • Chairman of Governors’ warning.
  • Permanent exclusion, involving the Governing Body and the School Attendance Panel

Feel free to add your own points in the comments section.

Assessment for learning: a powerful way to improve learning and raise standards.

Assessment for learning involves using assessment in the classroom to raise pupils’ achievement. It is based on the idea that pupils will improve most if they understand the aim of their learning, where they are in relation to this aim and how they can achieve the aim (or close the gap in their knowledge).