Maths topics overview

This provides an overview of the various maths topics that children will have to master as they progress through school. Included here are samples of maths resources for all age groups and topics.  

All types of mathematical work take practice and a knowledge of numbers starting with recognition of numbers, addition, subtraction and then moving on to multiplication and division.

Guidance on teaching methods and how maths is taught in schools. 

INTRODUCING NUMBERS

At the start of learning, children need a variety of methods to reinforce and stimulate the concepts being taught. It is always easier to help children to concentration if the work is colourful and enjoyable. Visual aids in the form of counters, sea shells, conkers or apples help ensure that the children have a visual image as well as the written question. I find that it is useful to work with your child to ensure that they have support and can ask questions or they may have a question about the progression, result or need more explanation.

Number topic for foundation stage
FS maths
Exploring shape and colour for FS
Maths ideas for using at home

FOUR RULES OF NUMBER

The four rules of number are addition, subtraction, multiplication and division.
Children can be encouraged to enjoy practical maths in many ways:
  • As you go around the supermarket ask the child to pick 5 oranges to put into your trolley.
  • Encourage the children to lay the table for the family. Tell them they will need 4 cups, 4 place mats, 4 forks etc.
  • Encourage your child by asking questions when you are out and about e.g. please can you collect 5 different leaves? How many will you have if you drop 2?
  • How many birds can you count on the tree? How many more would make 10?
  • There are 4 squirrels over there - how many acorns do you need to give them 2 acorns each?

You can see how such ideas can be adapted as they progress from adding and subtracting to multplying and dividing. 

MEASURING

Children love to measure. They can use Lego bricks to measure the length of the rug in their bedroom, use blocks to measure the length of the kitchen table, use a cane to measure the height of their sunflower in the garden. As children progress they can use a ruler or a tape measure e.g. to measure the length of their bed or their doll's house etc. It's always popular to have a height chart so they can see how much they grow each month.

Later, it is a good idea to ask your child to estimate first then measure accurately afterwards. This reinforces the concepts of measurement and relative sizes of things.

FS worksheet on measuring
Scales - part 1
Teaching length
Capacity

Place value

Place value is essential in understanding the concepts of numbers. Place value is the position that each individual number has in our number system. The value of a digit depends on its place, or position, in the number.

For example, you can explain in the number 6 there are 6 units but in the number 34 there are 3 tens and 4 units. Each place has a value of 10 times the place to its right. So in the number 27 the 7 is in the Units column and the 2 is in the Tens column etc.

Explaining numbers
Introducing place value
Place value hundreds, tens, units
Place value to 99

Fractions and percentages

Every day we use fractions. Things you can talk to your child about:
  • If I share my 2 biscuits with my friend this means that I give away 1 biscuit and eat 1 biscuit. This means that we each only eat half of the number of biscuits.
  • When mum cuts my birthday cake she cuts it into 10 equal pieces so each friend gets one tenth of the cake.
  • At the table share the grapes so that each person has the same number e.g. 20 grapes divided among 4 people means each person has one quarter of the grapes which is 25%.
Worksheet 8-Fill the correct fraction
Percentage of amount problems
Fraction questions Key stage 2
Percentages for KS3

Data handling

Data handling is a visual way of displaying mathematical statistics. Different coloured cars, flowers or other toys can be represented simply with blocks or rows of blocks. Children also find it great fun to collect and count acorns, chestnuts, flowers, and seeds. Then create a simple bar graph or pictogram to display the number of each found. As pupils get older in school they will use data handling to make comparisons using Venn and Carol diagrams.

Two graphs Years 1 and 2
Carroll diagrams
Venn diagrams 2
Frequency for KS3

Time

Playground games are a fun and practical way to introduce time to young children. Games such as 'What's the time Mr Wolf?' and playground races against the stop watch are fun and can introduce children to the concept of time. As children get older they can use a watch to time each other working on questions associated with time. Working on timetables, timing each other in science experiments, watching the time in cooking and relaying all this information on graphs and tabulating it so that comparisons can be made are all ways to help with learning about time. Children need to understand twelve hour and twenty four hour clocks as both are used in everyday life.
 
Teaching time
Time problems for KS2
Help your child with telling the time - FS
Time worksheet 1

Fun maths

All maths can be made fun in various ways: collecting shells, conkers or anything and then collating these into graphs of various forms, compiling a timetable for your ideal school day, devising a maths quiz etc are useful ways to consolidate use of maths. As pupils get older they will likely use a computer, tablet or phone to enjoy mathematical games and programs.

Maths fun for year 3
Fun maths for year 2
Fun maths for year 6
Maths fun

Shapes

Children are often introduced to shapes at an early age with shape sorters and building bricks. Jigsaws emphasise shape and symmetry and also illustrates the relationship of one object to another. Older children may be encouraged to use shapes to enjoy designing the plans for their ideal house, spaceship or moon rocket.

Exploring shape and colour for FS
Revision of shape for KS1
Symmetry
Platonic shapes

Money

Understanding the basic concepts of money will stand children in good stead for the future. Young children love using money and playing shops at home. As your child progresses into KS2, they could bake cakes for a good cause and sell them to their friends. At the School Fair children may be encouraged to run their own stalls such as books and toys, or set up games with balls and hoops that children have to pay to enjoy.

Money recognition
Money questions
Money Practice
Functional maths project

Mental maths

Mental maths helps in all aspects of life. It encourages children to think and process problems in their heads. There is often more than one way of arriving at the correct answer. Such mental agility can be encouraged by doing simple maths without using pencil and paper.

Mental maths 1
Maths game for Year 6
Mental maths 2
Mental arithmetic for KS3

Equations

The word equation means making both sides equal. This involves algebra. It is easier to start working step by step. As your child becomes more proficient they may be able to merge some steps but do not hurry and miss out steps, as it is better to arrive carefully at the correct answer. Equations start with addition and progress to algebra and then to linear and simultaneous equations.

Solving simultaneous equations
Introduction and how to teach equations
Linear and simultaneous equations
Equations for KS3

Revision

You will find many revision papers referenced through the Worksheet Finder. These are useful to work through from time to time as reminders to methods of working. Revision does reinforce learning and is beneficial as it gives a child more faith in themselves when approaching exams. Make sure your child revises any areas they are unsure about as it will give them more confidence which, in turn, enables them to achieve their full potential.

Maths ideas for using at home
Numbers and sums
Revision ideas for ks1 maths
Maths revision help

KS3 and KS4

KS3 & KS4 maths is a continuation of the foundation work covered in earlier years, so it is important to make sure all the concepts covered in primary school are understood fully before moving on.

Sequences and the nth term 2
Questions on angles for KS3
Area teaching ideas for KS3
Questions for year 7 maths

General maths

These worksheets can be used as reference for everyone.

Key ideas in the teaching of number
A dictionary of mathematics
Chart for help with maths revision
Formulae explained

Examination papers & tests

Here is a selection of typical examination and test papers for maths you will find through the Worksheet Finder.

Maths paper for entry to Prep school at 7
Revision & guidance for KS1 maths SATS 2
2008 KS2 maths test B
11+ Maths multichoice Paper 4
Maths optional-type Year 3
Progress tests 2006 maths 1
Progress in maths 14
AQA GCSE Maths Intermediate 1 2007

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