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Programme Of Study For Key Stage 3 Mathematics

These are the Transum resources related to the statement: "Pupils should be taught 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"

Here are some specific activities, investigations or visual aids we have picked out. Click anywhere in the grey area to access the resource.

- Arithmagons An extensive collection of Arithmagons arranged in levels according to their features. Find the missing numbers in these online, self-checking exercises and discover the wonders of Arithmagons.
- Basic Addition A self marking exercise on addition with increasing levels of difficulty.
- Beat The Clock It is a race against the clock to answer 30 mental arithmetic questions. There are nine levels to choose from.
- Bidmaze Find your way through the maze encountering mathematical operations in the correct order to achieve the given total.
- Decimal Plus Practise mental and written methods for adding and subtracting decimal numbers.
- Discombobulated A fun game requiring you to find numbers which add up to the target number as quickly as possible.
- Expedite Drag the numbered cards to produce a multiplication fact. Complete twenty mixed times tables questions to earn a trophy.
- Formal Written Methods Examples of formal written methods for addition, subtraction, multiplication and division.
- Fractions A series of self-marking exercises on adding, subtracting, multiplying and dividing fractions.
- Heptaphobia Research Use written methods to answer ten arithmetic questions. When you have finished you will find the results of this amazing research.
- Mixed Numbers A self marking quiz about the application of the four operations to mixed numbers.
- Multiplying and Dividing Decimals A straight forward, no nonsense demonstration of the methods of multiplying and dividing decimals.
- Negative Numbers Use negative numbers in basic arithmetic and algebraic calculations and word problems.
- Number Line This number line visual aid is designed to be projected onto a whiteboard for whole class exposition.
- Number Line Banner A printable banner (multiple A4 sheets) of a colourful number line for the classroom wall.
- Number Skills Inventory A checklist of basic numeracy techniques that every pupil should know.
- Powten Practise multiplying and dividing by powers of ten without using a calculator.
- Quickulations A mental arithmetic visual aid that displays random calculations then after a few seconds displays the answers.
- Thai Restaurant Calculate the restaurant bills for each of the tables in the Thai Restaurant.

Here are some exam-style questions on this statement:

- "
*Without using your calculator, work out the value of the following calculations giving each answer as a fraction in its lowest terms. You must show all your working.**(a)*" ... more - "
*Unit fractions have numerators equal to 1, for example \(\frac12\),\(\frac19\) and \(\frac{1}{36}\).*" ... more

Click on a topic below for suggested lesson starters, resources and activities from Transum.

- Arithmetic The ability to perform mathematical calculations is still very important despite our hi-tech environment. Good numeracy skills support the understanding of more advanced mathematical concepts at all levels. Mathematicians still consider mastery of the manual algorithms to be a necessary foundation for the study of algebra and computer science. Pupils should have a good grasp of the meaning of numbers and use their understanding of place value to multiply and divide whole numbers and fractions. They should be able to order, add and subtract negative numbers in context. They should use all four operations with decimals rounding answers where required. They should be able to solve simple problems involving ratio and direct proportion and calculate fractional or percentage parts of quantities and measurements, using a calculator where appropriate. See also the Mental Methods topic and our Number Skills Inventory.
- Decimals Working with decimals, for most pupils, presents little difficulty if the pupils have confidence working with whole numbers. The topic of decimals provides an extension to the place value system with the addition of tenths, hundredths, thousandths etc. For many pen and paper multiplication and division calculations the decimal numbers can be considered as whole numbers then the answers adjusted accordingly. So 2.4 x 2.34 can be considered as 24 x 234 รท 1000. The numbers are multiplied by ten and one hundred respectively then the answer needs to be divided by the ten and one hundred to compensate. Pupils should use their understanding of place value to round decimal numbers. They should also use decimal numbers in the context of measures and money. This topic also contains activities which encourage pupils to investigate and explore the properties of decimal numbers and gain a better understanding of them.
- Fractions A fraction is a part of a number. Fractions are either vulgar or decimal. Vulgar fractions can be proper, improper or mixed. Equivalent fractions have the same value. Pupils, at all stages of their learning, should practise using fractions. From dealing with halves, the most basic fraction, to manipulating algebraic fractions containing surds, this topic is always relevant. Proficiency also depends on reasonable numeracy skills particularly the multiplication tables and finding the lowest common multiple of two numbers. Pupils also need to be able to convert vulgar fractions to decimals and percentages and vice versa. Be wary of teaching the 'rules' for manipulation fractions by rote. Pupils need to understand the reason why and the time-honoured key to understanding starts with the imaginary pizza and the much-used fraction wall.
- Mental Methods Though using pencil and paper are as useful as having up-to-date technology skills, there is no substitute for strategic mental methods for working out calculations and solving problems. The activities in this topic are designed to improve pupils' abilities to use their brains. Calculating 'in your head' can be a difficult task. If you cannot remember what you have worked out or simply do not know how to solve a problem then it can be very challenging and frustrating. It is important to learn and practise mental arithmetic and using mathematical patterns, you can dramatically improve the speed and accuracy of your mental mathematics. See also the Arithmetic topic and our Number Skills Inventory.
- Negative Numbers A negative number is a real number that is less than zero. Such numbers are often used to represent the amount of a loss or absence. For example, a debt that is owed may be thought of as a negative asset, or a decrease in some quantity may be thought of as a negative increase. Negative numbers are also used to describe values on a scale that goes below zero, such as the Celsius and Fahrenheit scales for temperature. Here are some activities designed to strengthen a pupil's understanding of negative numbers.
- Tables Times Tables is the common term referring to the multiples of numbers 2 to 12 (or 2 to 10). Having a quick recall of these tables is an important pre-requisite for studying other aspects of mathematics and for coping with personal finance and other area of everyday live involving numbers. People of any age can improve their skills in recalling table facts. They should learn then as they would learn a song or a dance. You need to know your times tables forwards, backwards and all mixed up. Spend time learning them well and you'll reap the benefits in future. Here on this website we have developed many activities that help pupils learn their times tables and as then revise them in different ways so that the recall becomes easier and easier. Some of the activities are games and quizzes while others help pupils spot the patterns in the times tables in many different ways. Here's a plan for learning a new times table in only five days!