# Write an expression in terms of n for the nth term of this sequence

They extend the use of the number line to connect fractions, numbers and measures. They connect estimation and rounding numbers to the use of measuring instruments. Number - multiplication and division Pupils should be taught to: With this foundation in arithmetic, pupils are introduced to the language of algebra as a means for solving a variety of problems.

At this stage, pupils should develop their ability to solve a wider range of problems, including increasingly complex properties of numbers and arithmetic, and problems demanding efficient written and mental methods of calculation.

They begin to understand unit and non-unit fractions as numbers on the number line, and deduce relations between them, such as size and equivalence. Geometry - properties of shapes Pupils should be taught to: Statistics Pupils should be taught to: Number - fractions including decimals and percentages Pupils should be taught to: This should include correspondence questions such as the numbers of choices of a meal on a menu, or 3 cakes shared equally between 10 children.

They read, write and use pairs of co-ordinates, for example 2, 5including using co-ordinate-plotting ICT tools. Pupils understand the relation between unit fractions as operators fractions ofand division by integers.

Number - fractions including decimals Pupils should be taught to: They continue to use number in context, including measurement. Pupils learn decimal notation and the language associated with it, including in the context of measurements.

Number - addition and subtraction Pupils should be taught to: Pupils extend and apply their understanding of the number system to the decimal numbers and fractions that they have met so far. They use and understand the terms factor, multiple and prime, square and cube numbers.

Pupils practise adding and subtracting fractions with the same denominator through a variety of increasingly complex problems to improve fluency. They should be able to describe the properties of 2-D and 3-D shapes using accurate language, including lengths of lines and acute and obtuse for angles greater or lesser than a right angle.

Pupils connect decimals and rounding to drawing and measuring straight lines in centimetres, in a variety of contexts. Pupils are taught throughout that decimals and fractions are different ways of expressing numbers and proportions.

Pupils compare and order angles in preparation for using a protractor and compare lengths and angles to decide if a polygon is regular or irregular.

They should go beyond the [0, 1] interval, including relating this to measure. Year 4 programme of study Number - number and place value Pupils should be taught to: Pupils understand the relation between non-unit fractions and multiplication and division of quantities, with particular emphasis on tenths and hundredths.

Pupils practise to become fluent in the formal written method of short multiplication and short division with exact answers see Mathematics appendix 1.

They use multiplication to convert from larger to smaller units. This should develop the connections that pupils make between multiplication and division with fractions, decimals, percentages and ratio.

They apply all the multiplication tables and related division facts frequently, commit them to memory and use them confidently to make larger calculations.

They begin to extend their knowledge of the number system to include the decimal numbers and fractions that they have met so far. They practise counting using simple fractions and decimals, both forwards and backwards. They should recognise and describe linear number sequences for example, 3, 34, 4 …including those involving fractions and decimals, and find the term-to-term rule in words for example, add.

In this way they become fluent in and prepared for using digital hour clocks in year 4. Pupils continue to practise adding and subtracting fractions with the same denominator, to become fluent through a variety of increasingly complex problems beyond one whole. Pupils use both analogue and digital hour clocks and record their times.

Pupils draw symmetric patterns using a variety of media to become familiar with different orientations of lines of symmetry; and recognise line symmetry in a variety of diagrams, including where the line of symmetry does not dissect the original shape.

Roman numerals should be put in their historical context so pupils understand that there have been different ways to write whole numbers and that the important concepts of 0 and place value were introduced over a period of time.

Measurement Pupils should be taught to: Pupils should read, spell and pronounce mathematical vocabulary correctly. This includes relating the decimal notation to division of whole number by 10 and later Teaching in geometry and measures should consolidate and extend knowledge developed in number.

The decimal recording of money is introduced formally in year 4.To find the nth term of a fraction, find the pattern in the first few terms of the sequence for the numerator and denominator. Then write a general expression for the sequence of fractions in terms of the variable "n." First find the pattern in the numerators of the fraction sequence.