read, write and interpret mathematical statements involving addition (+), subtraction (−) and equals (=) signs 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. using concrete objects and pictorial representations, including those involving numbers, quantities and measures Pupils can explore and make conjectures about converting a simple fraction to a decimal fraction (for example, 3 ÷ 8 = 0.375). For simple fractions with recurring decimal equivalents, pupils learn about rounding the decimal to three decimal places, or other appropriate approximations depending on the context. Pupils multiply and divide numbers with up to 2 decimal places by one-digit and two-digit whole numbers. Pupils multiply decimals by whole numbers, starting with the simplest cases, such as 0.4 × 2 = 0.8, and in practical contexts, such as measures and money. Teachers may find this guidance helpful in planning and prioritising the curriculum following the coronavirus (COVID-19) pandemic. This guidance is intended to support teaching. It can be used alongside other high-quality plans and resources, including textbooks.

generate theoretical sample spaces for single and combined events with equally likely, mutually exclusive outcomes and use these to calculate theoretical probabilities add and subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractionsuse standard units of mass, length, time, money and other measures, including with decimal quantities become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately develop their use of formal mathematical knowledge to interpret and solve problems, including in financial mathematics

derive and apply formulae to calculate and solve problems involving: perimeter and area of triangles, parallelograms, trapezia, volume of cuboids (including cubes) and other prisms (including cylinders) Pupils understand the relation between non-unit fractions and multiplication and division of quantities, with particular emphasis on tenths and hundredths. They practise counting as reciting numbers and counting as enumerating objects, and counting in 2s, 5s and 10s from different multiples to develop their recognition of patterns in the number system (for example, odd and even numbers), including varied and frequent practice through increasingly complex questions.identify and represent numbers using objects and pictorial representations including the number line, and use the language of: equal to, more than, less than (fewer), most, least

describe, interpret and compare observed distributions of a single variable through: appropriate graphical representation involving discrete, continuous and grouped data; and appropriate measures of central tendency (mean, mode, median) and spread (range, consideration of outliers) Pupils both encounter and draw graphs relating 2 variables, arising from their own enquiry and in other subjects. appropriate measures of central tendency (including modal class) and spread {including quartiles and inter-quartile range} Pupils write statements about the equality of expressions (for example, use the distributive law 39 × 7 = 30 × 7 + 9 × 7 and associative law (2 × 3) × 4 = 2 × (3 × 4)). They combine their knowledge of number facts and rules of arithmetic to solve mental and written calculations for example, 2 x 6 x 5 = 10 x 6 = 60.They practise mental calculations with increasingly large numbers to aid fluency (for example, 12,462 – 2,300 = 10,162). Number - multiplication and division illustrate and name parts of circles, including radius, diameter and circumference and know that the diameter is twice the radius The principal focus of mathematics teaching in upper key stage 2 is to ensure that pupils extend their understanding of the number system and place value to include larger integers. This should develop the connections that pupils make between multiplication and division with fractions, decimals, percentages and ratio.

They understand the terms factor, multiple and prime, square and cube numbers and use them to construct equivalence statements (for example, 4 x 35 = 2 x 2 x 35; 3 x 270 = 3 x 3 x 9 x 10 = 9² x 10). They use larger numbers to at least 1,000, applying partitioning related to place value using varied and increasingly complex problems, building on work in year 2 (for example, 146 = 100 + 40 + 6, 146 = 130 +16). Mathematics is a creative and highly interconnected discipline that has been developed over centuries, providing the solution to some of history’s most intriguing problems. It is essential to everyday life, critical to science, technology and engineering, and necessary for financial literacy and most forms of employment. A high-quality mathematics education therefore provides a foundation for understanding the world, the ability to reason mathematically, an appreciation of the beauty and power of mathematics, and a sense of enjoyment and curiosity about the subject. Aims Pupils use the whole number system, including saying, reading and writing numbers accurately. Number - addition, subtraction, multiplication and division

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count up and down in hundredths; recognise that hundredths arise when dividing an object by 100 and dividing tenths by 10 solve problems involving percentage change, including: percentage increase, decrease and original value problems and simple interest in financial mathematics interpret and compare numbers in standard form A x 10 n 1≤A<10, where n is a positive or negative integer or 0 develop their mathematical knowledge, in part through solving problems and evaluating the outcomes, including multi-step problems identify properties of, and describe the results of, translations, rotations and reflections applied to given figures