Multiplication and Division of Fractions multiply proper fractions and mixed numbers by whole numbers, supported by materials and diagrams multiply simple pairs of proper fractions, writing the answer in its simplest form (e.g. 1/4 × 1/2 = 1/8) multiply one-digit numbers with up to two decimal places by whole numbers divide proper fractions by whole numbers (e.g. 1/3 ÷ 2 = 1/6) Multiplication and Division of Decimals multiply one-digit numbers with up to two decimal places by whole numbers find the effect of dividing a or two-digit number by 10 and 100, identifying the value of the digits in the answer as ones, tenths and hundredths multiply and divide numbers by 10, 100 and 1000 where the answers are up to three decimal places identify the value of each digit to three decimal places and multiply and divide numbers by 10, 100 and 1000 where the answers are up to three decimal places associate a fraction with division and calculate decimal fraction equivalents (e.g. 0.375) for a simple fraction (e.g. 3/8) use written division methods in cases where the answer has up to two decimal places Problem Solving solve problems that involve all of the above solve problems involving increasingly harder fractions to calculate quantities, and fractions to divide quantities, including fractions where the answer is a whole number solve problems involving numbers up to three decimal places solve simple measure and money problems involving fractions and decimals to two decimal places. solve problems which require knowing percentage and decimal equivalents of 1/2, 1/4, 1/5, 2/5, 4/5 and those with a denominator of a multiple of 10 or 25. Ratio and Proportion solve problems involving the relative sizes of two quantities where missing values can be found by using integer multiplication and division facts solve problems involving the calculation of percentages [for example, of measures, and such as 15% of 360] and the use of percentages for comparison solve problems involving similar shapes where the scale factor is known or can be found solve problems involving unequal sharing and grouping using knowledge of fractions and multiples
Early Years Key Stage 1 Lower Key Stage 2 Upper Key Stage 2 Strand Reception Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Algebra Equations solve one-step problems that involve addition and subtraction, using concrete objects and pictorial representations, and missing number problems such as 7 = * - 9 (copied from Addition and Subtraction) recognise and use the inverse relationship between addition and subtraction and use this to check calculations and missing number problems. (copied from Addition and Subtraction) solve problems, including missing number problems, using number facts, place value, and more complex addition and subtraction. (copied from Addition and Subtraction) use the properties of rectangles to deduce related facts and find missing lengths and angles (copied from Geometry: Properties of Shapes) express missing number problems algebraically solve problems, including missing number problems, involving multiplication and division, including integer scaling (copied from Multiplication and Division) recall and use addition and subtraction facts to 20 fluently, and derive and use related facts up to 100 (copied from Addition and Subtraction) find pairs of numbers that satisfy number sentences involving two unknowns represent and use number bonds and related subtraction facts within 20 (copied from Addition and Subtraction) enumerate all possibilities of combinations of two variables Formulae Perimeter can be expressed algebraically as 2(a + b) where a and b are the dimensions in the same unit. (Copied from NSG measurement) use simple formulae recognise when it is possible to use formulae for area and volume of shapes (copied from Measurement) Sequences sequence events in chronological order using language such as: before and after, next, first, today, yesterday, tomorrow, morning, afternoon and evening (copied from Measurement) compare and sequence intervals of time (copied from Measurement) generate and describe linear number sequences order and arrange combinations of mathematical objects in patterns (copied from Geometry: position and direction)