Medium Term Plans Year 6 NB- These plans are not static and will change year on year and sometimes within a year depending on cohort needs and knowledge and understanding needs. Year 6 big ideas NUMBER AND PLACE VALUE Numbers can be ordered based on the number of digits but this does not apply to decimal numbers For numbers with the same number of digits or decimals, we order based on the size of the most significant digits Numbers can be broken down in different ways, e.g. 4000 can be described as 4 thousands or 40 hundreds or 400 tens Large quantities are hard to estimate - benchmarks can help e.g. 60 000 people went to the match; 3 million people live in Wales Numbers can be rounded in different ways and not always to powers of 10 e.g. 374 rounded to the nearest 50 is 350 NUMBER ADDITION AND SUBTRACTION Number facts can be approximated or calculated by adjusting numbers, e.g. 3415-2996 is equivalent to 3419-3000 The most appropriate method for calculation can differ depending on the numbers involved Using estimates or different calculation strategies reduce the likelihood of errors NUMBER MULTIPLICATION AND DIVISION Some calculations involving large numbers can be done mentally; others require written methods Many new number facts can be derived from a number sentence e.g. 24×16 = 384 so 12×32 = 384 and 24×8 = 192 Multiplication and division is used in a range of areas of mathematics e.g. calculating fractions, finding prime numbers NUMBER FRACTIONS The size of a fraction is inversely related to the size of the denominator and directly related to the size of the numerator Fractions can be compared using benchmarks e.g. how far they are from 0, 1/2 or 1 or by finding equivalent fractions Different fraction questions use the same ideas and skills e.g. finding fractions of quantities and ratio ALGEBRA = means ‘the same as’ e.g. 4a = 20-b Letters or symbols are used for unknown values Equations can be used to represent problems more simply Sequences follow patterns which can be represented in different ways e.g. in pictures, with words, with formulae MEASUREMENT Measurements can be compared when they are converted into the same unit Benchmark measures help when estimating e.g. the park is 1km away so... a bag of sugar is 1kg so… The relationship between the area and perimeter of a shape is complex e.g. doubling the area doesn’t double the perimeter GEOMETRY The transformation of a 2D net into a 3D shape can be visualised Shapes with different numbers of sides and vertices can still share other characteristics Shapes can belong to more than one classification e.g. a square is a rhombus and a rectangle Properties of shapes are interdependent e.g. a rectangle has parallel lines because it has four right-angles STATISTICS Graphs can be used to make inferences and deductions as well as for retrieving information The type of graph used will depend on the type of data being shown e.g. bar charts can be used for discrete data (information counted in set groups); line graphs can be used to show continuous data (information measured where ‘in-between’ values exist) When displaying discrete data, pie charts show relative proportions whereas bar graphs show quantities

WEEK

AUTUMN

SPRING

SUMMER

1-3

read, write, order and compare numbers up to 10 000 000 and determine the value of each digit • round any whole number to a required degree of accuracy • solve number and practical problems that involve all of the above

perform mental calculations, including with mixed operations and large numbers • use their knowledge of the order of operations to carry out calculations involving the four operations

use knowledge of the order of operations to carry out calculations involving the four operations • solve problems involving addition, subtraction, multiplication and division • use estimation to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy

perform mental calculations, including with large numbers • solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why • solve problems involving addition, subtraction, multiplication and division • use estimation to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy recognise, describe and build simple 3-D shapes, including making nets

solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why • solve problems involving addition, subtraction, multiplication and division use negative numbers in context, and calculate intervals across zero use simple formulae • generate and describe linear number sequences • express missing number problems algebraically • find pairs of numbers that satisfy an equation with two unknowns • enumerate possibilities of combinations of two variables draw 2-D shapes using given dimensions and angles • compare and classify geometric shapes based on their properties and sizes and find unknown angles in any triangles, quadrilaterals, and regular polygons

use simple formulae • generate and describe linear number sequences • express missing number problems algebraically • find pairs of numbers that satisfy an equation with two unknowns • enumerate possibilities of combinations of two variables draw shapes accurately, using measuring tools and conventional markings and labels for lines and angles * • illustrate and name parts of circles, including radius, diameter and circumference and know that the diameter is twice the radius

4-6

perform mental calculations, including with large numbers • solve problems involving addition, subtraction, multiplication and division • use estimation to check answers to calculations

use common factors to simplify fractions; use common multiples to express fractions in the same denomination • compare and order fractions, including fractions > 1 • add and subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractions

describe positions on the full coordinate grid (all four quadrants) • draw and translate simple shapes on the coordinate plane, and reflect them in the axes

• recognise angles where they meet at a point, are on a straight line, or are vertically opposite, and find missing angles practise multiplication for larger numbers, using the formal written method of long multiplication* • multiply multi-digit numbers up to 4 digits by a two digit whole number using the formal written method of long multiplication • perform mental calculations, including large numbers • use estimation to check answers to calculations 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 * • perform mental calculations • use estimation to check answers to calculations multiply one-digit numbers with up to two decimal places by whole numbers solve problems involving the calculation and conversion of units of measure, using decimal notation up to three decimal places where appropriate • use, read, write and convert between standard units, converting measurements of mass from a smaller unit of

multiply multi-digit numbers up to 4 digits by a two digit whole number using the formal written method of long multiplication • solve problems involving addition, subtraction, multiplication and division • use estimation to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy multiply one-digit numbers with up to two decimal places by whole numbers use common factors to simplify fractions; use common multiples to express fractions in the same denomination • add and subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractions Multiply simple pairs of proper fractions, writing the answer in its simplest form [for example, 1/4 × 1/2 = 1/8]. Divide proper fractions by whole numbers [for example, 1/3 ÷ 2 = 1/6]. solve problems involving the calculation and conversion of units of measure, using decimal notation up to three decimal places where appropriate • use, read, write and convert between standard units, converting measurements of volume from a smaller unit of measure to a larger unit, and vice versa, using decimal notation up to three decimal places

7-9

solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why • solve problems involving addition, subtraction, multiplication and division • use estimation to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy identify the value of each digit in numbers given to three decimal places and multiply and divide numbers by 10, 100 and 1000 giving the answers up to three decimal places solve problems which require answers to be rounded to specified degrees of accuracy solve problems involving the calculation and conversion of units of measure, using decimal notation up to three decimal places where appropriate • use, read, write and convert between standard units,

measure to a larger unit, and vice versa, using decimal notation up to three decimal places

• recognise when it is possible to use formulae for volume of shapes • calculate, estimate and compare volume of cubes and cuboids using standard units, including cubic centimetres (cm3) and cubic metres (m3), and extending to other units [for example, mm3]

use common factors to simplify fractions; use common multiples to express fractions in the same denomination • add and subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractions

perform mental calculations, including with mixed operations and large numbers • use their knowledge of the order of operations to carry out calculations involving the four operations • solve problems involving addition, subtraction, multiplication and division

Multiply simple pairs of proper fractions, writing the answer in its simplest form [for example, 1/4 × 1/2 = 1/8]. Divide proper fractions by whole numbers [for example, 1/3 ÷ 2 = 1/6]. 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 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 interpret and construct pie charts and line graphs

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 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 describe positions on the full coordinate grid (all four quadrants) • draw and translate simple shapes on the coordinate plane, and reflect them in the axes

10-12

converting measurements of length from a smaller unit of measure to a larger unit, and vice versa, using decimal notation up to three decimal places • convert between miles and kilometres divide numbers up to 4 digits by a two-digit number using the formal written method of short division where appropriate • perform mental calculations, including with large numbers • identify common factors, common multiples and prime numbers • solve problems involving addition, subtraction, multiplication and division • use estimation to check answers to calculations associate a fraction with division and calculate decimal fraction equivalents [for example, 0·375] for a simple fraction [for example, 3 8] • recall and use equivalences between simple fractions, decimals and percentages • solve problems involving the calculation of percentages [for example, of measures, and such as 15% of 360] and the use of percentages for comparison use, read, write and convert between standard units, converting measurements of time from a smaller unit of

and use these to solve problems calculate and interpret the mean as an average

divide numbers up to 4 digits by a two-digit whole number using the formal written method of long division, and interpret remainders as whole number remainders or fractions • perform mental calculations, including with large numbers • use estimation to check answers to calculations

perform mental calculations • solve problems involving addition, subtraction, multiplication and division • solve problems which require answers to be rounded to specified degrees of accuracy • use estimation to check answers to calculations • perform mental calculations • use estimation to check answers to calculations use written division methods in cases where the answer has up to two decimal places

recognise that shapes with the same areas can have

multiply multi-digit numbers up to 4 digits by a two-digit whole number using the formal written method of long multiplication • divide numbers up to 4 digits by a two-digit whole number using the formal written method of long division • divide numbers up to 4 digits by a two-digit number using the formal written method of short division where appropriate • perform mental calculations • identify common factors, common multiples • solve problems involving addition, subtraction, multiplication and division • solve problems which require answers to be rounded to specified degrees of accuracy • use estimation to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy multiply one-digit numbers with up to two decimal places by whole numbers • use written division methods in cases where the answer has up to two decimal places associate a fraction with division and calculate decimal fraction equivalents [for example, 0·375] for a simple fraction [for example, 3 8]

measure to a larger unit, and vice versa

different perimeters and vice versa • recognise when it is possible to use formulae for area of shapes • calculate the area of parallelograms and triangles

• solve problems which require answers to be rounded to specified degrees of accuracy • recall and use equivalences between simple fractions, decimals and percentages, including in different contexts • solve problems involving the calculation of percentages [for example, of measures, and such as 15% of 360] and the use of percentages for comparison interpret and construct pie charts and line graphs and use these to solve problems calculate and interpret the mean as an average