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Maths Band 6 Long Term Planning Autumn 1 Autumn 2 Mrs Howell/Mrs Cornelius Week 1 Week 2 Week 3 Week 4 Place value Place value Statistics (data/timetables) * Read, write, order and compare numbers up to 10, 000,000 and determine the value of each digit * Solve number and practical problems * Read, write, order and compare numbers up to 10, 000,000 and determine the value of each digit * Round any whole number to a degree of accuracy * Use negative numbers in context and calculate intervals across 0 * Solve number and practical problems that involve all of the above * Interpret and construct pie charts and line graphs and use these to solve problems. (Robinwood) Additions & subtraction * Perform mental Ratio & Proportion Measurement * Measurement (Perimeter, area and volume) * Recognise that shapes with the same areas have different perimeters and vice versa * Recognise when it is possible to use formulae for area and volume of shapes * Calculate the area of parallelograms and triangles * Calculate, * Solve problems involving the relative sizes of 2 quantities where missing values can be found by using integer multiplication and division facts. * Solve problems involving the calculation of percentages (for Week 5 Week 6 Multiplication & Multiplication & division division calculations, including with mixed operations and large numbers * Identify common factors, common multiples and prime numbers * Use their knowledge of the order of operations to carry out calculations involving the four operations * 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, fractions, or by rounding, as appropriate for the context. * Divide numbers up to 4 digits by a two digit number using the formal written method of short division where appropriate, interpreting remainders according to the context. * Solve addition and subtraction multi-step problems in context, deciding which operations and methods to use and why. * 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 mixed operations and large numbers * Identify common factors, common multiples and prime 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 * Use estimation to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy. Geometry Fractions 4 operations Geometry – circles and angles * Compare and classify geometric shapes based on their properties and sizes and find unkown angles in any triangles, quadrilaterals, and regular polygons * Illustrate and name parts of circles, including radius, diameter and * Multiply simple pairs of proper fractions, writing the answer in its simplest form (e.g. ¼ x ½ =1/8) * Divide proper fractions by whole numbers, e.g. 1/3 ÷ 2 = 1/6 * Identify the value of each digit in numbers given to 3 decimal places and multiply and divide numbers by 10, 100 and 1000 giving answers up to – Addition, subtraction, multiplication and division * Perform mental calculations, including with mixed operations and large numbers * Identify common factors, common multiples and prime numbers * Multiply multi-digit numbers up to 4 digits Additional week on written methods as children struggled. Measurement – Measurement * Solve problems involving the calculation and conversion of units of measure, using deimal notation up to 3 decimal places where appropriate. * Use, read, write and convert between standard units, converting measurements of length, Week 7 Week 8 Fractions Algebra * To compare and order fractions, including fractions >1 * To use common factors to simplify fractions; use common multiples to express fractions in the same denominations * To associate a fraction with division and calculate decimal fraction equivalents for a simple fraction. * To add and subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractions. * Use simple formulae * Generate and describe linear sequences * Express missing number problems algebraically * Find pairs of numbers that satisfy an equation with 2 unknowns * Enumerate possibilities of combinations of 2 variables N/A N/A example, of measures 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. estimate and compare volume of cubes and cuboids using standard units, including cubic centimetres (cm3) and cubic metres (m3), and extending to other units (e.g. mm3 and km3) circumference and know that the diameter is twice the radius * Recognise angles where they meet at a point, are on a straight line, or are vertically opposite, and find missing angles. 3 decimal places. * Recall and use equivalences between simple fractions, decimals and percentages, including in different contexts. by a two-digit whole number using the formal written method of long multiplication * Use their knowledge of the order of operations to carry out calculations involving the four operations * 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, fractions, or by rounding, as appropriate for the context. * Divide numbers up to 4 digits by a two digit number using the formal written method of short division where appropriate, interpreting remainders according to the context. * Solve addition and subtraction multi-step problems in context, deciding which operations and methods to use and why. * Use estimation to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy. mass, volume and time from a smaller unit of measure to a larger unit, and vise versa, using decimal notation up to 3 decimal places. * Convert between miles and kilometres Spring 1 Geometry * Recognise, describe and build 3D shapes, including nets. * Describe positions on the full coordinate grid (all 4 quadrants) * Draw and translate simple shapes on the coordinate plane, and reflect them in the axis. Number – number and place value * Read, write, order and compare numbers up to 10, 000,000 and determine the value of each digit * Round any whole number to a degree of accuracy * Use negative numbers in context and calculate intervals across 0 * Solve number and practical problems that involve all of the above Fraction – multiplying and dividing decimals * To multiply one-digit numbers with up to two decimal places by whole numbers. * To use written division methods in cases where the answer has up to two decimal places. * To use written division methods in cases where the answer has up to two decimal places. * To solve problems which require answers to be rounded. Spring 2 Geometry Recognise, describe and build 3D shapes, including nets. Geometry – circles and angles Compare and classify geometric shapes based on their properties and sizes and find unknown angles in any triangles, quadrilaterals, and regular polygons Illustrate and name parts of circles, including radius, diameter and circumference and know that the diameter is twice the radius Recognise angles where they meet at a point, are on a straight line, or are vertically opposite, and find missing angles. Number – number and place value Read, write, order and compare numbers up to 10, 000,000 and determine the value of each digit Round any whole number to a degree of accuracy Use negative numbers in context and calculate intervals across 0 Solve number and practical problems that involve all of the above – Addition, subtraction, multiplication and division 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 and interpret remainders as whole number remainders, fractions, or by rounding, as appropriate for the context. Ratio and Proportion Solve problems involving the relative sizes of 2 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 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. – Measurement Solve problems involving the calculation and conversion of units of measure, using decimal notation up to 3 decimal places where appropriate. Use, read, write and convert between Ratio and Proportion * Solve problems involving the relative sizes of 2 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 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. Algebra * Use simple formulae * Generate and describe linear sequences * Express missing number problems algebraically * Find pairs of numbers that satisfy an equation with 2 unknowns * Enumerate possibilities of combinations of 2 variables Statistics – data/timetables * Interpret and construct pie charts and line graphs and use these to solve problems. *Calculate and interpret the mean as an average. N/A N/A N/A N/A N/A Revision with a focus on problem solving Fractions To compare and order fractions, including fractions >1 To use common factors to simplify fractions; use common multiples to express fractions in the same denominations To associate a fraction with division and calculate decimal fraction equivalents for a simple fraction. To 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 (e.g. ¼ x ½ =1/8) Divide proper fractions by whole numbers, e.g. 1/3 ÷ 2 = 1/6 * Identify the value of each digit in numbers given to 3 decimal places and multiply and divide numbers by 10, 100 and 1000 giving answers up to 3 decimal places. Recall and use equivalences between – Geometry Recognise, describe and build 3D shapes, including nets. Describe positions on the full coordinate grid (all 4 quadrants) Draw and translate simple shapes on the coordinate plane, and reflect them in the axis. Statistics – data/timetables Interpret and construct pie charts and line graphs and use these to solve problems. Calculate and interpret the mean as an average. Summer 1 Geometry – circles and angles Compare and classify geometric shapes based on their properties and sizes and find unknown angles in any triangles, quadrilaterals, and regular polygons Illustrate and name parts of circles, including radius, diameter and circumference and know that the diameter is twice the radius Recognise angles where they meet at a point, are on a straight line, or are vertically opposite, and find missing angles – Geometry Recognise, describe and build 3D shapes, including nets. Describe positions on the full coordinate grid (all 4 quadrants) Draw and translate simple shapes on the coordinate plane, and reflect them in the axis. Statistics – data/timetables Interpret and construct pie charts and line graphs and use these to solve problems. Calculate and interpret the mean as an average Divide numbers up to 4 digits by a two-digit number using the formal written method of short division where appropriate, interpreting remainders according to the context. Solve addition and subtraction multi-step problems in context, deciding which operations and methods to use and why. Use estimation to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy. Ratio and Proportion Solve problems involving the relative sizes of 2 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 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. – Measurement Solve problems involving the calculation and conversion of units of measure, using decimal notation up to 3 decimal places where appropriate. Use, read, write and convert between standard units, converting measurements of length, mass, volume and time from a smaller unit of measure to a larger unit, and vise versa, using decimal notation up to 3 decimal places standard units, converting measurements of length, mass, volume and time from a smaller unit of measure to a larger unit, and vise versa, using decimal notation up to 3 decimal places Convert between miles and kilometres simple fractions, decimals and percentages, including in different contexts. Algebra Use simple formulae Generate and describe linear sequences Express missing number problems algebraically Find pairs of numbers that satisfy an equation with 2 unknowns Enumerate possibilities of combinations of 2 variables Fractions To compare and order fractions, including fractions >1 To use common factors to simplify fractions; use common multiples to express fractions in the same denominations To associate a fraction with division and calculate decimal fraction equivalents for a simple fraction. To 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 (e.g. ¼ x ½ =1/8) Divide proper fractions by whole numbers, e.g. 1/3 ÷ 2 = 1/6 * Identify the value of each digit in numbers given to 3 decimal places and multiply and divide numbers by 10, 100 and 1000 giving answers up to 3 decimal places. Recall and use equivalences between simple fractions, decimals and percentages, including in different contexts. Algebra Number – number and place value Read, write, order and compare numbers up to 10, 000,000 and determine the value of each digit Round any whole number to a degree of accuracy Use negative numbers in context and calculate intervals across 0 Solve number and practical problems that involve all of the above – Addition, subtraction, multiplication and division 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 and interpret remainders as whole number remainders, fractions, or by rounding, as appropriate for the context. Divide numbers up to 4 digits by a two-digit number using the formal written method of short division where appropriate, interpreting remainders according to the context. SAT’s Band 7 place value Rounding numbers using significant figures. Solving problems and equations using trial and improvement methods. Using significant figures to estimate the answers to difficult calculations Understanding that all measurements are approximate. Finding the bounds between which a rounded measurement lies. Looking at powers beyond squares and cubes. Introducing the laws of indices - dealing with multiplication, division and brackets. Band 7 fractions Dividing one fraction by another. Multiplying two decimals N/A Convert between miles and kilometres Summer 2 Band 7 algebra Linking coordinates, equations and graphs by plotting simple lines. Linking coordinates, equations and graphs by plotting lines with different gradients. Simplifying expressions such as a+a+b+b+b. Simplifying expressions such as 2a×3a. Expanding by multiplying a term over a single brackets such as 3(3x-2). Expanding and simplifying expressions such as (3x+2)(2x+5). Factorising by taking out common factors. Understanding how to solve equations where the variable appears on both sides. Band 7 ratio and proportion Using multipliers to calculate percentage increases and decreases. Writing one number as a percentage of another, and working out the change as a percentage. Calculating densities using the formula mass divided by volume. Use simple formulae Generate and describe linear sequences Express missing number problems algebraically Find pairs of numbers that satisfy an equation with 2 unknowns Enumerate possibilities of combinations of 2 variables Band 7 measurement Understanding and using simple interest, sometimes called flat rate. Knowing that people can be paid in different ways. Understanding wages and salaries. Looking at other ways of earning money, including piecework, commission and casual work. Looking at different ways to pay for goods such as cash, credit cards and hire purchase. Learning to manage your money based on good budgeting will help you make better use of your earnings and avoid getting into debt. Solve addition and subtraction multi-step problems in context, deciding which operations and methods to use and why. Use estimation to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy. Band 7 geometry Compare and classify geometric shapes based on their properties and sizes and find unknown angles in any triangles, quadrilaterals, and regular polygons Alternate angles, supplementary angles and corresponding angles on parallel lines. Discover your own rules. Internal and external angles of polygons. Understand and use the formula for the sum of the interior angles of a polygon with n sides. The circumference of a circle is PI × diameter. The area of a circle relies on a value called PI which is roughly 3.14159265358979323 Understanding rotational symmetry and rotating simple shapes. Year 7 statistics Types of data, advantages and disadvantages of primary and secondary data, and population, census and sample. How to take a random, systematic or stratified sample from a population. Designing questionnaires, and problems including bias and missing data. Scatter graphs and correlation. An excellent way to show whether or not two sets of data are linked in some way, or correlated. Drawing the line of best fit through the mean point, and finding the equation of the line. Band 7 probability Using words and ideas of probability and the probability scale. Listing outcomes from two events using sample space diagrams. N/A N/A