A summary of maths in year 5


 Frederica McCoy
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1 Handale Primary School Maths Curriculum Year 5 (910 years old) A summary of maths in year 5 In Year 5 pupils extend their understanding of the number system and place value to include larger numbers, including millions. Pupils recognise the connections between fractions, decimals, percentages and ratio and how these relate to division and multiplication. Their knowledge of and use of negative numbers is developed from year 4 and prime, square and cube numbers are introduced. When solving problems involving addition, subtraction, multiplication and division, pupils are expected to be using an efficient formal written method of calculation. The basics of algebra are taught explicitly for the first time and pupils add, subtract and order fractions. Pupil s o a ular of D a d D shapes is de eloped a d the are taught to al ulate area a d olu e. Pupils also compare basic imperial and metric measurements and solve problems involving angles on a straight line and around a point. In year 5 the maths curriculum is taught in 5 strands: NUMBER SENSE ADDITIVE REASONING MULTIPLICATIVE REASONING GEOMETRIC REASONING FRACTIONS For more details, the medium term plan that teachers use to deliver maths in year 5 can be viewed here.
2 YEAR 5 NUMBER SENSE Number sense is taught in 3 units totalling 6 weeks. UNIT 5.1 Pupils can represent and explain how to multiply and divide by 10, 100 and They make appropriate decisions about when to use their understanding of counting, place value and rounding for solving problems including adding and subtracting. Pupils extend counting from Year 4, using decimals and fractions including below zero, for example on a number line. Pupils say, read and write decimal fractions and related tenths, hundredths and thousandths accurately and are confident in checking the reasonableness of their answers to problems. They extend their knowledge of fractions to thousandths and connect to decimals and measures. Can you explain and represent how you know that 71.7 m is greater than 71.57m? Can you explain why it is easy to subtract 0.7 m from 71.7 m Can you show why rounding 71.7m and 71.57m to the nearest metre gives the same result? Can you suggest other numbers that would also round to 72 m? UNIT 5.5 Pupils can make appropriate decisions about when to use their understanding of counting (including negative numbers), place value and rounding for solving problems including adding and subtracting. Pupils can read and write threedigit positive numbers as Roman numerals. Pupils use their knowledge of place value and multiplication and division to convert between standard units of measurement, e.g. from kilometres to metres; metres to centimetres; kilograms to grams; litres to millilitres. Pupils should recognise and describe linear number sequences, including those involving fractions and decimals, and be able to extend these finding the termtoterm rule. Can you explain and represent how you know that 206 is greater than 206 and explain why it is easier to subtract 6 from 206 than 206? Can you explain and represent the difference between the day time temperature in the desert, 53, and a night time temperature of 7? Can you explain how to represent 206 in Roman numerals but why this is not possible for 20.6? UNIT 5.10 Pupils can use their knowledge of how to multiply and divide by 10, 100 and 1000 to convert between different units of measures. Pupils use their knowledge of place value and multiplication and division to convert between standard units of measurement Pupils continue to develop their skills in applying place value knowledge to problem solving. Pupils recognize, describe and extend more complex linear number sequences. Can you explain and represent how you know which is a better deal: a 1.5 litre bottle of orange juice for 4.50 or a 500ml bottle of orange juice for 1.75?
3 YEAR 5 ADDITIVE REASONING Additive Reasoning is taught in 3 units totalling 7 weeks. UNIT 5.2 Pupils can solve addition and subtraction problems in different contexts using their understanding of place value and their mental and written methods. Pupils practise using the formal written methods of column addition and subtraction with increasingly large numbers to aid fluency. They practise adding and subtracting decimals including a mix of whole numbers and decimals and decimals with different numbers of decimal places. Pupils continue to develop their mental addition and subtraction with increasingly large numbers and decimal numbers Pupils draw, read and interpret time graphs and can comment upon which graphs and charts are most appropriate for a given set of data. When given a table of data showing distances between major cities in the world, can you find pairs of numbers where you would use a mental method to find the difference or total; and pairs of numbers where you would use a written method to find the difference or total? UNIT 5.6 Pupils can solve addition and subtraction problems in different contexts and involving decimal numbers. Pupils can estimate the answers to problems and comment on the accuracy of their answer. Pupils continue to develop their written methods of column addition and subtraction, applied to more complex problems. When asked to solve kg kg and kg 75.9 kg, can you round each part of the calculation to arrive and an estimated answer? Can you find the exact solution using an efficient written method? UNIT 5.11 Pupils can solve addition and subtraction problems in different contexts and involving decimal numbers. Pupils can estimate the answers to problems and comment on the accuracy of their answer. Pupils continue to develop their written methods of column addition and subtraction, applied to more complex problems. Can you explain and represent an efficient way of calculating whether it is quicker to travel from Plymouth to London by train or by coach using timetables? Can you explain and represent how you know is nearly 900 and that the difference between 845 and 639 is around 200 using rounding?
4 YEAR 5 MULTIPLICATIVE REASONING Multiplicative Reasoning is taught in 3 units totalling 8 weeks. UNIT 5.3 Pupils can solve problems involving multiplication and division in different contexts. They demonstrate they can choose and use the appropriate number facts and show their understanding of place value and mental and written methods. UNIT 5.8 Pupils practise and extend their use of the formal written methods of short multiplication and short division. They apply all the facts from the multiplication tables and the related division facts, committing them to memory and using them confidently to solve larger calculations. Pupils interpret answers to division problems by expressing results in different ways according to the context. E.g. for some calculations the answer can be given exactly (4.56kg) and for some more interpretation is needed. (the answer 4.5 buses would normally require rounding to either 4 or 5 buses.) Pupils use all four operations to solve problems involving time and money, including converting between different units. Can you explain and represent different ways of solving 216m 4 and 220m 5, give reasons for which would be the most efficient and suggest contexts where these calculations might be needed. Can you explain why the solutions to 8 people need to travel in taxis that each carry 6 people, how a ta is do ou eed? a d 8 eggs ha e ee olle ted, ho a o es of 6 a e filled? result in different answers even though the calculation is the same in each 83 6? Pupils can explain and show properties of prime, composite (nonprime), square and cube numbers and explain how the factors of these sets of numbers differ. Pupils investigate the properties of different numbers, looking at their factors to develop a set of rules for prime, composite (nonprime), square and cube numbers (e.g. square numbers have an odd number of factors) Pupils use their knowledge of the properties of the different types of number to solve problems in different contexts. Can you explain and represent how I know 16 is a square number and 27 is a cube number and how can you identify a prime number and a composite number between 16 and 27. Can you use your knowledge of factor pairs to organise a class of 32 children into a variety of teams. UNIT 5.13 Pupils can solve problems involving multiplication and division in more complex contexts. They can explain and represent the connection between fractions and division. Pupils practise and extend their use of the formal written methods of short multiplication and short division. Pupils investigate the Distributive Law i.e. a(b+c) = ab + ac e.g. 4 x (3 + 2) = 4 x x 2 A s hool trip to London costs 175 per pupil. 19 children are booked on the trip; how much money ill e olle ted? 80 hildre are going to the county show and need to travel in mini buses which each hold nine children. How many mini buses need to be ooked?
5 YEAR 5 GEOMETRIC REASONING Geometric Reasoning is taught in 3 units totalling 7 weeks. UNIT 5.4 Pupils can explain angle as a measure of turn. They draw and measure angles using a protractor (angle measurer) and use their understanding of angles to describe the properties of different shapes. UNIT 5.9 Pupils become accurate in drawing lines with a ruler to the nearest millimetre, and measuring with a protractor. They use conventional markings for parallel lines and right angles. Pupils use the term diagonal and test theories about the angles formed between sides, and between diagonals and parallel sides, and other properties of quadrilaterals. Pupils should use angle sum facts and other properties to make deductions about missing angles and relate these to missing number problems. (e.g. using the fact that the angles in a triangle add up to 180 o to find a missing angle.) Can you explain what an angle is? Can you draw and measure angles? Can you use your understanding of angle to describe the properties of different shapes? Pupils can explain how to reflect and translate (move) shapes on a grid and use this knowledge and understanding to solve problems. Pupils recognise and use reflection and translation in a variety of diagrams, including continuing to use a 2D grid with positive coordinates. I can draw a rightangled triangle on a grid, identify the coordinates of the vertices and explain what happens to the coordinates if the triangle is reflected in a line parallel to the y axis I can explain why I know that the triangles are congruent (shapes of exactly the same shape and size, although they may be rotated, reflected or moved) UNIT 5.14 Pupils can explain how to find the perimeter and area of different shapes and use this knowledge to solve problems. Pupils calculate the perimeter of rectangles and related composite shapes, including using the properties of rectangles to find unknown lengths. Pupils are introduced to algebra through the representation of perimeter and area. Pupils calculate the area of scale drawings using given measurements. I can find the missing lengths on a scale drawing of an L shaped garden without measuring. I can calculate the perimeter of the shape. I can explain and represent how rectangles with an area of 36 cm 2 can have different perimeters and explain how I know which one has the longest perimeter.
6 YEAR 5 FRACTIONS Fractions are taught in 2 units totalling 8 weeks. UNIT 5.7 Pupils can represent and explain the relationship between decimals, fractions and percentages. They use this understanding to solve problems. They understand and can explain the relationship between multiplication and division and fractions and percentages. They use this understanding to derive facts and solve problems. UNIT 5.12 Pupils should be taught throughout that percentages, decimals and fractions are different ways of expressing proportions. Pupils connect the answer to a division calculation to improper and mixed number fractions (e.g = 3 r 2 so 11 / 3 = 3 2 / 3 ) Pupils say, read and write decimal fractions and related tenths, hundredths and thousandths accurately and are confident in checking the reasonableness of their answers to problems. Pupils connect multiplication by a fraction to using fractions as operators (finding fractions of amounts) Pupils make connections between percentages, fractions and decimals (for example, 100% represents a whole quantity and 1% is 1 100, 50% is , 25% is ) a d relate this to fi di g fra tio s of. I can explain and represent how I know how to order the fractions 15 10, 5 10, 15 20, 1 2, 1 5 and and convert the fractions to decimals and percentages. I can explain and represent how I know how close each fraction is to 1. I can explain and represent which I would rather win: 1 4 of 300 or 40% of 150. Pupils can solve problems involving the addition and subtraction of fractions where the denominators are the same or simple multiples of each other. Pupils multiply fractions (including improper fractions and mixed numbers) by whole numbers Pupils continue to link fractions, decimals and percentages, solving increasingly complex problems. Pupils use diagrams and real life contexts to investigate the addition and subtraction of fractions. Pupils know the relative size of fractions that have denominators which are multiples of each other and use this information to add and subtract them. Pupils are taught to multiply fractions by whole numbers. They should be confident converting between including improper fractions and mixed numbers to allow for multiplication. Pupils should know the decimal and percentage equivalent for common proper fractions. Can you count in quarters from 73 and can explain and represent why I will not say 75.4? I can show that 1 / / 10 = 5 / 10 using diagrams if necessary to explain my understanding. I can explain how I could use the same 1l measuring jug, marked in 100 ml intervals, to measure 2 3 litre, 0.75 litre and 890 ml and explain why 2 3 is difficult to represent as a decimal? I can represent and explain that 4 5 is both four lots of 1 5 and 4 5 and represent and explain why 10 and are equivalent fractions.
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