Year 3 Maths Scheme of Work

Transcription

1 Year 3 New National Curriculum The principal focus of mathematics teaching in lower key stage 2 is to ensure that pupils become increasingly fluent with whole numbers and the four operations, including number facts and the concept of place value. This should ensure that pupils develop efficient written and mental methods and perform calculations accurately with increasingly large whole numbers. At this stage, pupils should develop their ability to solve a range of problems, including with simple fractions and decimal place value. Teaching should also ensure that pupils draw with increasing accuracy and develop mathematical reasoning so they can analyse shapes and their properties, and confidently describe the relationships between them. It should ensure that they can use measuring instruments with accuracy and make connections between measure and number. Pupils should read and spell mathematical vocabulary correctly and confidently, using their growing word reading knowledge and their knowledge of spelling. Pupils should be taught to: Count from 0 in multiples of 4, 8, 50 and 100; find 10 or 100 more or less than a given number Compare and order numbers up to 1000 Identify, represent and estimate numbers using different representations Read and write numbers up to 1000 in numerals and in words Solve number problems and practical problems involving these ideas. Addition and Subtraction Pupils should be taught to: Estimate the answer to a calculation and use inverse operations to check answers Multiplication and Division Pupils should be taught to: Recall and use multiplication and division facts for the 3, 4 and 8 multiplication tables Write and calculate mathematical statements for multiplication and division using the multiplication tables that they know, including for two-digit numbers times onedigit numbers, using mental and progressing to Solve problems, including missing number problems, involving multiplication and division, including positive integer scaling problems and correspondence problems in which n objects are connected to m objects.

2 Fractions Pupils should be taught to: Count up and down in tenths; recognise that tenths arise from dividing an object into 10 equal parts and in dividing one-digit numbers or quantities by 10 Recognise, find and write fractions of a discrete set of objects: unit fractions and non-unit fractions with small denominators Recognise and use fractions as numbers: unit fractions and non-unit fractions with small denominators Recognise and show, using diagrams, equivalent fractions with small denominators Add and subtract fractions with the same denominator within one whole [for example, = 76] Compare and order unit fractions, and fractions with the same denominators Solve problems that involve all of the above. Pupils should be taught to: Measure the perimeter of simple 2-D shapes Add and subtract amounts of money to give change, using both and p in practical contexts Tell and write the time from an analogue clock, including using Roman numerals from I to XII, and 12-hour and 24-hour clocks Estimate and read time with increasing accuracy to the nearest minute; record and compare time in terms of seconds, minutes and hours; use vocabulary such as o clock, a.m./p.m., morning, afternoon, noon and midnight Know the number of seconds in a minute and the number of days in each month, year and leap year Compare durations of events [for example to calculate the time taken by particular events or tasks]. Geometry (Properties of shapes) Pupils should be taught to: Draw 2-D shapes and make 3-D shapes using modelling materials; recognise 3-D shapes in different orientations and describe them Recognise angles as a property of shape or a description of a turn Identify right angles, recognise that two right angles make a half-turn, three make three quarters of a turn and four a complete turn; identify whether angles are greater than or less than a right angle Identify horizontal and vertical lines and pairs of perpendicular and parallel lines. Statistics Pupils should be taught to: Interpret and present data using bar charts, pictograms and tables Solve one-step and two-step questions [for example, How many more? and How many fewer? ] using information presented in scaled bar charts and pictograms and tables.

3 Weekly Overview Day Monday Tuesday Wednesday Thursday Friday Focus Assessment Monday Numbers and the Number System Numbers and the Number System Pattern/Algebra/Calculating Geometry/

4 Year Three Long Term Plan Autumn 1 Week 1 (W/B ) NC Learning Objectives Compare and order numbers up to (W/B ) Solve number problems and practical problems involving these ideas. Addition and Subtraction Add and subtract numbers with up to three digits, using of column addition and subtraction Geometry Identify horizontal and vertical lines and pairs of perpendicular and parallel lines. Draw 2-D shapes and make 3-D shapes using modelling materials; recognise 3-D shapes in different orientations and describe them 3 (W/B ) Count from 0 in multiples of 4, 8, 50 and 100; find 10 or 100 more or less than a given number Identify, represent and estimate numbers using different representations. Geometry Draw 2-D shapes and make 3-D shapes using modelling materials; recognise 3-D shapes in different orientations and describe them 4 (W/B ) Compare and order numbers up to 1000 Read and write numbers up to 1000 in numerals and in words Estimate the answer to a calculation and use inverse operations to check answers

5 Geometry Identify right angles, recognise that two right angles make a half-turn, three make three quarters of a turn and four a complete turn; identify whether angles are greater than or less than a right angle 5 (W/B ) Count from 0 in multiples of 4, 8, 50 and 100; find 10 or 100 more or less than a given number Geometry Identify right angles, recognise that two right angles make a half-turn, three make three quarters of a turn and four a complete turn; identify whether angles are greater than or less than a right angle 6 (W/B ) Count from 0 in multiples of 4, 8, 50 and 100; find 10 or 100 more or less than a given number Estimate the answer to a calculation and use inverse operations to check answers Geometry Draw 2-D shapes and make 3-D shapes using modelling materials; recognise 3-D shapes in different orientations and describe them Recognise angles as a property of shape or a description of a turn Identify right angles, recognise that two right angles make a half-turn, three make three quarters of a turn and four a complete turn; identify whether angles are greater than or less than a right angle 7 (W/B ) Identify horizontal and vertical lines and pairs of perpendicular and parallel lines. Milestone Assessment Calculating, Numbers and the Number System, Pattern and Algebra (AP1): Fluently recall adding and subtracting facts of all numbers to 10 and use these when adding lists of small numbers. Fluently recall most adding and subtracting facts of all numbers to 20 and use efficient strategies to calculate those not known. Know and use patterns in adding and subtracting facts for any number to 20 and beyond to recall facts, to organise them systematically and to check that all combinations have been found. Milestone Assessment Geometry, and Statistics (AP1): Find examples of horizontal, vertical and perpendicular lines. Describe the properties of 3D shapes and build them. Move objects as angled turns. Show how right angled turns are the same as quarter turns. Make and order right angles and angles greater or less than a right angle. Recognise angles in 2D shapes and relate to the properties of irregular and regular shapes. Use sorting diagrams to organise 2D and 3D shapes and explain reasoning.

6 8 (W/B ) Use known adding and subtracting facts to derive facts to 30. Give a sensible estimate of numbers of more than 100 objects. Count aloud across multiples of 100 and multiples of Read, write and build (with apparatus) 2 and 3 digit numbers. Relate grouping and place value notation to say the value of each digit in a 3 digit number. Recap any areas needed to be revised in preparation for assessment week

7 Autumn 2 Week 1 (W/B ) 2 (W/B ) 3 (W/B ) 4 (W/B ) Mathematical Area Count from 0 in multiples of 4, 8, 50 and 100; find 10 or 100 more or less than a given number. Identify, represent and estimate numbers using different representations. Read and write numbers up to 1000 in numerals and in words. Tell and write the time from an analogue clock, including using Roman numerals from I to XII, and 12-hour and 24-hour clocks Identify, represent and estimate numbers using different representations. Read and write numbers up to 1000 in numerals and in words.. Tell and write the time from an analogue clock, including using Roman numerals from I to XII, and 12-hour and 24-hour clocks Identify, represent and estimate numbers using different representations. Read and write numbers up to 1000 in numerals and in words. Count from 0 in multiples of 4, 8, 50 and 100; find 10 or 100 more or less than a given number Estimate and read time with increasing accuracy to the nearest minute; record and compare time in terms of seconds, minutes and hours; use vocabulary such as o clock, a.m./p.m., morning, afternoon, noon and midnight

8 Estimate the answer to a calculation and use inverse operations to check answers Know the number of seconds in a minute and the number of days in each month, year and leap year 5 (W/B ) 6 (W/B ) 7 (W/B ) Solve number problems and practical problems involving these ideas. Compare durations of events [for example to calculate the time taken by particular events or tasks]. Milestone Assessment Calculating, Numbers and the Number System, Pattern and Algebra (AP2): Milestone Assessment Geometry, and Statistics (AP2): Explain how three related numbers are connected through the inverse relation and write all Tell times to the nearest minute, both past and to, shown on analogue clocks. the related adding and subtracting facts. Discuss differences and similarities between digital and analogue clocks including Roman Use understanding of equivalence, the = symbol and knowledge of the inverse relation numerals and explain how they display time. between adding and subtracting to solve problems where the symbol represents an Say times shown on a 12-hour digital clock. unknown number. Calculate a given number of minutes earlier and later, than times shown on a 12-hour digital Understand the use of zero as a place holder. clock. Know what multiples of 10 and 100 are important milestones on the number line. Use terms such as midday, midnight, a.m, p.m, to explain how time progresses and is labelled Count forwards and backwards in sequences of multiples within their working range. in a 24 hour day. Recognise when a given number is a multiple of 2, 3, 4, 5, 8 or 10 (at this stage a few children Find and compare durations of time across 24 hours, including time starting at half past the may recognise common multiples but this is not a milestone) hour. Notice patterns in sequences of multiples, explain the rule for the sequence and use this to Compare and order units of time, and know the number of seconds in a minute, minutes in find missing numbers. an hour and hours in a day. Know how to adjust calculations and compensate when adding and subtracting 9 and when Recall, or know how to work out, the number of days in each month and the number of days to use this relationship. in a year, or leap year. Recall and use adding and subtracting facts to 10 and the bridging strategy in any adding and subtracting calculations that involves crossing multiples of 10, and explain the steps they have taken. Understand that multiplying is a form of calculating used instead of repeated adding and recognise when they need to multiply to solve a problem. Read multiplying number sentences. Read and write multiplying sentences using the x symbol, model them with structured apparatus showing understanding of the word product. Solve number problems and practical problems involving these ideas.

9 Recall and use multiplication and division facts for the 3, 4 and 8 multiplication tables Write and calculate mathematical statements for multiplication and division using the multiplication tables that they know, including for two-digit numbers times one-digit numbers, using mental and progressing to Solve problems, including missing number problems, involving multiplication and division, including positive integer scaling problems and correspondence problems in which n objects are connected to m objects. Estimate and read time with increasing accuracy to the nearest minute; record and compare time in terms of seconds, minutes and hours; use vocabulary such as o clock, a.m./p.m., morning, afternoon, noon and midnight

10 Spring 1 Week 1 (W/B ) 2 (W/B ) Mathematical Area Count from 0 in multiples of 4, 8, 50 and 100; find 10 or 100 more or less than a given number Identify, represent and estimate numbers using different representations Read and write numbers up to 1000 in numerals and in words Compare and order numbers up to 1000 Read and write numbers up to 1000 in numerals and in words Solve problems, including missing number problems, involving multiplication and division, including positive integer scaling problems and correspondence problems in which n objects are connected to m objects. Measure the perimeter of simple 2-D shapes 3 (W/B ) 4 (W/B ) Identify, represent and estimate numbers using different representations Solve problems, including missing number problems, involving multiplication and division, including positive integer scaling problems and correspondence problems in which n objects are connected to m objects. Statistics Interpret and present data using bar charts, pictograms and tables Solve one-step and two-step questions [for example, How many more? and How many fewer? ] using information presented in scaled bar charts and pictograms and tables. Identify, represent and estimate numbers using different representations.

11 5 (W/B ) 6 (W/B ) Milestone Assessment Calculating, Numbers and the Number System, Pattern and Algebra (AP3): Milestone Assessment Geometry, and Statistics (AP3): Understand relative values of numbers to 1000, including recognising the idea of a range of numbers and use of symbols -, <, and > for labelling a range of numbers. Explain and interpret a realistic context as one inviting either multiplying or dividing and Partition numbers up to 1000 into hundreds, tens and units and to derive other ways of use the inverse relation between multiplying and dividing when solving problems. partitioning them. Know that multiplying has a commutative property and use this to help solving dividing Relate pounds and pence and notation to hundreds, tens and units. questions. Use knowledge of partitioning to solve money problems. Interpret a remainder as what is left after grouping. Relate knowledge of patterns on a 100 square to an array for 1000 and use patterns when finding numbers in different arrays and number squares. Use fluent recall of adding and subtracting facts to 10 when adding and subtracting multiples of 10 and multiples of 100, first whole tens or whole hundreds moving on to add whole tens Recall most multiplying facts of 2, 3, 4, 5, 8 and 10 multiplying tables. and whole hundreds to 2 and 3 digit numbers. Know and use the commutative property of multiplying. Show understanding of m, cm and mm by making sensible estimates of lengths using suitable Represent multiplying problems with structured apparatus and arrays. units. Know that changing the order of numbers in multiplying problems does not change the Convert between m and cm, and cm and mm. product. Solve real-life measure problems by adding and subtracting lengths, including those given in Recognise that dividing can be expressed as finding how many groups are in? mixed units. Read, build with structured apparatus and write dividing number sentences using the Measure accurately to calculate the perimeter of rectangular shapes. symbol. Complete tally charts and pictograms to collect and present data, then discuss their findings. Notice and explain the inverse relation between dividing and multiplying and know that they can use multiplying facts to derive dividing facts. Identify, represent and estimate numbers using different representations Solve number problems and practical problems involving these ideas. Estimate the answer to a calculation and use inverse operations to check answers

12 Spring 2 Week 1 (W/B ) Mathematical Area Identify, represent and estimate numbers using different representations Add and subtract amounts of money to give change, using both and p in practical contexts 2 (W/B ) Compare and order numbers up to 1000 Identify, represent and estimate numbers using different representations Statistics Interpret and present data using bar charts, pictograms and tables Add and subtract amounts of money to give change, using both and p in practical contexts 3 (W/B ) Count from 0 in multiples of 4, 8, 50 and 100; find 10 or 100 more or less than a given number Statistics Interpret and present data using bar charts, pictograms and tables Recall and use multiplication and division facts for the 3, 4 and 8 multiplication tables

13 Solve problems, including missing number problems, involving multiplication and division, including positive integer scaling problems and correspondence problems in which n objects are connected to m objects. Add and subtract amounts of money to give change, using both and p in practical contexts 4 (W/B ) Milestone Assessment Calculating, Numbers and the Number System, Pattern and Algebra (AP4): Use knowledge of sequences of multiples to label intervals. Use knowledge of number relationships to read values in between marked intervals. Count in multiples of 25 and 50. Find halfway between two multiples of 10 and two multiples of 100. Round any 2 and 3 digit number to the nearest 10 or 100. Record work systematically in order to quickly spot patterns. Explain how they are using place value and known number facts to solve similar calculations. Use knowledge of equivalence and number relationships to adjust numbers involved in a variety of calculating situations and explain their reasoning. Use fluent recall of doubles of numbers to 10 when solving problems that involve doubling and halving higher numbers. Use fluent recall of adding and subtracting facts of 10 when finding complements to 100. Develop fluent recall of many facts from 2, 3, 4, 5, 8 and 10 times tables. Recognise that some times tables have multiples in common. Use doubling and halving as a strategy for deriving related multiplying facts between 2, 4, and 8 times tables and between 5 and 10 times tables. Know that we can use dividing to solve problems involving sharing as well as those involving grouping. Know that there can be remainders in sharing situations. Write dividing sentences in response to problems illustrated by arrays, Numicon Shapes or number rods. Use the inverse relation between multiplying and dividing when solving sharing problems Milestone Assessment Geometry, and Statistics (AP4): Use mathematical apparatus to model and discuss the relationship between the values 1p, 10p and 1 coins. Make given amounts of money up to 10, using fewest coins and/or notes. Calculate the total of two prices given in pounds and pence, and discuss their strategy e.g. adjusting, rounding. Decide if goods are affordable, given a certain budget and calculate the change they should receive. 5 (W/B ) Count from 0 in multiples of 4, 8, 50 and 100; find 10 or 100 more or less than a given number Recall and use multiplication and division facts for the 3, 4 and 8 multiplication tables Solve problems, including missing number problems, involving multiplication and division, including positive integer scaling problems and correspondence problems in which n objects are connected to m objects. Add and subtract amounts of money to give change, using both and p in practical contexts

14

15 Summer 1 Week 1 (W/B ) 2 (W/B ) 3 (W/B ) Mathematical Area Solve number problems and practical problems involving these ideas. Estimate the answer to a calculation and use inverse operations to check answers Solve number problems and practical problems involving these ideas. Estimate the answer to a calculation and use inverse operations to check answers Solve number problems and practical problems involving these ideas. Estimate the answer to a calculation and use inverse operations to check answers

16 4 (W/B ) 5 (W/B ) 6 (W/B ) Solve number problems and practical problems involving these ideas. Estimate the answer to a calculation and use inverse operations to check answers Milestone Assessment Calculating, Numbers and the Number System, Pattern and Algebra (AP5): Milestone Assessment Geometry, and Statistics (AP5): Know that finding a constant difference is a useful strategy for finding the rule for a sequence. Use a dial weighing scale to measure individual amounts in 100g increments, up to 5kg. Choose whether a mental or column method is the most appropriate before solving different Recognise equivalences between g and kg, e.g. 1000g=1kg etc. adding and subtracting problems. Find the total mass of two or more items and the difference in mass between items. Use rounding when making a reasonable estimate of the possible answer to an adding and Interpret word problems involving mass, modelling with weights or other apparatus, as subtracting problem. appropriate. Use partitioning into hundreds, tens and units as a strategy for adding and subtracting Recall that there are 1000ml in 1l and know, or work out, the volume of 1/2l, 1/4l and ¾l in problem. ml. Use structured apparatus when adding and subtracting 2 and 3 digit numbers to show Understand the term capacity and make sensible estimates of volumes of liquid held in understanding of how these are partitioned, regrouped, recombined, or redistributed and can different containers. transfer this to a written method of recording in columns. Measure out a precise volume of liquid using the scale on a jug or other scaled vessel. Illustrate mental strategies for adding and subtracting 2 and 3 digit numbers on an empty Solve capacity word problems, e.g. What is the total volume of? and How much is left if I number line. pour out? Add or subtract amounts of money over 1 using a written method. Present data that they have collected in tables and scaled bar charts. Use the inverse relation between adding and subtracting to check solutions to calculations. Notice patterns in tables and bar charts. Illustrate scaling up and ratio problems with structured apparatus and use the language of scaling and ratio to explain their solutions. Make general statements about what happens when multiplying and dividing by 10. Illustrate and find solutions to multiplying and dividing problems involving teen numbers using structures apparatus and recall of facts. Recall and use multiplication and division facts for the 3, 4 and 8 multiplication tables Solve problems, including missing number problems, involving multiplication and division, including positive integer scaling problems and correspondence problems in which n objects are connected to m objects.

17 Summer 2 Week 1 (W/B ) 2 (W/B ) 3 (W/B ) 4 (W/B ) 5 (W/B ) Mathematical Area Fractions Recognise, find and write fractions of a discrete set of objects: unit fractions and non-unit fractions with small denominators Recognise and use fractions as numbers: unit fractions and non-unit fractions with small denominators Recognise and show, using diagrams, equivalent fractions with small denominators Add and subtract fractions with the same denominator within one whole [for example, = 76] Fractions Recognise, find and write fractions of a discrete set of objects: unit fractions and non-unit fractions with small denominators Recognise and show, using diagrams, equivalent fractions with small denominators Add and subtract fractions with the same denominator within one whole [for example, = 76] Fractions Recognise, find and write fractions of a discrete set of objects: unit fractions and non-unit fractions with small denominators Recognise and use fractions as numbers: unit fractions and non-unit fractions with small denominators Add and subtract fractions with the same denominator within one whole [for example, = 76] Fractions Count up and down in tenths; recognise that tenths arise from dividing an object into 10 equal parts and in dividing one-digit numbers or quantities by 10 Recognise, find and write fractions of a discrete set of objects: unit fractions and non-unit fractions with small denominators Fractions Count up and down in tenths; recognise that tenths arise from dividing an object into 10 equal parts and in dividing one-digit numbers or quantities by 10 Recognise, find and write fractions of a discrete set of objects: unit fractions and non-unit fractions with small denominators

18 6 (W/B ) 7 (W/B ) Recognise and use fractions as numbers: unit fractions and non-unit fractions with small denominators Recognise and show, using diagrams, equivalent fractions with small denominators Add and subtract fractions with the same denominator within one whole [for example, = 76] Compare and order unit fractions, and fractions with the same denominators Solve problems that involve all of the above. Milestone Assessment Calculating, Numbers and the Number System, Pattern and Algebra (AP5): Milestone Assessment Geometry, and Statistics (AP5): Connect ordinal number names with names for fractions and understand that the Recall that there are 1000ml in a l and know or work out the volume of 1/2l 1/4l and 3/4l. denominator tells us how many parts a whole has been divided into and the numerator tells Understand the term capacity and make sensible estimates of volumes of liquid held in us how many of those parts are represented. different containers. Fluently recall double and half facts and use these to find halves and quarters of numbers Measure out a precise volume of liquid using the scale on a jug or other scaled vessels. within their working range. Solve capacity word problems. Make connections between unit fractions as operators and division by integers. Present data that they have collected in tables and scaled bar charts. Interpret remainders as fractions and notice that the context will affect how we deal with the Notice patterns in tables and bar charts. remainder when dividing odd numbers into two or four parts. Identify positions on a grid, using letter/number grid references. Differentiate between finding half of a number and finding how many halves are in a number. Describe movements on a grid with increased accuracy. Know that fractions have places on the number line between whole numbers. Know that the greater the number of parts a number is divided into, the smaller each of the parts becomes. Know that half can be represented by different equivalent fractions. Illustrate written fractions with apparatus and can write a fraction in response to seeing it built with apparatus. Add and subtract fractions with the same denominator within one whole shape and within one set. Investigate suitable problems and work systematically to show that they have tried and tested all possibilities. Choose efficient recording systems. Express a general statement and explain their reasoning. Summer activities