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PROGRAMME OF STUDY
Knowledge, skills and understanding
Teaching should ensure that appropriate connections are made between the sections on number , shape, space and measures , and handling data . During key stage 2 pupils use the number system more confidently. They move from counting reliably to calculating fluently with all four number operations. They always try to tackle a problem with mental methods before using any other approach. Pupils explore features of shape and space and develop their measuring skills in a range of contexts. They discuss and present their methods and reasoning using a wider range of mathematical language, diagrams and charts. The mathematics programmes of study and the National Numeracy Strategy Framework for teaching mathematics are fully aligned. The Framework provides a detailed basis for implementing the statutory requirements of the programme of study for key stage 2 in mathematics. Note about sections
>There is no separate section of the programme of study numbered Ma1 that corresponds to the first attainment target, using and applying mathematics . Teaching requirements relating to this attainment target are included within the other sections of the programme of study.
Using and applying number
1) Pupils should be taught to:
Problem solving
a) make connections in mathematics and appreciate the need to use numerical skills and knowledge when solving problems in other parts of the mathematics curriculum
b) break down a more complex problem or calculation into simpler steps before attempting a solution; identify the information needed to carry out the tasks
c) select and use appropriate mathematical equipment, including ICT
d) find different ways of approaching a problem in order to overcome any difficulties
e) make mental estimates of the answers to calculations; check results
Communicating
f) organise work and refine ways of recording
g) use notation diagrams and symbols correctly within a given problem
h) present and interpret solutions in the context of the problem
i) communicate mathematically, including the use of precise mathematical language
Reasoning
j)
understand and investigate general statements [ for example, 'there are four prime numbers less than 10', 'wrist size is half neck size']
k) search for pattern in their results; develop logical thinking and explain their reasoning.
Numbers and the number system
2) Pupils should be taught to:
Counting
a) count on and back in tens or hundreds from any two- or three-digit number; recognise and continue number sequences formed by counting on or back in steps of constant size from any integer, extending to negative integers when counting back
Number patterns and sequences
b) recognise and describe number patterns, including two- and three-digit multiples of 2, 5 or 10, recognising their patterns and using these to make predictions; make general statements, using words to describe a functional relationship, and test these; recognise prime numbers to 20 and square numbers up to 10 * 10; find factor pairs and all the prime factors of any two-digit integer
Integers
c) read, write and order whole numbers, recognising that the position of a digit gives its value; use correctly the symbols <, >, =; multiply and divide any integer by 10 or 100 then extend to multiplying and dividing by 1000; round integers to the nearest 10 or 100 and then 1000; order a set of negative integers, explaining methods and reasoning; multiply and divide decimals by 10 or 100
Fractions, percentages and ratio
d)
understand unit fractions [for example, one-third or one-eighth] then fractions that are several parts of one whole [for example, two-thirds or five-eighths], locate them on a number line and use them to find fractions of shapes and quantities
e) understand simple equivalent fractions and simplify fractions by cancelling common factors; compare and order simple fractions by converting them to fractions with a common denominator, explaining their methods and reasoning
f) recognise the equivalence between the decimal and fraction forms of one half, quarters, tenths and hundredths; understand that 'percentage' means the 'number of parts per 100' and that it can be used for comparisons; find percentages of whole number quantities, using a calculator where appropriate
g) recognise approximate proportions of a whole and use simple fractions and percentages to describe them, explaining their methods and reasoning
h) solve simple problems involving ratio and direct proportion
Decimals
i)
understand and use decimal notation for tenths and hundredths in context [for example, order amounts of money, round a sum of money to the nearest ?, convert a length such as 1.36 metres to centimetres and vice versa] ; locate on a number line, and order, a set of numbers or measurements; then recognise thousandths (only in metric measurements)
j) round a number with one or two decimal places to the nearest integer or tenth; convert between centimetres and millimetres or metres, then between millimetres and metres, and metres and kilometres, explaining methods and reasoning.
Calculations
3) Pupils should be taught to:
Number operations and the relationships between them
a) develop further their understanding of the four number operations and the relationships between them including inverses; use the related vocabulary; choose suitable number operations to solve a given problem, and recognise similar problems to which they apply
b) find remainders after division, then express a quotient as a fraction or decimal; round up or down after division, depending on the context
c) understand the use of brackets to determine the order of operations; understand why the commutative, associative and distributive laws apply to addition and multiplication and how they can be used to do mental and written calculations more efficiently
Mental methods
d) recall all addition and subtraction facts for each number to 20
e)
work out what they need to add to any two-digit number to make 100, then add or subtract any pair of two-digit whole numbers; handle particular cases of three-digit and four-digit additions and subtractions by using compensation or other methods [for example, 3000 - 1997, 4560 + 998]
f) recall multiplication facts to 10 * 10 and use them to derive quickly the corresponding division facts
g) double and halve any two-digit number
h)
multiply and divide, at first in the range 1 to 100 [for example, 27 * 3, 65 divided by 5] , then for particular cases of larger numbers by using factors, distribution or other methods
Written methods
i) use written methods to add and subtract positive integers less than 1000, then up to 10000, then add and subtract numbers involving decimals; use approximations and other strategies to check that their answers are reasonable
j)
use written methods for short multiplication and division by a single-digit integer of two-digit then three-digit then four-digit integers, then of numbers with decimals; then use long multiplication, at first for two-digit by two-digit integer calculations, then for three-digit by two-digit calculations; extend division to informal methods of dividing by a two-digit divisor [for example, 64 divided_by 16] ; use approximations and other strategies to check that their answers are reasonable
Calculator methods
k)
use a calculator for calculations involving several digits, including decimals; use a calculator to solve number problems [for example, 4 ? * 7 = 343] ; know how to enter and interpret money calculations and fractions; know how to select the correct key sequence for calculations with more than one operation [for example, 56 * (87 48)].
Solving numerical problems
4) Pupils should be taught to:
a) choose, use and combine any of the four number operations to solve word problems involving numbers in 'real life', money or measures of length, mass, capacity or time, then perimeter and area
b) choose and use an appropriate way to calculate and explain their methods and reasoning
c)
estimate answers by approximating and checking that their results are reasonable by thinking about the context of the problem, and where necessary checking accuracy [for example, by using the inverse operation, by repeating the calculation in a different order]
d)
recognise, represent and interpret simple number relationships, constructing and using formulae in words then symbols [for example, c = 15 n is the cost, in pence, of n articles at 15p each]
e)
read and plot coordinates in the first quadrant, then in all four quadrants [for example, plot the vertices of a rectangle, or a graph of the multiples of 3] .
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