National Curriculum 2014: Mathematics Year 1Year 2 coverage
Mathematics
Purpose of study
Mathematics is a creative and highly inter-connected discipline that has been developed over centuries, providing the solution to some of history’s most intriguing problems. It is essential to everyday life, critical to science, technology and engineering, and necessary for financial literacy and most forms of employment. A high-quality mathematics education therefore provides a foundation for understanding the world, the ability to reason mathematically, an appreciation of the beauty and power of mathematics, and a sense of enjoyment and curiosity about the subject.
Aims
The national curriculum for mathematics aims to ensure that all pupils:
- become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately.
- reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language
- can solve problems by applying their mathematics to a variety of routine and non-routine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions.
Mathematics is an interconnected subject in which pupils need to be able to move fluently between representations of mathematical ideas. The programmes of study are, by necessity, organised into apparently distinct domains, but pupils should make rich connections across mathematical ideas to develop fluency, mathematical reasoning and competence in solving increasingly sophisticated problems. They should also apply their mathematical knowledge to science and other subjects.
The expectation is that the majority of pupils will move through the programmes of study at broadly the same pace. However, decisions about when to progress should always be based on the security of pupils’ understanding and their readiness to progress to the next stage. Pupils who grasp concepts rapidly should be challenged through being offered rich and sophisticated problems before any acceleration through new content. Those who are not sufficiently fluent with earlier material should consolidate their understanding, including through additional practice, before moving on.
Information and communication technology (ICT)
Calculators should not be used as a substitute for good written and mental arithmetic. They should therefore only be introduced near the end of key stage 2 to support pupils’ conceptual understanding and exploration of more complex number problems, if written and mental arithmetic are secure. In both primary and secondary schools, teachers should use their judgement about when ICT tools should be used.
Spoken language
The national curriculum for mathematics reflects the importance of spoken language in pupils’ development across the whole curriculum – cognitively, socially and linguistically. The quality and variety of language that pupils hear and speak are key factors in developing their mathematical vocabulary and presenting a mathematical justification, argument or proof. They must be assisted in making their thinking clear to themselves as well as others and teachers should ensure that pupils build secure foundations by using discussion to probe and remedy their misconceptions.
School curriculum
The programmes of study for mathematics are set out year-by-year for key stages 1 and 2. Schools are, however, only required to teach the relevant programme of study by the end of the key stage. Within each key stage, schools therefore have the flexibility to introduce content earlier or later than set out in the programme of study. In addition, schools can introduce key stage content during an earlier key stage, if appropriate. All schools are also required to set out their school curriculum for mathematics on a year-by-year basis and make this information available online.
Attainment targets
By the end of each key stage, pupils are expected to know, apply & understand the matters, skills & processes specified in the relevant programme of study.
Key Stage 1
The principal focus of mathematics teaching in key stage 1 is to ensure that pupils develop confidence and mental fluency with whole numbers, counting and place value. This should involve working with numerals, words and the four operations, including with practical resources [for example, concrete objects and measuring tools].
At this stage, pupils should develop their ability to recognise, describe, draw, compare and sort different shapes and use the related vocabulary. Teaching should also involve using a range of measures to describe and compare different quantities such as length, mass, capacity/volume, time and money.
By the end of year 2, pupils should know the number bonds to 20 and be precise in using and understanding place value. An emphasis on practice at this early stage will aid fluency.
Pupils should read and spell mathematical vocabulary, at a level consistent with their increasing word reading and spelling knowledge at key stage 1.
Key Learning in Mathematics by Year Group and Strand
Whilst each strand has been separated into individual aspects to support the identification of progression, it is crucial that teachers support children in making and using links between these different but related parts. Objectives in italic are non-statutory but have been added where there are gaps in progression in the statutory elements of the National Curriculum, to aid progression and enable the learning process to be more secure.
Year 1
Number – number and place value / Number – addition and subtraction / Measurement- Count to and across 100, forwards and backwards, beginning with 0 or 1, or from any given number
- Count in multiples of twos, fives and tens
- Read and write numbers to 100 in numerals
- Read and write numbers from 1 to 20 in numerals and words
- Begin to recognise the place value of numbers beyond 20 (tens and ones)
- Identify and represent numbers using objects and pictorial representations including the number line
- Use the language of: equal to, more than, less than (fewer), most, least
- Given a number, identify one more and one less
- Recognise and create repeating patterns with numbers, objects and shapes
- Identify odd and even numbers linked to counting in twos from 0
and 1 - Solve problems and practical problems involving all of the above
- Read, write and interpret mathematical statements involving addition (+), subtraction (-) and equals (=) signs
- Represent and use number bonds and related subtraction facts within 20
- Add and subtract one-digit and two-digit numbers to 20, including zero (using concrete objects and pictorial representations)
- Solve one-step problems that involve addition and subtraction, using concrete objects and pictorial representations, and missing number problems such as 7 = - 9
- Measure and begin to record:
standard units (m/cm)
- mass/weight, using non-standard and then manageable standard
units (kg/g)
- capacity and volume using non-standard and then manageable
standard units (litres/ml)
- time (hours/minutes/seconds)
within children’s range of counting competence
- Compare, describe and solve practical problems for:
tall/short, double/half)
- mass/weight (for example, heavy/light, heavier than, lighter than)
- capacity and volume (for example, full/empty, more than, less than,
half, half full, quarter)
- time (for example, quicker, slower, earlier, later)
- Recognise and use language relating to dates, including days of the week, weeks, months and years
- Sequence events in chronological order using language (for example, before and after, next, first, today, yesterday, tomorrow, morning, afternoon and evening
- Tell the time to the hour and half past the hour and draw the hands on a clock face to show these times
- Recognise and know the value of different denominations of coins and notes
Number – multiplication and division
- Recall and use doubles of all numbers to 10 and corresponding halves
- Solve one-step problems involving multiplication and division, by calculating the answer using concrete objects, pictorial representations and arrays with the support of the teacher
Number – fractions / Geometry – properties of shapes
- Understand that a fraction can describe part of a whole
- Understand that a unit fraction represents one equal part of a whole
- Recognise, find and name a half as one of two equal parts of an objectshape or quantity (including measure)
- Recognise, find and name a quarter as one of four equal parts of an object, shape or quantity (including measure)
- Recognise and name common 2-D shapes, including rectangles (including squares), circles and triangles
- Recognise and name common 3-D shapes, including cuboids (including cubes), pyramids and spheres.
Statistics / Geometry – position and direction
- Sort objects, numbers and shapes to a given criterion and their own
- Present and interpret data in block diagrams using practical equipment
- Ask and answer simple questions by counting the number of objects in each category
- Ask and answer questions by comparing categorical data
- Describe movement, including whole, half, quarter and three-quarter turns
- Recognise and create repeating patterns with objects and shapes
- Describe position and direction
Year 2
Number – number and place value / Number – addition and subtraction / Measurement- Count in steps of 2, 3, and 5 from 0, and in tens from any number, forward and backward
- Read and write numbers to at least 100 in numerals and in words
- Recognise the place value of each digit in a two-digit number (tens, ones)
- Identify, represent and estimate numbers using different representations, including the number line
- Partition numbers in different ways (e.g. 23 = 20 + 3 and
23 = 10 + 13) - Compare and order numbers from 0 up to 100; use <, > and = signs
- Find 1 or 10 more or less than a given number
- Round numbers to at least 100 to the nearest 10
- Understand the connection between the 10 multiplication table and place value
- Describe and extend simple sequences involving counting on or back in different steps
- Use place value and number facts to solve problems
- Choose an appropriate strategy to solve a calculation based upon the numbers involved (recall a known fact, calculate mentally, use a jotting)
- Select a mental strategy appropriate for the numbers involved in the calculation
- Show that addition of two numbers can be done in any order (commutative) and subtraction of one number from another cannot
- Understand subtraction as take away and difference (how many more, how many less/fewer)
- Recall and use addition and subtraction facts to 20 fluently, and derive and use related facts up to 100
- Recall and use number bonds for multiples of 5 totalling 60 (to support telling time to nearest 5 minutes)
- Add and subtract numbers using concrete objects, pictorial representations, and mentally, including:
- a two-digit number and tens
- two two-digit numbers
- adding three one-digit numbers
- Recognise and use the inverse relationship between addition and subtraction and use this to check calculations and solve missing number problems
- using concrete objects and pictorial representations, including those
involving numbers, quantities and measures
- applying their increasing knowledge of mental and written methods /
- Choose and use appropriate standard units to estimate and measure length/height in any direction (m/cm); mass (kg/g); temperature (°C); capacity and volume (litres/ml) to the nearest appropriate unit, using rulers, scales, thermometers and measuring vessels
- Compare and order lengths, mass, volume/capacity and record the results using >, < and =
- Recognise and use symbols for pounds (£) and pence (p)
- Combine amounts to make a particular value
- Find different combinations of coins that equal the same amounts of money
- Compare and sequence intervals of time
- Tell and write the time to five minutes, including quarter past/to the hour and draw the hands on a clock face to show these times
- Know the number of minutes in an hour and the number of hours in a day
- Solve simple problems in a practical context involving addition and subtraction of money of the same unit, including giving change and measures (including time)
Number – fractions / Number – multiplication and division / Geometry – properties of shapes
- Understand and use the terms numerator and denominator
- Understand that a fraction can describe part of a set
- Understand that the larger the denominator is, the more pieces it is split into and the smaller each part will be
- Recognise, find, name and write fractions , , and of a length, shape, set of objects or quantity
- Write simple fractions for example, of 6 = 3 and recognise the equivalence of and
- Count on and back in steps of and
- Understand multiplication as repeated addition
- Understand division as sharing and grouping and that a division calculation can have a remainder
- Show that multiplication of two numbers can be done in any order (commutative) and division of one number by another cannot
- Recall and use multiplication and division facts for the 2, 5 and 10 multiplication tables, including recognising odd and even numbers
- Derive and use doubles of simple two-digit numbers (numbers in which the ones total less than 10)
- Derive and use halves of simple two-digit even numbers (numbers in which the tens are even)
- Calculate mathematical statements for multiplication using repeated addition) and division within the multiplication tables and write them using the multiplication (×), division (÷) and equals (=) signs
- Solve problems involving multiplication and division (including those with remainders), using materials, arrays, repeated addition, mental methods, and multiplication and division facts, including problems in contexts
- Identify and describe the properties of 2-D shapes, including the number of sides and line symmetry in a vertical line
- Identify and describe the properties of 3-D shapes, including the number of edges, vertices and faces
- Identify 2-D shapes on the surface of 3-D shapes, [for example, a circle on a cylinder and a triangle on a pyramid]
Statistics / Geometry – position and direction
- Compare and sort objects, numbers and common 2-D and 3-D shapes and everyday objects
- Interpret and construct simple pictograms, tally charts, block diagrams and simple tables
- Ask and answer simple questions by counting the number of objects in each category and sorting the categories by quantity
- Ask and answer questions about totalling and comparing categorical data
- Order/arrange combinations of mathematical objects in patterns/sequences
- Use mathematical vocabulary to describe position, direction and movement, including movement in a straight line and distinguishing between rotation as a turn and in terms of right angles for quarter, half and three-quarter turns (clockwise and anti-clockwise)