Primary Mathematics: Extending Knowledge in Practice

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Alice Hansen

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    The Author

    Alice Hansen is a Principal Lecturer in Primary Mathematics Education at the University of Cumbria. She has taught extensively at primary level in England and abroad. Alice has particular interests in how children construct geometrical definitions, the design of mathematical tasks and the use of ICT to enhance mathematics teaching and learning.

  • Objectives Index

    The Early Years Foundation Stage
    Early Learning Goals: Problem Solving, Reasoning and Numeracy
    ObjectivePage
    Recognise numerals 1 to 98
    Use developing mathematical ideas and methods to solve practical problems8
    Count reliably up to ten everyday objects19
    Find one more or one less than a number from 1 to 1033
    Use language such as ‘circle’ or ‘bigger’ to describe the shape and size of solids and flat shapes 68
    Use everyday words to describe position68
    Sort familiar objects to identify their similarities and differences100
    National Curriculum
    Key Stage 1
    ObjectivePage
    Ma2.1a: communicate in spoken, pictorial and written form, at first using informal language and recording, then mathematical language and symbols6, 8
    Ma2.1e: use the correct language, symbols and vocabulary associated with number and data21
    Ma2.2b: create and describe number patterns, explore and record patterns6
    related to addition and subtraction, and then patterns of multiples 2, 5 and 10 explaining the patterns and using them to make predictions; recognise sequences … recognise the relationship between halving and52
    doubling
    Ma2.2c: read and write numbers to 20 at first and then to 100 or beyondrecognise that the position of the digit gives its value and know what each digit represents, including zero as a place holder …21
    Ma2.3a: understand subtraction as both ‘take away’ and ‘difference’ and use the related vocabulary; recognise that subtraction is the inverse of addition; give the subtraction corresponding to an addition and vice versa; use the symbol ‘=’ to represent equality; solve simple missing number problems49
    Ma2.3c: develop rapid recall of number facts: know addition and subtraction facts to 10 and use these to derive facts with totals of 20 …36
    Ma2.5a: solve a relevant problem by using simple lists, tables and charts to sort, classify and organise information102
    Ma2.5b: discuss what they have done and explain their results102
    Ma3.2a: describe properties of shapes that they can see or visualise using the related vocabulary70
    Ma3.2b: observe, handle and describe common 2D and 3D shapes; name and describe the mathematical features of common 2D and 3D shapes …70
    Ma3.4a: estimate the size of objects … compare and measure objects using uniform non-standard units …85
    Ma3.4c: estimate, measure and weigh objects; choose and use simple measuring instruments, reading and interpreting numbers, and scales to the nearest labelled division87
    Key Stage 2
    ObjectivePage
    Ma2.1a: make connections in mathematics and appreciate the need to use numerical skills and knowledge when solving problems in other parts of the mathematics curriculum45
    Ma2.1b: break down a more complex problem or calculation into simpler steps before attempting a solution; identify the information needed to carry out the tasks12, 15
    Ma2.1c: select and use appropriate mathematical equipment, includingICT15
    Ma2.1g: use notation diagrams and symbols correctly within a given problem11
    Ma2.1e: make mental estimates of the answers to calculations; check results40
    Ma2.2b: 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 …37, 59
    Ma2.2c: … multiply and divide decimals by 10 or 10045
    Ma2.2d: understand unit fractions then fractions that are several parts of one whole, locate them on a number line and use them to find fractions of shapes and quantities26
    Ma2.2g: recognise approximate proportions of a whole and use simple fractions and percentages to describe them, explaining their methods and reasoning30
    Ma2.3g: halve and double any two-digit number52
    Ma2.3h: multiply and divide, at first in the range 1 to 100, then for particular cases of larger numbers by using factors, distribution or other methods43
    Ma2.3i: use written methods to add and subtract positive integers less than 1,000 …55
    Ma2.3k: use a calculator for calculations involving several digits, including decimals; use a calculator to solve number problems; know how to enter and interpret money calculations and fractions; know how to select the correct key sequence for calculations with more than one operation62
    Ma2.4a: 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 area57
    Ma3.1d: use checking procedures to confirm that their results of geometrical problems are reasonable79
    Ma3.1e: recognise simple spatial patterns and relationships and make predictions about them75
    Ma3.2b: visualise and describe 2D and 3D shapes and the way they behave, making more precise use of geometrical language, especially that of triangles …79
    Ma3.3b: transform objects in practical situations; transform images using ICT; visualise and predict the position of a shape following a rotation, reflection or translation76
    Ma3.4a: recognise the need for standard units of length, mass and capacity, choose which ones are suitable for a task, and use them to make sensible estimates in everyday situations; convert one metric unit to another … 91, 94
    Ma3.4b: read scales with increasing accuracy; record measurement using decimal notation87
    Ma3.4c: recognise angles as greater or less than a right angle or half-turn, estimate their size and order them …72
    Ma3.4e: find perimeters of simple shapes; find areas or rectangles using the formula, understanding its connection to counting squares and how it extends its approach; calculate the perimeter and area of shapes composed of rectangles96
    Ma4.2a: solve problems involving data 106, 108
    Ma4.2d: know that mode is a measure of average and that range is a measure of spread, and to use both ideas to describe data sets111
    Primary Framework for Mathematics
    Using and applying mathematics
    ObjectivePage
    Year 1: Describe simple patterns and relations involving numbers or shapes; decide whether examples satisfy given conditions6
    Year 1: Describe ways of solving puzzles and problems, explaining choices and decisions orally or using pictures6
    Year 4: Represent a puzzle or problem using number sentences, statements or diagrams; use these to solve the problem; present and interpret the solution in the context of the problem11
    Year 5: Solve one-step and two-step problems involving whole numbers and decimals and all four operations, choosing and using appropriate calculation strategies, including calculator use13
    Year 6: Tabulate systematically the information in a problem or puzzle; identify and record the steps or calculations needed to solve it, using symbols where appropriate; interpret solutions in the original context and check their accuracy15
    Counting and understanding number
    ObjectivePage
    Year 2: Read and write two-digit and three-digit numbers in figures and words …21
    Year 5: Express a smaller whole number as a fraction of a larger one; relate fractions to their decimal representations26
    Year 6: Express one quantity as a percentage of another; find equivalent percentages, decimals and fractions30
    Knowing and using number facts
    ObjectivePage
    Year 1: Derive and recall all pairs of numbers with a total of 10 …36
    Year 4: Derive and recall multiplication facts up to 10 ×10, the corresponding division facts and multiples of numbers to 10 up to the tenth multiple37
    Year 4: Use knowledge and understanding of rounding, number operations and inverses to estimate and check calculations40
    Year 5: Identify pairs of factors of two-digit whole numbers and find common multiples43
    Year 6: Use knowledge of place value … to derive related multiplication and division facts involving decimals45
    Calculating
    ObjectivePage
    Year 1: Understand subtraction as ‘take away’ and find a ‘difference’ by counting up …49
    Year 1: Solve practical problems that involve combining groups of 2, 5 or 1052
    Year 2: Use practical informal methods and related vocabulary to support multiplication and division52
    Year 3: Find unit fractions of numbers and quantities52
    Year 4: Refine and use efficient written methods to add and subtract two-digit and three-digit whole numbers and £pD.p55
    Year 4: Multiply and divide numbers to 1,000 by 10 and then 100, understanding the effect; relate to scaling up or down57
    Year 4: Find fractions of numbers, quantities or shapes52
    Year 5: Find fractions using division52
    Year 6: Relate fractions to multiplication and division52, 59
    Year 6: Use a calculator to solve problems involving multi-step calculations62
    Understanding shape
    ObjectivePage
    Year 2: Visualise common 2D shapes and 3D solids; identify shapes from pictures of them in different positions and orientations; sort, make and describe shapes, referring to their properties70
    Year 4: Know that angles are measured in degrees and that one whole turn is 360; compare and order angles less than 180°73
    Year 5: Complete patterns with up to two lines of symmetry; draw the position of a shape after a reflection or translation76
    Year 6: Visualise and draw on grids of different types where a shape will be after reflection, after translation, or after rotation through 90° or 180° about its centre or one of its vertices76
    Year 6/7: Extend knowledge of properties of triangles and quadrilaterals and use these to visualise and solve problems, explaining reasoning with diagrams79
    Measuring
    ObjectivePage
    Year 1: Estimate, measure, weigh and compare objects, choosing and using suitable uniform non-standard or standard units and measuring instruments85
    Year 2: Read the numbered divisions on a scale, and interpret the divisions between them87
    Year 4: Choose and use standard metric units and their abbreviations when estimating, measuring and recording length, weight and capacity; know the meaning of ‘kilo’, ‘centi’ and ‘milli’…91, 94
    Year 5: Interpret a reading that lies between two unnumbered divisions on a scale87
    Year 6: Calculate the perimeter and area of rectilinear shapes; estimate the area of an irregular shape by counting squares96
    Handling data
    ObjectivePage
    Year 1: Answer a question by recording information in lists and tables; present outcomes using practical resources, pictures, block graphs or pictograms103
    Year 1: Use diagrams to sort objects into groups according to a given criterion; suggest a different criterion for grouping the same objects103
    Years 1–4: Answer a question by identifying what data to collect; organise, present, analyse and interpret the data in tables, diagrams, tally charts, pictograms and bar charts, using ICT where appropriate108
    Year 5: Answer a set of questions …106
    Year 6: Solve problems by collecting, selecting, processing and interpreting data, using ICT where appropriate; draw conclusions and identify further questions to ask106
    Year 6: Describe and interpret results and solutions to problems using the mode, range, median and mean111

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