Part of Cross-curricular skills frameworks
Numeracy
Developing mathematical proficiency
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| Progression step 1 | Progression step 2 | Progression step 3 | Progression step 4 | Progression step 5 |
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| Conceptual understanding | ||||
I can make connections so that basic mathematical concepts can be transferred during play and classroom activities. |
I can make connections so that mathematical concepts can be transferred during play and classroom activities. |
I can make connections so that mathematical concepts can be built on and deepened. |
I can make connections so that mathematical concepts can be built on and deepened. |
I can make connections so that mathematical concepts can be built on and deepened. |
I can understand and use basic mathematical concepts in a variety of ways. |
I can represent a concept in different ways, flowing between different representations including verbal, concrete, visual, digital and abstract. |
I can draw on my understanding of the basic structures of mathematics and can apply them in different contexts. |
I can draw on my understanding of the basic structures of mathematics and can apply them in different contexts. |
I can draw on my understanding of the basic structures of mathematics and can apply them in different contexts. |
I can explore answers within the context of the problem and I am beginning to consider whether answers are sensible. |
I can interpret answers within the context of the problem and consider whether answers are sensible. |
I can explain and express concepts, and find examples (or non-examples). |
I can explain and express concepts, and find examples (or non-examples). |
I can explain and express concepts, and find examples (or non-examples). |
I can represent a concept in different ways, flowing between different representations including verbal, concrete, visual, digital and abstract. |
I can represent a concept in different ways, flowing between different representations including verbal, concrete, visual, digital and abstract. |
I can represent a concept in different ways, flowing between different representations including verbal, concrete, visual, digital and abstract. |
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I can interpret answers within the context of the problem and consider whether answers, including calculator, analogue and digital displays, are sensible. |
I can interpret answers within the context of the problem and consider whether answers, including calculator, analogue and digital displays, are sensible. |
I can interpret answers within the context of the problem and consider whether answers, including calculator, analogue and digital displays, are sensible. |
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| Logical reasoning | ||||
I can use everyday and mathematical language to talk about my own ideas and choices. |
I can use everyday and mathematical language to talk about and explain my own ideas and choices. |
I can construct and develop a mathematical argument. |
I can construct and develop a mathematical argument. |
I can construct and develop a mathematical argument. |
I can verify results and solutions. |
I can justify my procedures and predictions. |
I can justify my procedures, predictions and conjectures. |
I can justify my procedures, predictions and conjectures. |
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I can verify results and solutions. |
I can verify and prove results and solutions. |
I can verify and prove results and solutions. |
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I can explain results and procedures precisely using appropriate mathematical language. |
I can explain results and procedures precisely using appropriate mathematical language. |
I can explain results and procedures precisely using appropriate mathematical language. |
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| Fluency | ||||
I am beginning to apply relevant facts and techniques. |
I can identify relevant facts and techniques in order to apply an efficient method. |
I can use firmly established, memorable and usable facts and techniques in order to apply the most efficient methods. |
I can use firmly established, memorable and usable facts and techniques in order to apply the most efficient methods. |
I can use firmly established, memorable and usable facts and techniques in order to apply the most efficient methods. |
I can use checking strategies to decide if answers are reasonable. |
I can select and apply appropriate checking strategies. |
I can select and apply appropriate checking strategies. |
I can select and apply appropriate checking strategies. |
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I can use a calculator effectively and efficiently to carry out calculations. |
I can use a scientific calculator effectively and efficiently to carry out calculations using the available range of function keys. |
I can use a scientific calculator effectively and efficiently to carry out calculations using the available range of function keys. |
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| Strategic competence | ||||
I can select the appropriate equipment and resources to help me. |
I can identify the required information, and select appropriate equipment and resources. |
I can recognise, model and apply the underlying mathematical structures and ideas within problems, in order to formulate and solve them. |
I can recognise, model and apply the underlying mathematical structures and ideas within problems, in order to formulate and solve them. |
I can recognise, model and apply the underlying mathematical structures and ideas within problems, in order to formulate and solve them. |
I can suggest what I might need to do to complete the task or reach a solution. |
I can identify steps to complete the task or reach a solution. |
I can identify, measure or obtain required information to complete the task. |
I can identify, measure or obtain required information to complete the task. |
I can identify, measure or obtain required information to complete the task. |
I can explore appropriate mathematics and techniques to use. |
I can select appropriate mathematics and techniques to use. |
I can identify what further information might be required and select what information is most appropriate. |
I can identify what further information might be required and select what information is most appropriate. |
I can identify what further information might be required and select what information is most appropriate. |
I can choose an appropriate mental or written strategy and know when it is appropriate to use a calculator. |
I can select, trial and evaluate a variety of possible approaches and break problems into a series of tasks. |
I can select, trial and evaluate a variety of possible approaches and break complex problems into a series of tasks. |
I can select, trial and evaluate a variety of possible approaches and break complex problems into a series of tasks. |
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I can prioritise and organise the relevant steps needed to complete the task or reach a solution. |
I can prioritise and organise the relevant steps needed to complete the task or reach a solution. |
I can prioritise and organise the relevant steps needed to complete the task or reach a solution. |
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I can choose an appropriate mental or written strategy and know when it is appropriate to use a calculator. |
I can choose an appropriate mental or written strategy and know when it is appropriate to use a calculator. |
I can choose an appropriate mental or written strategy and know when it is appropriate to use a calculator. |
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| Communicating with symbols | ||||
I can explore informal, personal methods of recording, moving towards using symbols. |
I can use appropriate notation, symbols and units of measurement. |
I can communicate my answers using correct mathematical form. |
I can communicate my answers using correct mathematical form. |
I can communicate my answers using correct mathematical form. |
I can devise and refine informal, personal methods of recording, moving to using words and symbols in number sentences. |
I can use appropriate notation, symbols and units of measurement. |
I can use appropriate notation, symbols and units of measurement, including compound measures. |
I can use appropriate notation, symbols and units of measurement, including compound measures. |
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I can refine methods of recording calculations. |
I can refine methods of recording calculations. |
I can refine methods of recording calculations. |
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Understanding the number system helps us to represent and compare relationships between numbers and quantities
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| Progression step 1 | Progression step 2 | Progression step 3 | Progression step 4 | Progression step 5 |
|---|---|---|---|---|
| The number system | ||||
I can count reliably, forwards and backwards, to beyond 10. |
I can read, write and interpret numbers using figures and words up to at least 1000. |
I can read and write numbers to 1 million and numbers to 3 decimal places. |
I can read and write numbers of any size. |
I can recognise and define limitations on accuracy of measurements, e.g. upper and lower bounds. |
I can notice, read and write numbers from 0 to beyond 10, and relate a number to its respective quantity. |
I can compare, round and estimate with numbers up to 100. |
I can use the terms square and square root. |
I can use the terms cube, cube root and reciprocal. |
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I can compare and order numbers beyond 10. |
I can count in different steps of uniform size, and recognise odd and even numbers. |
I can estimate by rounding to the nearest 10, 100, 1000 or whole number. |
I can show awareness of the need for standard form and its representation on a calculator. |
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I can demonstrate an understanding of one-to-one correspondence by matching pairs of objects or pictures. |
I can check subtraction using addition. |
I can use and interpret numbers in standard form within calculations. |
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I can use my visual sense of number to make estimates and comparisons. |
I can check halving using doubling. |
I can use rounding to estimate and check answers. |
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I can explore estimates by using counting or measuring. |
I can present answers to a given number of decimal places or significant figures. |
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I can make and justify estimates and approximations of calculations. |
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I can choose the appropriate degree of accuracy to present answers. |
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| Relationships within the number system | ||||
I can use halves and quarters. |
I can use understanding of simple fraction, decimal and percentage equivalences, e.g. find 25% of 60cm and know that this is equivalent to ¼ of 60cm. |
I can use equivalence of fractions, decimals and percentages to select the most appropriate one for a calculation. |
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I can halve 2-digit numbers in the context of number, money and measures. |
I can simplify a calculation by using fractions in their simplest terms. |
I can recognise that some fractions are recurring decimals, e.g. 1/3 is 0.333˙ |
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I can find fractional quantities linked to known multiplication facts, e.g. 1/3 of 18, 1/5 of 15. |
I can use and interpret different representations of fractions, e.g. mixed numbers and improper fractions. |
I can use powers and understand the importance of powers of 10. |
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I can use equivalence of fractions, decimals and percentages to compare proportions. |
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| Calculation | ||||
I can understand and use the concept of ‘one more’ in my play. |
I can find differences within at least 100. |
I can use mental strategies to recall multiplication tables up to 10 x 10 and use to solve division problems. |
I can use the four operations and the connections between them, e.g. apply division as the inverse of multiplication. |
I can use multipliers as an efficient method when working with percentages, e.g. multiply by 1.2 to increase an amount by 20%. |
I can understand and use the concept of ‘one less’ in my play. |
I can use mental strategies to add and subtract at least 2-digit numbers. |
I can multiply numbers and decimals by a multiple of 10, e.g. 15 x 30, 1.4cm x 20. |
I can use efficient written methods to add and subtract numbers and decimals of any size, including a mixture of large and small numbers with differing numbers of decimal places. |
I can use and understand the idea of reverse percentage to find an original quantity. |
I can combine two groups of objects to find ‘how many altogether?’. |
I can use partitioning to double and halve 2-digit numbers. |
I can halve 3-digit numbers in the context of number, money and measures. |
I can use appropriate strategies for multiplication and division, including application of known facts to derive others, e.g. use 7 x 6 to derive 0.7 x 6. |
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I can take away objects to find ‘how many are left?’. |
I can use mental strategies to recall number facts within 20. |
I can calculate a percentage, fraction and decimal of any quantity with a calculator where appropriate. |
I can use efficient methods for multiplication and division of whole numbers and decimals, including decimals such as 0.6 or 0.06. |
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I can find and use number facts to compose a number (up to 10) in different ways. |
I can recall 2, 3, 4, 5 and 10 multiplication tables and use to solve multiplication and division problems. |
I can use ratio and proportion to calculate quantities. |
I can use the order of operations including brackets and powers. |
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I can multiply numbers by 10. |
I can calculate percentage quantities based on 10%, e.g. 20%, 5%, 15%. |
I can calculate a percentage increase or decrease. |
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I can check multiplication using repeated addition. |
I can add and subtract numbers using whole numbers and decimals. |
I can express one quantity as a percentage of another. |
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I can multiply 2- and 3-digit numbers by a 2-digit number. |
I can calculate percentages of quantities using non-calculator methods where appropriate. |
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I can divide 3-digit numbers by a 2-digit number. |
I can use ratio and proportion including map scales. |
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I can use a range of strategies to check calculations including the use of inverse operations, equivalent calculations and the rules of divisibility. |
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| Financial literacy | ||||
I can exchange money for items and use the language of money. |
I can use different combinations of money to pay for items up to at least £2 and calculate the change. |
I can add and subtract totals less than £100 using correct notation, e.g. £28.18 + £33.45. |
I can calculate using foreign money and exchange rates. |
I can understand and demonstrate the real-life process of foreign exchange. |
I can demonstrate an awareness of the purpose of money through role play and in real-life situations. |
I can order and compare items up to £10. |
I can manage money, compare costs from different retailers and determine what can be bought within a given budget. |
I can make informed decisions relating to discounts and special offers. |
I can understand and calculate income tax and understand the implications of taxation. |
I can make comparisons between prices and understand which is best value for money. |
I can carry out calculations relating to VAT, saving and borrowing. |
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I can use profit and loss in buying and selling calculations. |
I can appreciate the basic principles of budgeting, saving (including understanding compound interest) and borrowing. |
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I can realise that budgeting is important. |
I can understand the advantages and disadvantages of using bank accounts, including bank cards. |
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I can understand the advantages and disadvantages of using bank accounts. |
I can understand the risks involved in different ways of saving and investing. |
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I can plan and track money and savings by keeping accurate records. |
I can use and understand efficient methods of calculating compound interest. |
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I can describe why insurance is important and understand the impact of not being insured. |
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Learning about geometry helps us understand shape, space and position, and learning about measurement helps us quantify in the real world
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| Progression step 1 | Progression step 2 | Progression step 3 | Progression step 4 | Progression step 5 |
|---|---|---|---|---|
| Measurement | ||||
I can use non-standard units of measure to discuss my sense of size. |
I can use non-standard units to measure. |
I can read and interpret scales or divisions on a range of measuring instruments. |
I can represent and use compound measures, using standard units. |
I can understand and use a variety of compound measures. |
I can use direct comparisons with:
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I can progress to use standard units of measure:
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I can record measurements in different ways, e.g. 1.3kg = 1kg 300g, 4.2cm = 4cm 2mm. |
I can read and interpret scales on a range of measuring instruments. |
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I can anticipate events related to elements of daily routines and use the terms ‘before’ and ‘after’. |
I can use the concept of time in terms of my daily and weekly activities and the seasons of the year. |
I can convert metric units of length to smaller units, e.g. cm to mm, m to cm, km to m. |
I can demonstrate an understanding of the relationship between a formula representing a measurement and the units used. |
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I can use the basic concept of time in terms of my daily activities. |
I can use standard units of time to read 'o'clock', 'half past', 'quarter past' and 'quarter to' using both analogue and 12-hour digital clocks. |
I can use the language of imperial units in daily use, e.g. miles, pints. |
I can use the common units of measure, convert between related units of the metric system and carry out calculations. |
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I can demonstrate a developing sense of how long tasks and everyday events take. |
I can read and use analogue and digital clocks. |
I can use rough metric equivalents of imperial units in daily use. |
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I can use and interpret calendars, timetables and schedules to plan events and activities, and make calculations as part of the planning journey. |
I can interpret fractions of a second appropriately. |
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I can carry out practical activities involving timed events and explain which unit of time is the most appropriate. |
I can use timetables and time zones to calculate travel time. |
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I can time events in minutes and seconds, and order the results. |
I can convert temperatures between appropriate temperature scales. |
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I can estimate how long a journey takes. |
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I can measure and record temperatures involving positive and negative readings. |
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| Shape and space | ||||
I can discuss the properties of shapes that I use in my everyday learning. |
I can discuss the properties of two-dimensional and three-dimensional shapes that I use in my everyday learning. |
I can recognise that perimeter is the distance around a shape. |
I can find circumferences of circles using my understanding of π (Pi). |
I can apply proportional change to two-dimensional designs. |
I can measure and calculate perimeter. |
I can calculate the areas of two-dimensional simple and compound shapes, including circles. |
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I can find areas by counting squares, progressing to calculating the area of squares and rectangles using formulae. |
I can apply the formulae for the volume of simple prisms. |
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I can use mathematical language to accurately describe two-dimensional and three-dimensional shapes. |
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I can find volumes by counting and other practical methods. |
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| Position | ||||
I can explore movements and directions. |
I can use the language of position. |
I can use grid references to specify location. |
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I can describe position. |
I can use the four compass points to describe directions. |
I can use coordinates to find position. |
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| Angle | ||||
I can recognise half and quarter turns, clockwise and anti-clockwise. |
I can use angle as a measure of rotation. |
I can measure and draw angles. |
I can measure and draw angles. |
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I can apply understanding of bearings and scale to interpret maps and plans, and to create plans and drawings to scale. |
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Learning that statistics represent data and that probability models chance helps us make informed inferences and decisions
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| Progression step 1 | Progression step 2 | Progression step 3 | Progression step 4 | Progression step 5 |
|---|---|---|---|---|
| Collecting data | ||||
I have collected data found in my environment. |
I can collect information by voting or sorting. |
I can collect relevant data to answer posed questions. |
I can collect own data for a survey, e.g. through designing a questionnaire. |
I can collect data in a suitable way according to my hypothesis. |
I can plan how to collect data to test a simple hypotheses. |
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I can collect both quantitative and qualitative data. |
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| Representing data | ||||
I can sort and match sets of objects or pictures by recognising similarities and can communicate my choices. |
I can sort and classify objects using more than one criterion. |
I can select and construct appropriate charts, diagrams and graphs with suitable scales. |
I can select and construct appropriate charts, diagrams and graphs with suitable scales. |
I can select and construct appropriate charts, diagrams and graphs with suitable scales. |
I can present work orally, pictorially and in written form, and use a variety of ways to represent collected data. |
I can present work orally, in objects, pictorially and in written form, and use a variety of ways to represent collected data with suitable scales including:
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I can represent data using:
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I can construct frequency tables for sets of data in equal class intervals, selecting groups as appropriate. |
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I can use mark-making to begin to record collections. |
I can construct and interpret graphs and diagrams (including pie charts) to represent discrete or continuous data, choosing an appropriate scale. |
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I can construct graphs to represent data including scatter diagrams to investigate correlation. |
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| Interpreting data | ||||
I can interpret information presented in charts and diagrams, and draw appropriate conclusions. |
I can extract and interpret information presented in charts, timetables, diagrams and graphs. |
I can extract and interpret information from an increasing range of diagrams, timetables and graphs (including pie charts). |
I can interpret graphs that describe real-life situations, including those used in the media, recognising that some graphs may be misleading. |
I can interpret graphs that describe real-life situations, including those used in the media, recognising that some graphs may be misleading. |
I can draw conclusions from data and recognise that some conclusions may be misleading or uncertain. |
I can draw conclusions from data and recognise that some conclusions may be misleading or uncertain. |
I can interpret mathematical information; drawing inferences from graphs, diagrams and data, including discussion on limitations of data. |
I can interpret mathematical information; drawing inferences from graphs, diagrams and data, including discussion on limitations of data. |
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I can use mean to interpret a simple data set. |
I can draw conclusions from data and recognise that some conclusions may be misleading or uncertain. |
I can draw conclusions from data and recognise that some conclusions may be misleading or uncertain. |
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I can use mean, median, mode and range to compare data (continuous and discrete), and can choose the most appropriate average. |
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I can explore trends and extreme values (outliers) for data sets. |
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I can examine results critically, select and justify choice of statistics, recognising the limitations of any assumptions and their effect on the conclusions drawn. |
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