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## Mathematics Curriculum

The objective of the Mathematics curriculum is to foster confident mathematicians capable of problem-solving, unleashing their creativity, conducting independent investigations, and deriving enjoyment from exploring numbers, shapes, and mathematical concepts.

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Reception

The Reception Mathematics curriculum aligns with the EYFS Development Matters framework.

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In Reception, children embark on a journey to:

1. Master counting with precision from 1 to 20, arranging numbers in sequential order and identifying numbers that are one more or one less than a given number.

2. Utilise quantities and objects to engage in addition and subtraction of two single-digit numbers, employing strategies to count forward or backward and derive solutions.

3. Employ everyday language to discuss attributes such as size, weight, capacity, position, distance, time, and money, facilitating comparisons and problem-solving.

4. Recognize, generate, and articulate patterns.

5. Explore the characteristics of common objects and shapes, employing mathematical terminology to describe them.

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Year 1

In Year 1, children delve into:

1. Counting fluently up to 100, in both ascending and descending sequences, starting from 0, 1, or any given number.

2. Reading and writing numbers up to 100 in numeral and word forms, including counting in multiples of 2, 5, and 10.

3. Identifying numbers that are one more or one less than a given number.

4. Using objects and visual representations to convey numbers, while employing terms like "equal to," "more than," "less than," "most," and "least."

5. Reading, writing, and interpreting mathematical statements encompassing addition (+), subtraction (-), and equality (=).

6. Grasping number bonds and associated subtraction facts within the range of 20.

7. Executing addition and subtraction operations involving one- and two-digit numbers up to 20, including zero.

8. Tackling one-step problems, encompassing addition, subtraction, and missing number scenarios, through the aid of concrete objects and visual representations.

9. Resolving one-step problems linked to multiplication and division, utilising concrete objects, visual representations, and arrays, with teacher guidance.

10. Recognising, discerning, and naming halves and quarters as equal parts of objects, shapes, or quantities.

11. Addressing practical problems related to lengths, heights, mass, weight, capacity, volume, and time.

12. Measuring and commencing basic records for lengths, heights, mass, weight, capacity, volume, and time.

13. Identifying the worth of various coin and note denominations and working with money.

14. Sequencing events chronologically and using chronological language.

15. Telling time to the nearest hour and half-hour, with the ability to depict these times on a clock face.

16. Identifying common 2-D and 3-D shapes and comprehending concepts of position, direction, and movement, including turns.

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Year 2

In Year 2, children continue their mathematical journey by:

1. Counting in intervals of 2, 3, 5, and 10, starting from 0, and counting in tens from any number, both forward and backward.

2. Understanding the place value of each digit within a two-digit number, emphasizing tens and ones.

3. Recognising, representing, and estimating numbers using diverse forms, including the number line.

4. Comparing and ordering numbers up to 1000, while employing the symbols <, >, and =.

5. Reading and writing numbers up to 1000 in both numeral and word formats.

6. Employing place value and number facts to tackle mathematical problems.

7. Mentally adding and subtracting numbers, including three-digit numbers and employing formal written methods for columnar addition and subtraction.

8. Estimating answers and verifying solutions through inverse operations.

9. Handling problems involving addition, subtraction, and number facts.

10. Recalling and applying multiplication and division facts, particularly for the 2, 5, and 10 multiplication tables.

11. Crafting and solving multiplication and division equations, progressing from mental methods to formal written procedures.

12. Tackling problems encompassing multiplication and division, utilizing various strategies and contexts.

13. Recognising, representing, and manipulating fractions, including unit fractions and those with small denominators.

14. Adding and subtracting fractions with the same denominator within one whole.

15. Measuring, comparing, adding, and subtracting lengths, mass, volume, and capacity, and employing appropriate units of measurement.

16. Handling money, including making change and exploring different coin combinations.

17. Estimating and reading time to the nearest minute, recording and contrasting time in seconds, minutes, and hours.

18. Identifying and describing 2-D and 3-D shapes, as well as comprehending angles and symmetry.

19. Interpreting and displaying data through bar charts, pictograms, and tables, while answering one-step and two-step questions.

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Year 3

In Year 3, pupils advance their mathematical skills by:

1. Counting in multiples of 4, 8, 50, and 100, including finding numbers that are 10 or 100 more or less than a given number.

2. Understanding the place value of each digit in a three-digit number, involving hundreds, tens, and ones.

3. Comparing and ordering numbers up to 1000.

4. Identifying and estimating numbers through diverse representations.

5. Reading and writing numbers up to 1000 in both numeral and word forms.

6. Tackling numerical and practical problems effectively.

7. Mentally adding and subtracting numbers of varying magnitudes.

8. Utilising formal written methods for addition and subtraction.

9. Estimating solutions and validating them through inverse operations.

10. Solving problems, including those with missing numbers, employing number facts, place value, and advanced addition and subtraction techniques.

11. Recalling and applying multiplication and division facts related to the 3, 4, and 8 multiplication tables.

12. Writing and solving multiplication and division equations, starting with mental methods and progressing to formal written approaches.

13. Handling problems involving multiplication and division within a variety of contexts.

14. Grasping tenths and their relationship to dividing objects into ten equal parts.

15. Recognizing, representing, and writing fractions of objects, including unit fractions and those with small denominators.

16. Handling fractions as numerical quantities and understanding equivalent fractions.

17. Adding and subtracting fractions with the same denominator, along with comparing unit fractions.

18. Measuring, comparing, adding, and subtracting lengths, mass, volume, and capacity, while selecting suitable units of measurement.

19. Managing money, including making change, and exploring different coin combinations.

20. Estimating and reading time with increasing accuracy, encompassing seconds, minutes, and hours, and employing time-related vocabulary.

21. Calculating durations of events and tasks.

22. Identifying and describing properties of 2-D and 3-D shapes, including angles and symmetry.

23. Analyzing and presenting data through bar charts, pictograms, and tables, and addressing questions involving comparison and quantity.

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Year 4

In Year 4, pupils will:

1. Master counting in multiples of 6, 7, 9, 25, and 1000, and also understand how to find numbers 1000 greater or smaller than a given number. They'll also grasp the significance of each digit in a four-digit number.

2. Develop the ability to count backward through zero, which includes working with negative numbers.

3. Read, write, arrange, and compare numbers beyond 1000, and apply rounding to the nearest 10, 100, or 1000.

4. Solve various numerical and practical problems.

5. Gain proficiency in reading Roman numerals up to 100 (I to C) while learning about the historical evolution of the numeral system.

6. Add and subtract numbers with up to 4 digits, employing formal written methods such as columnar addition and subtraction where necessary.

7. Estimate results and employ inverse operations to verify calculations.

8. Tackle two-step addition and subtraction problems in different contexts, making informed choices about which operations and methods to use.

9. Recall multiplication and division facts for tables up to 12 × 12.

10. Use place value and derived facts for mental multiplication and division, with an emphasis on larger numbers.

11. Multiply two-digit and three-digit numbers by one-digit numbers.

12. Recognise and illustrate equivalent fractions through diagrams.

13. Count in hundredths and connect this to divisions by one hundred and ten.

14. Recognise and write decimal equivalents for tenths and hundredths.

15. Master rounding decimals with one decimal place to the nearest whole number.

16. Compare numbers with the same number of decimal places up to two decimal places.

17. Convert between different units of measurement.

18. Calculate the perimeter of rectilinear figures, including squares, and determine the area of rectilinear shapes.

19. Develop estimation skills for volume and capacity.

20. Identify 3-D shapes, including cubes and cuboids, from 2-D representations.

21. Understand and apply knowledge of angles, including acute and obtuse angles, and compare and order them.

22. Recognise lines of symmetry in 2-D shapes and complete symmetric figures.

23. Describe positions on a 2-D grid using coordinates.

24. Understand translations on a grid by moving left/right and up/down.

25. Plot specified points and connect them to form polygons.

26. Interpret and create various types of graphs, including bar charts and time graphs, to represent data.

27. Solve problems involving comparison, sum, and difference using information presented in graphs, tables, and pictograms.

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Year 5

In Year 5, pupils will:

1. Develop the ability to read, write, order, and compare numbers up to at least 1,000,000, and understand the value of each digit.

2. Count forward and backward in steps of powers of 10 for any given number up to 1,000,000.

3. Work with negative numbers and calculate intervals across zero.

4. Apply rounding to numbers up to 1,000,000 to verify calculations.

5. Tackle a variety of numerical and practical problems.

6. Master reading Roman numerals up to 1000 (M) and recognizing years written in Roman numerals.

7. Add and subtract whole numbers with more than 4 digits, including formal written methods.

8. Develop mental calculation skills, including mixed operations and larger numbers.

9. Identify multiples, factors, prime numbers, prime factors, and composite numbers.

10. Utilise estimation to check calculation results.

11. Understand and apply fractions, including simplification, equivalence, and comparison.

12. Associate fractions with division and calculate decimal fraction equivalents.

13. Understand algebraic concepts, solve problems, and generate and describe linear number sequences.

14. Solve problems involving the calculation and conversion of units of measure.

15. Work with shapes and understand the relationships between area and perimeter.

16. Recognize geometric shapes and angles, including parts of circles and their properties.

17. Understand coordinates and graphs and work with linear and quadratic functions.

18. Recognise and work with sequences and patterns.

19. Convert between different units of measurement.

20. Utilise scale factors, diagrams, and maps.

21. Employ ratio notation and solve problems involving ratios.

22. Solve problems related to percentages and decimals.

23. Understand concepts of volume, capacity, and 3-D shapes.

24. Work with lines, angles, reflections, and translations.

25. Interpret and analyse data represented in graphs, tables, and charts.

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Year 6

In Year 6, pupils will:

1. Read, write, order, use, and compare numbers up to 10,000,000 while understanding the value of each digit and rounding numbers.

2. Handle negative numbers in context and calculate across zero intervals.

3. Solve numerical and practical problems of varying complexity.

4. Multiply multi-digit numbers by two-digit whole numbers using formal written methods.

5. Perform mental calculations with mixed operations and larger numbers.

6. Identify common factors, common multiples, prime numbers, and use estimation for verifying calculations.

7. Grasp fractions, decimals, and algebraic concepts, including linear number sequences and missing number problems.

8. Tackle problems involving units of measure, shapes, area, perimeter, and relationships between them.

9. Recognise and work with geometric shapes, angles, and parts of circles.

10. Understand coordinates and graphing, including linear and quadratic functions.

11. Analyse and work with sequences and patterns.

12. Convert units of measurement.

13. Employ ratio notation for solving problems.

14. Address percentage and decimal-related problems.

15. Handle concepts of volume, capacity, and 3-D shapes.

16. Work with lines, angles, and transformations like reflections and translations.

17. Interpret and analyse data represented in various graphical forms, including line graphs, pie charts, and tables.

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Year 7 & 8

In Year 7 & 8, pupils will:

1. Grasp place value for decimals, measures, and integers of any magnitude.

2. Order and compare positive and negative integers, decimals, and fractions.

3. Deal with prime numbers, factors, multiples, prime factorization, and product notation.

4. Perform operations (addition, subtraction, multiplication, and division) on integers, decimals, and fractions, both positive and negative, using formal methods or mental calculations.

5. Use the order of operations and understand the concepts of brackets, powers, roots, and reciprocals.

6. Recognise and use inverse operations.

7. Employ estimation for calculation verification.

8. Utilise algebra to solve problems, including linear sequences and missing numbers.

9. Work with expressions, equations, inequalities, terms, factors, and standard mathematical formulae.

10. Translate real-world situations into algebraic expressions and formulae and use graphs for modeling.

11. Solve linear equations and handle coordinates in all four quadrants.

12. Graph linear and quadratic functions and interpret their mathematical relationships.

13. Identify and manipulate geometric and arithmetic sequences.

14. Convert between different units of measurement and handle scale factors and diagrams.

15. Understand ratio notation, reduction to simplest form, and use of ratios for problem-solving.

16. Solve problems related to percentages, direct proportion, compound units, and conversions.

17. Calculate areas and perimeters of shapes and comprehend the relationship between them.

18. Work with 3-D shapes, angles, and symmetry.

19. Interpret data and construct

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