Mathematics – United Kingdom – National Curriculum
Year 5 programme of study
KS2.Y5.N.NPV – Number - number and place value
Pupils should be taught to:
KS2.Y5.N.NPV.1 – Read, write, order and compare numbers to at least 1,000,000 and determine the value of each digit
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1 learning outcomes – click to view
Samples: Ordering large numbers No:1. Ordering large numbers No:2. Ordering large numbers.
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Ordering large numbers
- Activities: 0 course, 6 extra
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1 learning outcomes – click to view
KS2.Y5.N.NPV.2 – Count forwards or backwards in steps of powers of 10 for any given number up to 1,000,000
KS2.Y5.N.NPV.3 – Interpret negative numbers in context, count forwards and backwards with positive and negative whole numbers, including through 0
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1 learning outcomes – click to view
Samples: Integers on a number line.
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Integers on a number line
- Activities: 1 course, 0 extra
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1 learning outcomes – click to view
KS2.Y5.N.NPV.4 – Round any number up to 1,000,000 to the nearest 10, 100, 1,000, 10,000 and 100,000
KS2.Y5.N.NPV.5 – Solve number problems and practical problems that involve all of the above
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2 learning outcomes – click to view
Samples: Large numbers presented in tables. Numbers. Numbers Problem Solving. Number Operations 1 Extension.
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Large numbers presented in tables
- Activities: 1 course, 0 extra
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Numbers
- Activities: 1 course, 5 extra
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2 learning outcomes – click to view
KS2.Y5.N.NPV.6 – Read Roman numerals to 1,000 (M) and recognise years written in Roman numerals
KS2.Y5.N.AS – Number - addition and subtraction
Pupils should be taught to:
KS2.Y5.N.AS.1 – Add and subtract whole numbers with more than 4 digits, including using formal written methods (columnar addition and subtraction)
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4 learning outcomes – click to view
Samples: Addition of large numbers. Adding on to Multiples of 10. Addition and subtraction (problem solving).
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Adding large numbers
- Activities: 5 course, 29 extra
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Adding-on to multiples of ten
- Activities: 2 course, 1 extra
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Addition and subtraction (problem solving)
- Activities: 3 course, 4 extra
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Subtracting from 1000
- Activities: 6 course, 10 extra
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4 learning outcomes – click to view
KS2.Y5.N.AS.2 – Add and subtract numbers mentally with increasingly large numbers
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4 learning outcomes – click to view
Samples: Addition of four digit numbers. Subtracting large numbers. Subtracting from lots of 1000. Adding-on to make 1000.
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Four digit addition (Skill 62)
- Activities: 5 course, 7 extra
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Four digit subtraction (Skill 63)
- Activities: 6 course, 7 extra
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Subtracting from 1000 (Skill 64)
- Activities: 5 course, 7 extra
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Adding-on to make 1000 (Skill 65)
- Activities: 9 course, 8 extra
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4 learning outcomes – click to view
KS2.Y5.N.AS.3 – Use rounding to check answers to calculations and determine, in the context of a problem, levels of accuracy
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2 learning outcomes – click to view
Samples: Adding (problem solving). Subtracting large numbers. Adding (problem solving) Answer sheet.
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Adding (problem solving)
- Activities: 1 course, 3 extra
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Subtracting large numbers
- Activities: 4 course, 6 extra
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2 learning outcomes – click to view
KS2.Y5.N.AS.4 – Solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why
KS2.Y5.N.MD – Number - multiplication and division
Pupils should be taught to:
KS2.Y5.N.MD.1 – Identify multiples and factors, including finding all factor pairs of a number, and common factors of 2 numbers
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2 learning outcomes – click to view
Samples: Identifying multiples. Common factors. Common factors.
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Identifying multiples
- Activities: 1 course, 0 extra
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Common factors
- Activities: 2 course, 0 extra
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2 learning outcomes – click to view
KS2.Y5.N.MD.2 – Know and use the vocabulary of prime numbers, prime factors and composite (non-prime) numbers
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2 learning outcomes – click to view
Samples: Prime and Composite Numbers. Prime numbers. Identifying prime numbers.
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Prime and Composite Numbers
- Activities: 1 course, 0 extra
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Prime numbers
- Activities: 2 course, 0 extra
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2 learning outcomes – click to view
KS2.Y5.N.MD.3 – Establish whether a number up to 100 is prime and recall prime numbers up to 19
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1 learning outcomes – click to view
Samples: Identifying prime numbers < 100 (puzzle).
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Identifying prime numbers < 100 (puzzle)
- Activities: 1 course, 0 extra
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1 learning outcomes – click to view
KS2.Y5.N.MD.4 – Multiply numbers up to 4 digits by a one- or two-digit number using a formal written method, including long multiplication for two-digit numbers
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4 learning outcomes – click to view
Samples: 11x tables. 12x tables. Multiplying 2 by 2 digits. Times tables revision. 11x tables. 12x tables.
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11x tables
- Activities: 2 course, 1 extra
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12x tables
- Activities: 2 course, 1 extra
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Multiplying two-digit numbers
- Activities: 5 course, 10 extra
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Revision
- Activities: 5 course, 4 extra
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4 learning outcomes – click to view
KS2.Y5.N.MD.5 – Multiply and divide numbers mentally, drawing upon known facts
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5 learning outcomes – click to view
Samples: Multiplying by multiples of 10. Multiplying two-digit numbers by 11.
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Multiply a 2 digit number by a multiple of 10 (Skill 72)
- Activities: 5 course, 7 extra
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Multiplying two-digit numbers by 11 (Skill 73)
- Activities: 9 course, 8 extra
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Two digit division - with remainders (Skill 74)
- Activities: 5 course, 7 extra
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Three-fifths of a number (Skill 78)
- Activities: 8 course, 8 extra
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Balancing addition equations (Skill 79)
- Activities: 7 course, 8 extra
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5 learning outcomes – click to view
KS2.Y5.N.MD.6 – Divide numbers up to 4 digits by a one-digit number using the formal written method of short division and interpret remainders appropriately for the context
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3 learning outcomes – click to view
Samples: Dividing 3 digits by 1 digit (no remainders). Division (estimation) - 1. Division (no remainders).
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Dividing 3 digits by 1 digit
- Activities: 7 course, 11 extra
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Division (estimation)
- Activities: 2 course, 0 extra
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Dividing 4-digit numbers by 1-digit numbers
- Activities: 4 course, 5 extra
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3 learning outcomes – click to view
KS2.Y5.N.MD.7 – Multiply and divide whole numbers and those involving decimals by 10, 100 and 1,000
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4 learning outcomes – click to view
Samples: Multiplying by 10, 100 and 1000. Multiplying by 100. Multiplying by multiples of 10. Dividing Whole Numbers by 100.
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Multiplying by 10
- Activities: 4 course, 7 extra
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Multiplying by 100
- Activities: 3 course, 8 extra
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Multiplying by multiples of ten
- Activities: 4 course, 12 extra
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Dividing whole numbers by 100
- Activities: 4 course, 0 extra
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4 learning outcomes – click to view
KS2.Y5.N.MD.8 – Recognise and use square numbers and cube numbers, and the notation for squared (²) and cubed (³)
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3 learning outcomes – click to view
Samples: Squaring numbers. Square root. Square root. Squaring numbers. Square root. Index notation. Square root. Index notation.
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Index notation.
- Activities: 4 course, 6 extra
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Square root
- Activities: 3 course, 2 extra
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Square root
- Activities: 1 course, 0 extra
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3 learning outcomes – click to view
KS2.Y5.N.MD.9 – Solve problems involving multiplication and division, including using their knowledge of factors and multiples, squares and cubes
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4 learning outcomes – click to view
Samples: Factors. Challenge puzzle - identifying prime numbers. Index notation (puzzle). Challenge puzzle - square root.
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Factors
- Activities: 6 course, 2 extra
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Identifying prime numbers
- Activities: 1 course, 0 extra
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Index notation
- Activities: 1 course, 0 extra
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Square roots
- Activities: 1 course, 0 extra
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4 learning outcomes – click to view
KS2.Y5.N.MD.10 – Solve problems involving addition, subtraction, multiplication and division and a combination of these, including understanding the meaning of the equals sign
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6 learning outcomes – click to view
Samples: Challenge puzzle - flow diagram. Equivalent number sentences (written form). Identifying expressions.
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Challenge puzzle - flow diagram
- Activities: 1 course, 0 extra
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Equivalent number sentences (written form)
- Activities: 1 course, 0 extra
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Identifying expressions
- Activities: 1 course, 2 extra
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Brackets in number operations
- Activities: 1 course, 0 extra
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Brackets in number operations - Two Step
- Activities: 1 course, 0 extra
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Balancing equations - Equivalent number sentences
- Activities: 4 course, 2 extra
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6 learning outcomes – click to view
KS2.Y5.N.MD.11 – Solve problems involving multiplication and division, including scaling by simple fractions and problems involving simple rates
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7 learning outcomes – click to view
Samples: Multiplying multiples of 10 (missing number). Multiplying two 2 digit numbers (problem solving).
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Multiplying multiples of 10 (missing number)
- Activities: 3 course, 8 extra
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Multiplying by 2 digit numbers (problem solving)
- Activities: 1 course, 4 extra
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Dividing multiples of 10 by 1 digit (problem solving)
- Activities: 0 course, 1 extra
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Dividing 3 digits by 1 digit (problem solving)
- Activities: 0 course, 2 extra
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Dividing large numbers (problem solving)
- Activities: 1 course, 3 extra
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Division puzzle
- Activities: 1 course, 0 extra
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Division- answers as fractions
- Activities: 2 course, 0 extra
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7 learning outcomes – click to view
KS2.Y5.N.F – Number - fractions (including decimals and percentages)
Pupils should be taught to:
KS2.Y5.N.F.1 – Compare and order fractions whose denominators are all multiples of the same number
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2 learning outcomes – click to view
Samples: Comparing Fractions. Comparing fractions to a half. Compare to a half. Comparing fractions - identify the smallest.
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Comparing fractions
- Activities: 4 course, 2 extra
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Comparing fractions
- Activities: 4 course, 0 extra
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2 learning outcomes – click to view
KS2.Y5.N.F.2 – Identify, name and write equivalent fractions of a given fraction, represented visually, including tenths and hundredths
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4 learning outcomes – click to view
Samples: Modelling equivalent fractions. Hundredths in their lowest forms. Equivalent fractions.
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Modelling equivalent fractions
- Activities: 3 course, 3 extra
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Hundredths in their lowest forms
- Activities: 1 course, 0 extra
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Equivalent fractions
- Activities: 7 course, 10 extra
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Simplifying fractions
- Activities: 4 course, 2 extra
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4 learning outcomes – click to view
KS2.Y5.N.F.3 – Recognise mixed numbers and improper fractions and convert from one form to the other and write mathematical statements > 1 as a mixed number [for example, â…– + â…˜ = 6/5 = 1 â…• ]
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4 learning outcomes – click to view
Samples: Converting mixed numbers to improper fractions tutorial. Converting Improper Fractions. Adding mixed fractions.
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Converting mixed numbers to improper frac.
- Activities: 0 course, 1 extra
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Improper and mixed number fractions
- Activities: 6 course, 1 extra
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Adding mixed fractions
- Activities: 1 course, 0 extra
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Adding and subtracting fractions
- Activities: 4 course, 0 extra
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4 learning outcomes – click to view
KS2.Y5.N.F.4 – Add and subtract fractions with the same denominator, and denominators that are multiples of the same number
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3 learning outcomes – click to view
Samples: Adding fraction with common denominators tutorial. Adding and subtracting related fractions.
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Add and subtract fractions (same denominators)
- Activities: 0 course, 3 extra
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Adding and subtracting related fractions
- Activities: 6 course, 1 extra
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Adding fractions with the same denominators
- Activities: 0 course, 1 extra
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3 learning outcomes – click to view
KS2.Y5.N.F.5 – Multiply proper fractions and mixed numbers by whole numbers, supported by materials and diagrams
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1 learning outcomes – click to view
Samples: Fractions.
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Multiplying fractions by a whole number - visual
- Activities: 1 course, 0 extra
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1 learning outcomes – click to view
KS2.Y5.N.F.6 – Read and write decimal numbers as fractions [for example, 0.71 = 71/100 ]
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1 learning outcomes – click to view
Samples: Changing mixed fractions to decimals.
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Changing mixed fractions to decimals
- Activities: 0 course, 1 extra
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1 learning outcomes – click to view
KS2.Y5.N.F.7 – Recognise and use thousandths and relate them to tenths, hundredths and decimal equivalents
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3 learning outcomes – click to view
Samples: Read and write decimals in the thousandths. Place value (thousandths). Place value – thousandths.
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Read and write decimals in the thousandths
- Activities: 1 course, 0 extra
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Place value (thousandths)
- Activities: 1 course, 0 extra
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Place value - thousandths
- Activities: 1 course, 0 extra
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3 learning outcomes – click to view
KS2.Y5.N.F.8 – Round decimals with 2 decimal places to the nearest whole number and to 1 decimal place
KS2.Y5.N.F.9 – Read, write, order and compare numbers with up to 3 decimal places
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2 learning outcomes – click to view
Samples: Compare and order decimals. Comparing decimals in the thousandths. Compare Decimal Numbers.
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Compare and order decimals
- Activities: 1 course, 1 extra
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Comparing decimals in the thousandths
- Activities: 1 course, 0 extra
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2 learning outcomes – click to view
KS2.Y5.N.F.10 – Solve problems involving number up to 3 decimal places
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4 learning outcomes – click to view
Samples: Adding Decimals. Subtracting Decimals. Multiplying Decimals By A Single Digit Number. Paying for goods.
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Adding decimals
- Activities: 5 course, 3 extra
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Subtracting decimals
- Activities: 4 course, 3 extra
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Multiplying decimals by a whole number
- Activities: 2 course, 6 extra
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Calculations involving money
- Activities: 0 course, 2 extra
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4 learning outcomes – click to view
KS2.Y5.N.F.11 – Recognise the per cent symbol (%) and understand that per cent relates to ‘number of parts per 100’, and write percentages as a fraction with denominator 100, and as a decimal fraction
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2 learning outcomes – click to view
Samples: Converting fractions to percentages. Percentages as Decimals. Converting fractions and decimals to percentages.
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Matching fractions, decimals and percentages.
- Activities: 3 course, 6 extra
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Percentages as Decimals
- Activities: 1 course, 0 extra
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2 learning outcomes – click to view
KS2.Y5.N.F.12 – Solve problems which require knowing percentage and decimal equivalents of ½ , ¼ , â…• , â…– , â…˜ and those fractions with a denominator of a multiple of 10 or 25
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2 learning outcomes – click to view
Samples: Calculating Percentages. Fractions Problem Solving.
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Calculating percentages
- Activities: 1 course, 0 extra
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Simple fractions of quantities (problem solving)
- Activities: 0 course, 1 extra
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2 learning outcomes – click to view
KS2.Y5.M – Measurement
Pupils should be taught to:
KS2.Y5.M.1 – Convert between different units of metric measure [for example, kilometre and metre; centimetre and metre; centimetre and millimetre; gram and kilogram; litre and millilitre]
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6 learning outcomes – click to view
Samples: Units of measure. Converting between Kilometres and Metres tutorial.
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Converting between kilometers and meters
- Activities: 1 course, 0 extra
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Converting between metric units of length.
- Activities: 2 course, 8 extra
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Problem solving : Volume
- Activities: 0 course, 5 extra
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Converting between grams and kilograms
- Activities: 1 course, 0 extra
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Convert units of mass - between kilograms and grams
- Activities: 6 course, 22 extra
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6 learning outcomes – click to view
KS2.Y5.M.2 – Understand and use approximate equivalences between metric units and common imperial units such as inches, pounds and pints
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4 learning outcomes – click to view
Samples: Customary units - converting.
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Customary Units - converting between customary units of length.
- Activities: 1 course, 0 extra
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4 learning outcomes – click to view
KS2.Y5.M.3 – Measure and calculate the perimeter of composite rectilinear shapes in centimetres and metres
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5 learning outcomes – click to view
Samples: Calculating the Area of Irregular Shapes. Calculating the Area of Irregular Shapes. Perimeter of Regular Shapes.
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Area of irregular shapes
- Activities: 3 course, 1 extra
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Calculate the area of irregular shapes.
- Activities: 0 course, 3 extra
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Perimeter of Regular Shapes
- Activities: 0 course, 1 extra
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Area of Squares and Rectangles
- Activities: 0 course, 1 extra
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Area of Irregular Shapes
- Activities: 0 course, 1 extra
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5 learning outcomes – click to view
KS2.Y5.M.4 – Calculate and compare the area of rectangles (including squares), including using standard units, square centimetres (cm²) and square metres (m²), and estimate the area of irregular shapes
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1 learning outcomes – click to view
Samples: Area (problem solving). Area Problem Solving. Area Problem Solving. Area Problem Solving. Area Problem Solving.
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Area (problem solving)
- Activities: 1 course, 6 extra
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1 learning outcomes – click to view
KS2.Y5.M.5 – Estimate volume [for example, using 1 cm³ blocks to build cuboids (including cubes)] and capacity [for example, using water]
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1 learning outcomes – click to view
Samples: Volume and Capacity. Comparing the volume of liquids tutorial. Comparing the volume of liquids no.2 tutorial.
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Volume and Capacity
- Activities: 3 course, 7 extra
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1 learning outcomes – click to view
KS2.Y5.M.6 – Solve problems involving converting between units of time
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1 learning outcomes – click to view
Samples: Interpret timetables. Interpret and Use Timetables. Time Problem Solving. Interpret timetables: Activity 2.
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Interpreting timetables
- Activities: 2 course, 6 extra
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1 learning outcomes – click to view
KS2.Y5.M.7 – Use all four operations to solve problems involving measure [for example, length, mass, volume, money] using decimal notation, including scaling
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8 learning outcomes – click to view
Samples: Converting between units of length - problem solving. Calculating distances on a map. Length - problem solving.
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Converting between units of length
- Activities: 2 course, 1 extra
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Calculating distances on a map
- Activities: 2 course, 1 extra
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Length
- Activities: 0 course, 1 extra
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Calculating area (squares and rectangles)
- Activities: 5 course, 9 extra
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Challenge Puzzle - area of irregular shapes
- Activities: 1 course, 0 extra
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Units for measuring mass
- Activities: 4 course, 4 extra
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Mass (problem solving)
- Activities: 0 course, 1 extra
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Saving money and budgeting
- Activities: 1 course, 0 extra
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8 learning outcomes – click to view
KS2.Y5.G.PS – Geometry - properties of shapes
Pupils should be taught to:
KS2.Y5.G.PS.1 – Identify 3-D shapes, including cubes and other cuboids, from 2-D representations
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4 learning outcomes – click to view
Samples: Grouping shapes based on attributes. Features of three-dimensional objects. Naming three-dimensional objects.
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Grouping shapes based on attributes
- Activities: 1 course, 0 extra
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Describe the features of three-dimensional objects
- Activities: 4 course, 8 extra
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Naming three-dimensional objects
- Activities: 6 course, 6 extra
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Nets of three dimensional objects
- Activities: 4 course, 4 extra
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4 learning outcomes – click to view
KS2.Y5.G.PS.2 – Know angles are measured in degrees: estimate and compare acute, obtuse and reflex angles
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2 learning outcomes – click to view
Samples: Types of angles. Naming angles within shapes. Identifying angles at intersecting lines. Naming angles.
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Naming angles
- Activities: 5 course, 3 extra
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Naming angles within shapes
- Activities: 1 course, 0 extra
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2 learning outcomes – click to view
KS2.Y5.G.PS.3 – Draw given angles, and measure them in degrees (°)
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2 learning outcomes – click to view
Samples: Measure and name angles. Angles in shapes. Using a protractor to measure angles.
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Measure and classify angles.
- Activities: 1 course, 2 extra
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Angles in shapes
- Activities: 1 course, 0 extra
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2 learning outcomes – click to view
KS2.Y5.G.PS.4 – Identify:
KS2.Y5.G.PS.4.a: angles at a point and 1 whole turn (total 360°)
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1 learning outcomes – click to view
Samples: Angles within a circle.
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Angles within a circle
- Activities: 1 course, 0 extra
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1 learning outcomes – click to view
KS2.Y5.G.PS.4.b: angles at a point on a straight line and half a turn (total 180°)
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1 learning outcomes – click to view
Samples: Angles on a straight line. Angles on a Straight Line. Angles Problem Solving.
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Angles on a straight line
- Activities: 2 course, 1 extra
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1 learning outcomes – click to view
KS2.Y5.G.PS.4.c: other multiples of 90°
KS2.Y5.G.PS.4.d: use the properties of rectangles to deduce related facts and find missing lengths and angles
KS2.Y5.G.PS.4.e:distinguish between regular and irregular polygons based on reasoning about equal sides and angles
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1 learning outcomes – click to view
Samples: Angles of Polygons.
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Angles of Polygons
- Activities: 0 course, 1 extra
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1 learning outcomes – click to view
KS2.Y5.G.PD – Geometry - position and direction
Pupils should be taught to:
KS2.Y5.G.PD.1 – Identify, describe and represent the position of a shape following a reflection or translation, using the appropriate language, and know that the shape has not changed
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4 learning outcomes – click to view
Samples: Identify transformations - pictures. Identify line of symmetry. Rotational symmetry - shapes.
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Transformations
- Activities: 2 course, 2 extra
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Lines of symmetry
- Activities: 1 course, 1 extra
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Rotational symmetry
- Activities: 2 course, 1 extra
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Translations, reflections and rotations
- Activities: 3 course, 1 extra
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4 learning outcomes – click to view
KS2.Y5.S – Statistics
Pupils should be taught to:
KS2.Y5.S.1 – Solve comparison, sum and difference problems using information presented in a line graph
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1 learning outcomes – click to view
Samples: Line graphs. Line graphs.
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Line graphs
- Activities: 2 course, 0 extra
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1 learning outcomes – click to view
KS2.Y5.S.2 – Complete, read and interpret information in tables, including timetables
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1 learning outcomes – click to view
Samples: Interpret timetables. Interpret and Use Timetables. Time Problem Solving. Interpret timetables: Activity 2.
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Interpreting timetables
- Activities: 2 course, 6 extra
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1 learning outcomes – click to view