England

Number

• Number and place value

  • Count in multiples of 6, 7, 9, 25 and 1000.

    • Skip-counting by 6 (4-A.3)
    • Skip-counting by 7 (4-A.4)
    • Skip-counting by 9 (4-A.5)

  • Find 1000 more or less than a given number.

    • Add multiples of 10, 100 or 1,000 to whole numbers (4-C.13)
    • Subtract multiples of 10, 100 or 1,000 from whole numbers (4-D.10)

  • Count backwards through zero to include negative numbers.

    • Count on a number line with negative numbers (4-O.2)

  • Recognise the place value of each digit in a four-digit number (thousands, hundreds, tens, and ones).

    • Value of a digit (4-B.4)

  • Order and compare numbers beyond 1000.

    • Compare numbers up to 100,000 (4-A.13)
    • Compare numbers in tables: up to 100,000 (4-A.14)
    • Put numbers in order: up to 100,000 (4-A.16)

  • Identify, represent and estimate numbers using different representations.

    • Writing numbers up to 10,000 in words: convert words to digits (4-A.9)
    • Writing numbers up to 10,000 in words: convert digits to words (4-A.10)
    • Place value models up to thousands (4-B.1)
    • Convert to/from a number (4-B.5)
    • Convert between place values (4-B.6)
    • Convert from expanded form (4-B.7)
    • Convert between standard and expanded form (4-B.8)

  • Round any number to the nearest 10, 100 or 1000.

    • Round using a number line - nearest ten or hundred (4-Q.1)
    • Round to the nearest ten, hundred or thousand (4-Q.3)

  • Solve number and practical problems that involve all of the above and with increasingly large positive numbers.

    • Skip-counting puzzles (4-A.6)
    • Place value word problems (4-B.9)

  • Read Roman numerals to 100 (I to C) and know that over time, the numeral system changed to include the concept of zero and place value.

    • Roman numerals (4-A.11)

• Addition and subtraction

  • Add and subtract numbers with up to 4 digits using the formal written methods of columnar addition and subtraction where appropriate.

    • Add a two-digit number to a three-digit number (4-C.1)
    • Add a two-digit number to a three-digit number - word problems (4-C.2)
    • Add two three-digit numbers (4-C.6)
    • Addition input/output tables - up to three digits (4-C.7)
    • Add two three-digit numbers - word problems (4-C.8)
    • Add three or more numbers with up to three digits each (4-C.11)
    • Add three or more numbers with up to three digits - word problems (4-C.12)
    • Add two numbers with up to four digits (4-C.15)
    • Addition input/output tables - up to four digits (4-C.16)
    • Add two numbers with up to four digits - word problems (4-C.17)
    • Add three or more numbers with up to four digits (4-C.20)
    • Add three or more numbers with up to four digits - word problems (4-C.21)
    • Addition: fill in the missing digits (4-C.22)
    • Subtract a two-digit number from a three-digit number (4-D.1)
    • Subtract a two-digit number from a three-digit number - word problems (4-D.2)
    • Subtract three-digit numbers (4-D.5)
    • Subtraction input/output tables - up to three digits (4-D.6)
    • Subtract three-digit numbers - word problems (4-D.7)
    • Subtract numbers with up to four digits (4-D.12)
    • Subtraction input/output tables - up to four digits (4-D.13)
    • Subtract numbers with up to four digits - word problems (4-D.14)

  • Estimate and use inverse operations to check answers to a calculation.

    • Complete the addition sentence - add a two-digit number to a three-digit number (4-C.3)
    • Complete the addition sentence - three-digit numbers (4-C.9)
    • Complete the addition sentence - up to four digits (4-C.18)
    • Complete the subtraction sentence - three-digit numbers minus two-digit numbers (4-D.3)
    • Complete the subtraction sentence - three-digit numbers (4-D.8)
    • Complete the subtraction sentence - up to four digits (4-D.15)
    • Estimate sums up to 1,000 (4-Q.7)
    • Estimate sums (4-Q.8)
    • Estimate sums: word problems (4-Q.9)
    • Estimate differences up to 1,000 (4-Q.10)
    • Estimate differences (4-Q.11)
    • Estimate differences: word problems (4-Q.12)

  • Solve addition and subtraction two-step problems in contexts, deciding which operations and methods to use and why.

    • Addition and subtraction word problems (4-M.14)
    • Two-step addition and subtraction word problems (4-M.19)

• Multiplication and division

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

    • Multiply by 1 (4-F.2)
    • Multiply by 2 (4-F.3)
    • Multiply by 3 (4-F.4)
    • Multiply by 4 (4-F.5)
    • Multiply by 5 (4-F.6)
    • Multiply by 6 (4-F.7)
    • Multiply by 7 (4-F.8)
    • Multiply by 8 (4-F.9)
    • Multiply by 9 (4-F.10)
    • Multiply by 10 (4-F.11)
    • Multiply by 11 (4-F.12)
    • Multiply by 12 (4-F.13)
    • Multiplication facts to 12 (4-G.18)
    • Multiplication facts up to 12: true or false? (4-G.19)
    • Multiplication facts up to 12: sorting (4-G.20)
    • Multiplication sentences up to 12: true or false? (4-G.23)
    • Divide by 1 (4-J.1)
    • Divide by 2 (4-J.2)
    • Divide by 3 (4-J.3)
    • Divide by 4 (4-J.4)
    • Divide by 5 (4-J.5)
    • Divide by 6 (4-J.6)
    • Divide by 7 (4-J.7)
    • Divide by 8 (4-J.8)
    • Divide by 9 (4-J.9)
    • Divide by 10 (4-J.10)
    • Divide by 11 (4-J.11)
    • Divide by 12 (4-J.12)
    • Division facts up to 12 (4-K.13)
    • Division facts up to 12: true or false? (4-K.14)
    • Division facts up to 12: sorting (4-K.15)
    • Division sentences up to 12: true or false? (4-K.18)
    • Multiplication and division facts up to 12: true or false? (4-M.5)
    • Multiplication and division sentences up to 12: true or false? (4-M.6)

  • Use place value, known and derived facts to multiply and divide mentally, including: multiplying by 0 and 1; dividing by 1; multiplying together three numbers.

    • Multiply by 0 (4-F.1)
    • Multiply by 1 (4-F.2)
    • Multiply by a multiple of 10 using place value (4-H.7)
    • Multiply by a multiple of 10 (4-H.8)
    • Multiply by multiples of 10 and 100 (4-H.9)
    • Multiplication patterns over increasing place values (4-H.10)
    • Multiply three or more numbers (4-H.25)
    • Divide by 1 (4-J.1)
    • Division patterns over increasing place values (4-L.2)
    • Divide numbers ending in zeroes (4-L.3)
    • Multiply by 0 or 1: complete the sentence (4-N.12)

  • Recognise and use factor pairs and commutativity in mental calculations.

    • Multiplication facts up to 12: find the missing factor (4-G.21)
    • Multiplication facts up to 12: select the missing factors (4-G.22)
    • Complete the factor pairs of a number (4-H.5)
    • Division facts up to 12: find the missing number (4-K.16)
    • Division facts up to 12: select the missing numbers (4-K.17)

  • Multiply two-digit and three-digit numbers by a one-digit number using formal written layout.

    • Multiply one-digit numbers by two-digit numbers (4-H.19)
    • Multiply one-digit numbers by two-digit numbers: word problems (4-H.20)
    • Multiply one-digit numbers by three-digit numbers (4-H.23)
    • Multiply one-digit numbers by three-digit numbers: word problems (4-H.24)

  • Solve problems involving multiplying and adding, including using the distributive law to multiply two digit numbers by one digit, integer scaling problems and harder correspondence problems such as n objects are connected to m objects.

    • Multiply one-digit numbers by two-digit numbers using area models I (4-H.17)
    • Multiply one-digit numbers by two-digit numbers using area models II (4-H.18)
    • Multiply one-digit numbers by three-digit numbers using area models I (4-H.21)
    • Multiply one-digit numbers by three-digit numbers using area models II (4-H.22)
    • Distributive property: find the missing factor (4-N.7)
    • Multiply using the distributive property (4-N.8)

• Fractions (including decimals)

  • Recognise and show, using diagrams, families of common equivalent fractions.

    • Find equivalent fractions using area models: two models (4-DD.1)
    • Find equivalent fractions using area models: one model (4-DD.2)
    • Identify equivalent fractions on number lines (4-DD.3)
    • Find equivalent fractions using number lines (4-DD.4)
    • Graph equivalent fractions on number lines (4-DD.5)

  • Count up and down in hundredths; recognise that hundredths arise when dividing an object by one hundred and dividing tenths by ten.

    • What decimal number is illustrated? (4-FF.1)
    • One-tenth or one-hundredth more or less (4-FF.9)
    • Graph decimals on number lines (4-FF.11)
    • Decimal number lines (4-FF.12)

  • Solve problems involving increasingly harder fractions to calculate quantities, and fractions to divide quantities, including non-unit fractions where the answer is a whole number.

    • Fractions of a group (4-BB.6)
    • Fractions of number lines: unit fractions (4-BB.7)
    • Fractions of number lines (4-BB.8)
    • Unit fractions: modelling word problems (4-BB.12)
    • Unit fractions: word problems (4-BB.13)
    • Fractions of a whole: modelling word problems (4-BB.14)
    • Fractions of a whole: word problems (4-BB.15)
    • Fractions of a group: word problems (4-BB.16)
    • Fractions of a number - unit fractions (4-EE.1)
    • Fractions of a number (4-EE.2)
    • Fractions of a number - unit fractions: word problems (4-EE.3)
    • Fractions of a number: word problems (4-EE.4)

  • Add and subtract fractions with the same denominator.

    • Add fractions with the same denominator using number lines (4-EE.7)
    • Add fractions with the same denominator (4-EE.8)
    • Subtract fractions with the same denominator using number lines (4-EE.9)
    • Subtract fractions with the same denominator (4-EE.10)
    • Add and subtract fractions with the same denominator using number lines (4-EE.11)
    • Add and subtract fractions with the same denominator (4-EE.12)
    • Compare sums and differences of fractions with the same denominator (4-EE.13)
    • Add and subtract fractions with the same denominator: word problems (4-EE.14)
    • Add 3 or more fractions with the same denominator (4-EE.15)

  • Recognise and write decimal equivalents of any number of tenths or hundredths.

    • What decimal number is illustrated? (4-FF.1)
    • Model decimals and fractions (4-FF.2)
    • Convert fractions to decimals (4-FF.3)
    • Graph fractions as decimals on number lines (4-FF.13)

  • Recognise and write decimal equivalents to ¹/₄, ¹/₂, ³/₄.

    • Convert fractions to decimals (4-FF.3)

  • Find the effect of dividing a one- or two-digit number by 10 and 100, identifying the value of the digits in the answer as ones, tenths and hundredths.

    • Divide a decimal by 10 or 100 (4-GG.11)

  • Round decimals with one decimal place to the nearest whole number.

    • Round decimals to the nearest whole number (4-FF.6)

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

    • Compare decimals using models (4-FF.14)
    • Compare decimals on number lines (4-FF.15)
    • Inequalities with decimals (4-FF.16)
    • Which decimals are greater/less? (4-FF.17)
    • Which decimal comparisons are true? (4-FF.18)

  • Solve simple measure and money problems involving fractions and decimals to two decimal places.

    • Add and subtract money - up to £1 (4-T.7)
    • Add and subtract money amounts (4-T.8)
    • Add and subtract money - word problems - up to £1 (4-T.9)

Measurement

• Convert between different units of measure [for example, kilometre to metre; hour to minute].

  • Convert between hours and fractions of hours (4-U.12)
  • Compare and convert metric units of length (4-W.6)
  • Metric mixed units of length (4-W.7)
  • Compare and convert metric units of mass (4-W.9)
  • Compare and convert metric units of volume (4-W.13)
  • Conversion tables - metric units (4-W.14)

• Measure and calculate the perimeter of a rectilinear figure (including squares) in centimetres and metres.

  • Perimeter of rectangles (4-Z.1)
  • Perimeter of rectilinear shapes (4-Z.2)

• Find the area of rectilinear shapes by counting squares.

  • Find the area of figures made of unit squares (4-Z.6)
  • Select figures with a given area (4-Z.7)
  • Select two figures with the same area (4-Z.8)
  • Tile a rectangle and find the area (4-Z.9)
  • Multiply to find the area of a rectangle made of unit squares (4-Z.10)
  • Create figures with a given area (4-Z.11)
  • Create rectangles with a given area (4-Z.12)
  • Find the area of rectangles and squares (4-Z.13)

• Estimate, compare and calculate different measures, including money in pounds and pence.

  • Add and subtract money amounts - word problems (4-T.10)
  • Price lists (4-T.11)
  • Measure with different metric units (4-W.4)
  • Measure liquid volumes - metric units (4-W.11)

• Read, write and convert time between analogue and digital 12- and 24-hour clocks.

  • Match clocks and times (4-U.1)
  • Match analogue and digital clocks (4-U.2)
  • Read clocks and write times (4-U.3)
  • Convert between 12-hour and 24-hour time (4-U.13)

• Solve problems involving converting from hours to minutes; minutes to seconds; years to months; weeks to days.

  • Relate time units (4-U.10)
  • Convert between hours and fractions of hours (4-U.12)

Geometry

• Properties of shapes

  • Compare and classify geometric shapes, including quadrilaterals and triangles, based on their properties and sizes.

    • Acute, obtuse and right triangles (4-Y.1)
    • Scalene, isosceles and equilateral triangles (4-Y.2)
    • Parallel sides in quadrilaterals (4-Y.3)
    • Identify parallelograms (4-Y.4)
    • Identify trapeziums (4-Y.5)
    • Identify rectangles (4-Y.6)
    • Identify rhombuses (4-Y.7)
    • Classify quadrilaterals (4-Y.8)
    • Draw quadrilaterals (4-Y.9)

  • Identify acute and obtuse angles and compare and order angles up to two right angles by size.

    • Angles greater than, less than or equal to a right angle (4-X.8)
    • Acute, right and obtuse angles (4-X.9)
    • Acute, right and obtuse angles - with a protractor (4-X.10)

  • Identify lines of symmetry in 2-D shapes presented in different orientations.

    • Identify lines of symmetry (4-X.18)
    • Draw lines of symmetry (4-X.19)
    • Count lines of symmetry (4-X.20)

  • Complete a simple symmetric figure with respect to a specific line of symmetry.

• Position and direction

  • Describe positions on a 2-D grid as coordinates in the first quadrant.

    • Objects on a coordinate plane (4-V.1)
    • Graph points on a coordinate plane (4-V.2)
    • Coordinate planes as maps - find the coordinates (4-V.3)

  • Describe movements between positions as translations of a given unit to the left/right and up/down.

    • Translations (4-X.14)

  • Plot specified points and draw sides to complete a given polygon.

    • Graph triangles and quadrilaterals (5-U.5)

Statistics

• Interpret and present discrete and continuous data using appropriate graphical methods, including bar charts and time graphs.

  • Create bar graphs (4-V.13)
  • Create bar graphs for grouped data (4-V.15)
  • Create line graphs (4-V.21)

• Solve comparison, sum and difference problems using information presented in bar charts, pictograms, tables and other graphs.

  • Interpret tally charts (4-V.7)
  • Interpret frequency tables (4-V.8)
  • Interpret bar graphs (4-V.10)
  • Use bar graphs to solve problems (4-V.11)
  • Interpret bar graphs: two-step problems (4-V.12)
  • Interpret bar graphs for grouped data (4-V.14)
  • Interpret pictograms (4-V.18)
  • Interpret line graphs (4-V.20)