Maths Year 6

Number

• Number and place value
  • Read, write, order and compare numbers up to 10 000 000 and determine the value of each digit.
    • Place values (6-A.2)
    • Writing numbers up to ten million in words: convert words to digits (6-A.7)
    • Writing numbers up to ten million in words: convert digits to words (6-A.8)
    • Compare numbers up to ten million (6-A.10)
    • Put numbers in order: up to ten million (6-A.12)
  • Round any whole number to a required degree of accuracy.
    • Rounding: up to thousands place (6-A.14)
    • Rounding: up to millions place (6-A.15)
  • Use negative numbers in context, and calculate intervals across zero.
    • Understanding integers (6-O.1)
    • Integers on number lines (6-O.2)
    • Graph integers on horizontal and vertical number lines (6-O.3)
    • Understanding opposite integers (6-O.4)
  • Solve number and practical problems that involve all of the above.
    • Place value word problems (6-A.4)
    • Multi-step word problems: identify reasonable answers (6-R.6)
• Addition, subtraction, multiplication and division
  • Multiply multi-digit numbers up to 4 digits by a two-digit whole number using the formal written method of long multiplication.
    • Multiply 2-digit numbers by 3-digit or 4-digit numbers: complete the missing steps (6-D.17)
    • Multiply 2-digit numbers by 3-digit or 4-digit numbers (6-D.18)
    • Multiply 2-digit numbers by 3-digit or 4-digit numbers: word problems (6-D.19)
  • Divide numbers up to 4 digits by a two-digit whole number using the formal written method of long division, and interpret remainders as whole number remainders, fractions, or by rounding, as appropriate for the context.
    • Divide 4-digit numbers by 2-digit numbers (6-F.11)
    • Divide 4-digit numbers by 2-digit numbers: word problems (6-F.12)
  • Divide numbers up to 4 digits by a two-digit number using the formal written method of short division where appropriate, interpreting remainders according to the context.
    • Adjust quotients (6-F.13)
  • Perform mental calculations, including with mixed operations and large numbers.
    • Prime and composite numbers: up to 100 (6-G.6)
    • Highest common factor (6-G.8)
    • Lowest common multiple (6-G.9)
  • Use their knowledge of the order of operations to carry out calculations involving the four operations.
    • Evaluate numerical expressions (6-Q.4)
    • Evaluate numerical expressions with brackets (6-Q.5)
    • Evaluate numerical expressions with brackets and square brackets (6-Q.6)
  • Solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why.
    • Multi-step addition and subtraction word problems (6-R.3)
  • Solve problems involving addition, subtraction, multiplication and division.
    • Add, subtract, multiply and divide whole numbers (6-Q.1)
    • Add, subtract, multiply and divide whole numbers: word problems (6-Q.2)
    • Equations with mixed operations: true or false (6-Q.11)
    • Write numerical expressions for word problems (6-R.2)
    • Multi-step word problems (6-R.4)
  • Use estimation to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy.
    • Multi-step word problems involving remainders (6-R.5)
    • Multi-step word problems: identify reasonable answers (6-R.6)
• Fractions (including decimals and percentages)
  • Use common factors to simplify fractions; use common multiples to express fractions in the same denomination.
    • Equivalent fractions (6-L.4)
    • Patterns of equivalent fractions (6-L.5)
    • Write fractions in lowest terms (6-L.6)
    • Lowest common denominator (6-L.7)
  • Compare and order fractions, including fractions > 1.
    • Graph and compare fractions on number lines (6-L.10)
    • Compare fractions and mixed numbers (6-L.11)
    • Put fractions in order (6-L.12)
  • Add and subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractions.
    • Add fractions with different denominators (6-M.11)
    • Subtract fractions with different denominators (6-M.13)
    • Add and subtract fractions with different denominators (6-M.14)
    • Add and subtract fractions with different denominators: word problems (6-M.15)
    • Add three or more fractions with different denominators (6-M.16)
    • Add three or more fractions with different denominators: word problems (6-M.17)
    • Complete addition and subtraction sentences with fractions (6-M.18)
    • Add mixed numbers with different denominators (6-M.21)
    • Subtract mixed numbers with different denominators (6-M.22)
    • Add and subtract mixed numbers with different denominators (6-M.23)
    • Add and subtract mixed numbers with different denominators: word problems (6-M.24)
    • Complete addition and subtraction sentences with mixed numbers (6-M.25)
  • Multiply simple pairs of proper fractions, writing the answer in its simplest form [for example ¹/₄ × ¹/₂ = ¹/₈].
    • Multiply two fractions (6-N.16)
    • Multiply fractions: word problems (6-N.17)
    • Complete the fraction multiplication sentence I (6-N.18)
    • Complete the fraction multiplication sentence II (6-N.19)
  • Divide proper fractions by whole numbers [for example, ¹/₃ ÷ 2 = ¹/₆].
    • Divide unit fractions by whole numbers (6-N.22)
    • Divide fractions by whole numbers (6-N.23)
  • Associate a fraction with division and calculate decimal fraction equivalents [for example, 0.375] for a simple fraction [for example, ³/₈].
    • Convert fractions to decimals (6-H.13)
    • Relate division and fractions (6-L.17)
    • Understand fractions as division: word problems (6-L.18)
    • Fractions as division: decimal quotients (6-L.19)
  • Identify the value of each digit in numbers given to three decimal places and multiply and divide numbers by 10, 100 and 1000 giving answers up to three decimal places.
    • Place values in decimal numbers (6-H.4)
    • Relationship between decimal place values (6-H.5)
    • Multiply a decimal by 10, 100 or 1,000 (6-J.3)
    • Multiply by a power of ten with decimals: find the missing number (6-J.5)
    • Divide a whole number by 10, 100 or 1,000: decimal quotients (6-K.2)
    • Divide a decimal by 10, 100 or 1,000 (6-K.3)
    • Decimal division patterns over increasing place values (6-K.4)
  • Multiply one-digit numbers with up to two decimal places by whole numbers.
    • Multiply a decimal by a one-digit whole number using blocks (6-J.6)
    • Multiply a decimal by a one-digit whole number using the distributive property (6-J.7)
    • Multiply a decimal by a one-digit whole number (6-J.8)
    • Multiply a decimal by a one-digit whole number: word problems (6-J.9)
    • Multiply a decimal by a two-digit whole number using area models (6-J.11)
    • Multiply a decimal by a two-digit whole number (6-J.12)
    • Multiply a decimal by a one- or two-digit whole number: word problems (6-J.13)
    • Multiply three or more numbers, one of which is a decimal (6-J.14)
  • Use written division methods in cases where the answer has up to two decimal places.
    • Divide decimals using blocks: complete the equation (6-K.7)
    • Divide decimals using area models: complete the equation (6-K.8)
    • Divide decimals by one-digit whole numbers (6-K.9)
    • Divide money amounts (6-U.7)
    • Divide money amounts with decimals (6-U.9)
  • Solve problems which require answers to be rounded to specified degrees of accuracy.
    • Division with decimal quotients and rounding (6-K.10)
    • Division with decimal quotients: word problems (6-K.11)
  • Recall and use equivalences between simple fractions, decimals and percentages, including in different contexts.
    • Convert between percents, fractions and decimals (6-T.4)
    • Convert between percents, fractions and decimals: word problems (6-T.5)

Ratio and proportion

• Solve problems involving the relative sizes of two quantities where missing values can be found by using integer multiplication and division facts.
  • Identify equivalent ratios (6-S.4)
  • Write an equivalent ratio (6-S.5)
  • Ratio tables (6-S.6)
  • Equivalent rates (6-S.8)
  • Ratios and rates: word problems (6-S.9)
  • Do the ratios form a proportion? (6-S.10)
  • Solve the proportion (6-S.11)
• Solve problems involving the calculation of percentages [for example, of measures, and such as 15% of 360] and the use of percentages for comparison.
  • Percent of a number (6-T.8)
  • Percent of a number: word problems (6-T.9)
  • Compare percents of numbers (6-T.10)
• Solve problems involving similar shapes where the scale factor is known or can be found.
  • Scale drawings: word problems (6-S.12)
• Solve problems involving unequal sharing and grouping using knowledge of fractions and multiples.
  • Multi-step word problems: multiplicative comparison (6-F.14)
  • Fractions of a number: word problems (6-N.11)

Algebra

• Use simple formulae.
  • Evaluate variable expressions (6-X.3)
  • Properties of addition with variables (6-X.4)
  • Properties of multiplication with variables (6-X.5)
  • Find a value using two-variable equations (6-X.16)
• Generate and describe linear number sequences.
  • Use a rule to complete an addition or subtraction pattern (6-V.1)
  • Complete a linear number sequence (6-V.6)
  • Linear sequences: word problems (6-V.9)
• Express missing number problems algebraically.
  • Write a one-step equation from words (6-X.7)
  • Model and solve one-step equations using algebra tiles (6-X.8)
  • Write and solve one-step equations that represent diagrams (6-X.9)
  • Write one-step equations: word problems (6-X.13)
• Find pairs of numbers that satisfy an equation with two unknowns.
  • Does (x, y) satisfy an equation? (6-X.15)
  • Find a value using two-variable equations (6-X.16)
  • Write a two-variable equation (6-X.20)
• Enumerate possibilities of combinations of two variables.
  • Complete a table for a two-variable relationship (6-X.17)

Measurement

• Solve problems involving the calculation and conversion of units of measure, using decimal notation up to three decimal places where appropriate.
  • Choose the appropriate metric unit of measure (6-BB.3)
  • Choose the appropriate imperial unit of measure (6-BB.10)
• Use, read, write and convert between standard units, converting measurements of length, mass, volume and time from a smaller unit of measure to a larger unit, and vice versa, using decimal notation to up to three decimal places.
  • Convert time units (6-AA.1)
  • Add and subtract mixed time units (6-AA.2)
  • Compare and convert metric units of length (6-BB.4)
  • Compare and convert metric units of mass (6-BB.5)
  • Compare and convert metric units of volume (6-BB.6)
  • Add and subtract metric mixed units (6-BB.8)
  • Multi-step problems with metric unit conversions (6-BB.9)
  • Compare and convert imperial units of length (6-BB.11)
  • Compare and convert imperial units of weight (6-BB.12)
  • Compare and convert imperial units of volume (6-BB.13)
  • Imperial mixed units (6-BB.14)
• Convert between miles and kilometres.
  • Convert between miles and kilometres (6-BB.15)
• Recognise that shapes with the same areas can have different perimeters and vice versa.
  • Relationship between area and perimeter (6-HH.15)
• Recognise when it is possible to use formulae for area and volume of shapes.
  • Area and perimeter: word problems (6-HH.13)
  • Relationship between volume and the area of the base: word problems (6-HH.18)
• Calculate the area of parallelograms and triangles.
  • Understanding area of a parallelogram (6-HH.5)
  • Area of parallelograms (6-HH.6)
  • Understanding area of a triangle (6-HH.7)
  • Area of right triangles (6-HH.8)
  • Area of triangles (6-HH.9)
• Calculate, estimate and compare volume of cubes and cuboids using standard units, including cubic centimetres (cm³) and cubic metres (m³), and extending to other units [for example, mm³ and km³].
  • Volume of cubes and cuboids (6-HH.17)
  • Compare volumes and dimensions of cuboids: word problems (6-HH.19)

Geometry

• Properties of shapes
  • Draw 2-D shapes using given dimensions and angles.
    • Properties of polygons (6-CC.6)
    • Draw angles with a protractor (6-DD.3)
    • Draw quadrilaterals (6-EE.11)
  • Recognise, describe and build simple 3-D shapes, including making nets.
    • Identify three-dimensional figures (6-GG.1)
    • Count vertices, edges and faces (6-GG.2)
    • Which figure is being described? (6-GG.3)
    • Nets of three-dimensional figures (6-GG.4)
  • Compare and classify geometric shapes based on their properties and sizes and find unknown angles in any triangles, quadrilaterals, and regular polygons.
    • Classify triangles (6-EE.1)
    • Find missing angles in triangles (6-EE.2)
    • Classify quadrilaterals (6-EE.9)
    • Pick all the names for a quadrilateral (6-EE.10)
    • Find missing angles in quadrilaterals (6-EE.15)
  • Illustrate and name parts of circles, including radius, diameter and circumference and know that the diameter is twice the radius.
    • Parts of a circle (6-CC.9)
  • Recognise angles where they meet at a point, are on a straight line, or are vertically opposite, and find missing angles.
    • Types of angles (6-DD.1)
    • Find a missing angle - vertical angles (6-DD.4)
    • Find a missing angle - adjacent angles (6-DD.5)
    • Find a missing angle - vertical, adjacent and supplementary angles (6-DD.7)
• Position and direction
  • Describe positions on the full coordinate grid (all four quadrants).
    • Describe the coordinate plane (6-W.1)
    • Objects on a coordinate plane - all four quadrants (6-W.5)
    • Graph points on a coordinate plane - all four quadrants (6-W.6)
    • Quadrants (6-W.7)
  • Draw and translate simple shapes on the coordinate plane, and reflect them in the axes.
    • Translations: graph the image (6-FF.7)
    • Reflections: graph the image (6-FF.8)

Statistics

• Interpret and construct pie charts and line graphs and use these to solve problems.
  • Interpret line graphs (6-Y.4)
  • Create line graphs (6-Y.5)
  • Pie charts (6-Y.19)
  • Pie charts and central angles (6-Y.20)
• Calculate and interpret the mean as an average.
  • Find the mean (6-Z.9)
  • Mean: find the missing number (6-Z.13)
  • Interpret charts to find mean (6-Z.17)