Mathematics – United Kingdom – National Curriculum
Year 6 programme of study
KS2.Y6.N.NPV – Number - number and place value
Pupils should be taught to:
KS2.Y6.N.NPV.1 – Read, write, order and compare numbers up to 10,000,000 and determine the value of each digit
KS2.Y6.N.NPV.2 – Round any whole number to a required degree of accuracy
KS2.Y6.N.NPV.3 – Use negative numbers in context, and calculate intervals across 0
KS2.Y6.N.NPV.4 – Solve number and practical problems that involve all of the above
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2 learning outcomes – click to view
Samples: Order of Operations. Numbers. Numbers Problem Solving. Number Operations 1 Extension. Number Operations 2 Extension.
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Order of Operations
- 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.Y6.N.ASMD – Number - addition, subtraction, multiplication and division
Pupils should be taught to:
KS2.Y6.N.ASMD.1 – Multiply multi-digit numbers up to 4 digits by a two-digit whole number using the formal written method of long multiplication
KS2.Y6.N.ASMD.2 – 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
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1 learning outcomes – click to view
Samples: Long division - no remainders. Long division. Long division. Long division. Long Division. Long Division.
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Long division
- Activities: 3 course, 3 extra
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1 learning outcomes – click to view
KS2.Y6.N.ASMD.3 – 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
KS2.Y6.N.ASMD.4 – Perform mental calculations, including with mixed operations and large numbers
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7 learning outcomes – click to view
Samples: Short multiplication (missing number). 25% of a number. 10% off a number. Mixed operations (e.g. 80 x 5 + 29).
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Short multiplication - missing number (Skill 75)
- Activities: 4 course, 7 extra
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25% of a number (Skill 76)
- Activities: 8 course, 8 extra
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10% off a number (Skill 77)
- Activities: 8 course, 8 extra
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Mixed operations e.g. 80 x 5 + 19 (Skill 80)
- Activities: 4 course, 7 extra
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Mixed operations e.g. 81 x 9 + 42 (Skill 81)
- Activities: 4 course, 7 extra
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Order of operations E.g. 40 x 8 + 20 x 6 (Skill 82)
- Activities: 4 course, 7 extra
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Balancing equations: 80 x 6 + ____ = 502 (Skill 83)
- Activities: 8 course, 8 extra
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7 learning outcomes – click to view
KS2.Y6.N.ASMD.5 – Identify common factors, common multiples and prime numbers
KS2.Y6.N.ASMD.6 – Use their knowledge of the order of operations to carry out calculations involving the 4 operations
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3 learning outcomes – click to view
Samples: Order of operations eg 56 + 7 x 3. Order of operations eg 126 - 6 x 7. Order of operations: Activity 1.
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Order of operations : Multiply before adding
- Activities: 3 course, 0 extra
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Order of operations - Multiply before subtracting
- Activities: 2 course, 0 extra
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Order of operations - mixed
- Activities: 4 course, 2 extra
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3 learning outcomes – click to view
KS2.Y6.N.ASMD.7 – Solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why
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3 learning outcomes – click to view
Samples: Balancing equations Addition of larger numbers. Two step problem solving (addition and subtraction).
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Balancing equations - Equivalent number sentences
- Activities: 5 course, 10 extra
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Two step problem solving (addition and subtraction)
- Activities: 1 course, 0 extra
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Two step problem solving (money)
- Activities: 1 course, 0 extra
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3 learning outcomes – click to view
KS2.Y6.N.ASMD.8 – Solve problems involving addition, subtraction, multiplication and division
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5 learning outcomes – click to view
Samples: Two step problem solving. Two step problem solving. Two step problem solving. Two step problem solving.
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Two step problem solving
- Activities: 1 course, 0 extra
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Two step problem solving
- Activities: 1 course, 0 extra
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Two step problem solving
- Activities: 1 course, 0 extra
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Two step problem solving
- Activities: 1 course, 0 extra
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Long division - problem solving
- Activities: 0 course, 4 extra
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5 learning outcomes – click to view
KS2.Y6.N.ASMD.9 – Use estimation to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy
KS2.Y6.N.F – Number - Fractions (including decimals and percentages)
Pupils should be taught to:
KS2.Y6.N.F.1 – Use common factors to simplify fractions; use common multiples to
KS2.Y6.N.F.2 – Express fractions in the same denomination
KS2.Y6.N.F.3 – Compare and order fractions, including fractions >1
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1 learning outcomes – click to view
Samples: Comparing fractions to a half. Comparing fractions - identify the smallest.
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Comparing fractions
- Activities: 4 course, 0 extra
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1 learning outcomes – click to view
KS2.Y6.N.F.4 – Add and subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractions
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1 learning outcomes – click to view
Samples: Adding mixed fractions.
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Adding mixed fractions
- Activities: 1 course, 0 extra
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1 learning outcomes – click to view
KS2.Y6.N.F.5 – Multiply simple pairs of proper fractions, writing the answer in its simplest form [for example, ¼ × ½ = â…› ]
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1 learning outcomes – click to view
Samples: Fractions Problem Solving. Fractions Problem Solving. Multiplying Fractions - A Fraction by a Whole Number.
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Multiplying fractions
- Activities: 0 course, 3 extra
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1 learning outcomes – click to view
KS2.Y6.N.F.6 – Divide proper fractions by whole numbers [for example, â…“ ÷ 2 = â…™ ]
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3 learning outcomes – click to view
Samples: Fractions. Division - Answers as fractions. Multiplying and Dividing Fractions.
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Multiplying fractions by a whole number - visual
- Activities: 1 course, 0 extra
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Division- answers as fractions
- Activities: 2 course, 0 extra
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Multiplying and Dividing Fractions
- Activities: 4 course, 0 extra
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3 learning outcomes – click to view
KS2.Y6.N.F.7 – Associate a fraction with division and calculate decimal fraction
KS2.Y6.N.F.8 – Equivalents [for example, 0.375] for a simple fraction [for example, â…œ ]
KS2.Y6.N.F.9 – Identify the value of each digit in numbers given to 3 decimal places and multiply and divide numbers by 10, 100 and 1,000 giving answers up to 3 decimal places
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4 learning outcomes – click to view
Samples: Place value (thousandths). Dividing a whole number by 10. Multiplying Decimals By 10. Multiplying decimals by 1000.
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Place value (thousandths)
- Activities: 1 course, 0 extra
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Dividing whole numbers by 10 (problem solving)
- Activities: 3 course, 0 extra
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Multiplying decimals by 10
- Activities: 2 course, 4 extra
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Multiplying decimals by 1000
- Activities: 1 course, 0 extra
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4 learning outcomes – click to view
KS2.Y6.N.F.10 – Multiply one-digit numbers with up to 2 decimal places by whole numbers
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1 learning outcomes – click to view
Samples: Multiplying Decimals By A Single Digit Number. Multiplying decimals by a whole number.
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Multiplying decimals by a whole number
- Activities: 2 course, 6 extra
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1 learning outcomes – click to view
KS2.Y6.N.F.11 – Use written division methods in cases where the answer has up to 2 decimal places
KS2.Y6.N.F.12 – Solve problems which require answers to be rounded to specified degrees of accuracy
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2 learning outcomes – click to view
Samples: Rounding decimals to whole numbers. Division (estimation) - 1. Division (estimation) - 2.
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Rounding decimals to whole numbers
- Activities: 1 course, 0 extra
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Division (estimation)
- Activities: 2 course, 0 extra
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2 learning outcomes – click to view
KS2.Y6.N.F.13 – Recall and use equivalences between simple fractions, decimals and percentages, including in different contexts
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4 learning outcomes – click to view
Samples: Decreasing by a percentage. Simple Interest. Percentages as Decimals. Changing mixed fractions to decimals.
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Increasing and decreasing by percentages
- Activities: 3 course, 1 extra
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Simple Interest
- Activities: 0 course, 1 extra
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Percentages as Decimals
- Activities: 1 course, 0 extra
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Changing mixed fractions to decimals
- Activities: 0 course, 1 extra
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4 learning outcomes – click to view
KS2.Y6.RP – Ratio and proportion
Pupils should be taught to:
KS2.Y6.RP.1 – Solve problems involving the relative sizes of 2 quantities where missing values can be found by using integer multiplication and division facts
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2 learning outcomes – click to view
Samples: Simplifying Ratios. Calculating Equivalent Ratios.
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Simplifying Ratios
- Activities: 1 course, 0 extra
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Calculating Equivalent Ratios
- Activities: 1 course, 0 extra
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2 learning outcomes – click to view
KS2.Y6.RP.2 – Solve problems involving the calculation of percentages [for example, of measures and such as 15% of 360] and the use of percentages for comparison
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2 learning outcomes – click to view
Samples: Fractions of a number. Fractions Problem Solving. Fractions of a number. Simple fractions of quantities.
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Fractions of a number
- Activities: 12 course, 2 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.Y6.RP.3 – Solve problems involving similar shapes where the scale factor is known or can be found
KS2.Y6.RP.4 – Solve problems involving unequal sharing and grouping using knowledge of fractions and multiples
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2 learning outcomes – click to view
Samples: Simplifying Ratios Involving Units. Problem Solving - Unitary Method.
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Simplifying Ratios involving Units
- Activities: 1 course, 0 extra
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Problem Solving - Unitary Method
- Activities: 1 course, 0 extra
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2 learning outcomes – click to view
KS2.Y6.A – Algebra
Pupils should be taught to:
KS2.Y6.A.1 – Use simple formulae
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2 learning outcomes – click to view
Samples: Equivalent number sentences (written form). Identifying expressions. Identifying Expressions.
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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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2 learning outcomes – click to view
KS2.Y6.A.2 – Generate and describe linear number sequences
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2 learning outcomes – click to view
Samples: Continue number patterns. Rules defining number patterns. Continue number patterns (multiplication).
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Continuing number patterns
- Activities: 2 course, 0 extra
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Rules defining number patterns
- Activities: 1 course, 0 extra
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2 learning outcomes – click to view
KS2.Y6.A.3 – Express missing number problems algebraically
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2 learning outcomes – click to view
Samples: Applying rules to number tables. Continuing number sequences including fractions and decimals.
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Applying rules to number tables
- Activities: 1 course, 0 extra
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Continuing number sequences
- Activities: 1 course, 4 extra
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2 learning outcomes – click to view
KS2.Y6.A.4 – Find pairs of numbers that satisfy an equation with 2 unknowns
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2 learning outcomes – click to view
Samples: Substituting numbers for letters. Subtraction of Like Terms.
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Substituting numbers for letters
- Activities: 1 course, 0 extra
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Subtraction of Like Terms
- Activities: 0 course, 1 extra
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2 learning outcomes – click to view
KS2.Y6.A.5 – Enumerate possibilities of combinations of 2 variables
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2 learning outcomes – click to view
Samples: Represent problems using algebraic equation. Substituting Numerals. Equations Involving Addition.
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Represent problems using algebraic equation
- Activities: 1 course, 0 extra
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Substituting Numerals
- Activities: 1 course, 4 extra
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2 learning outcomes – click to view
KS2.Y6.M – Measurement
Pupils should be taught to:
KS2.Y6.M.1 – Solve problems involving the calculation and conversion of units of measure, using decimal notation up to 3 decimal places where appropriate
KS2.Y6.M.2 – 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 3 decimal places
KS2.Y6.M.3 – Convert between miles and kilometres
KS2.Y6.M.4 – Recognise that shapes with the same areas can have different perimeters and vice versa
KS2.Y6.M.5 – Recognise when it is possible to use formulae for area and volume of shapes
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3 learning outcomes – click to view
Samples: Calculating volume. Volume Extension. Circumference of a Circle. Calculating volumes of rectangular prisms.
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Volume of rectangular prisms
- Activities: 4 course, 6 extra
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Volume
- Activities: 0 course, 2 extra
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Circumference of a Circle
- Activities: 1 course, 0 extra
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3 learning outcomes – click to view
KS2.Y6.M.6 – Calculate the area of parallelograms and triangles
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2 learning outcomes – click to view
Samples: Area of Triangles. Area of Parallelograms.
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Area of Triangles
- Activities: 0 course, 1 extra
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Area of a Parallelogram
- Activities: 1 course, 0 extra
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2 learning outcomes – click to view
KS2.Y6.M.7 – 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]
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1 learning outcomes – click to view
Samples: Volume of a Cylinder.
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Volume of a Cylinder
- Activities: 0 course, 1 extra
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1 learning outcomes – click to view
KS2.Y6.G.PS – Geometry - properties of shapes
Pupils should be taught to:
KS2.Y6.G.PS.1 – Draw 2-D shapes using given dimensions and angles
KS2.Y6.G.PS.2 – Recognise, describe and build simple 3-D shapes, including making nets
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1 learning outcomes – click to view
Samples: Matching - three-dimensional objects with their nets. Identifying the nets of three-dimensional shapes.
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Nets of three dimensional objects
- Activities: 4 course, 4 extra
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1 learning outcomes – click to view
KS2.Y6.G.PS.3 – Compare and classify geometric shapes based on their properties and sizes and find unknown angles in any triangles, quadrilaterals, and regular polygons
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4 learning outcomes – click to view
Samples: Naming prisms and pyramids. Angle sum - triangles. Angle sum - quadrilaterals. Angles of Polygons.
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Prisms and pyramids
- Activities: 2 course, 8 extra
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Angle sum - triangles
- Activities: 1 course, 1 extra
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Angle sum - quadrilaterals
- Activities: 1 course, 4 extra
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Angles of Polygons
- Activities: 0 course, 1 extra
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4 learning outcomes – click to view
KS2.Y6.G.PS.4 – Illustrate and name parts of circles, including radius, diameter and circumference and know that the diameter is twice the radius
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2 learning outcomes – click to view
Samples: Angles within a circle. Parts of a circle. Parts of a circle. Learn the parts of a circle. Parts of a circle.
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Angles within a circle
- Activities: 1 course, 0 extra
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Parts of a Circle
- Activities: 5 course, 0 extra
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2 learning outcomes – click to view
KS2.Y6.G.PS.5 – Recognise angles where they meet at a point, are on a straight line, or are vertically opposite, and find missing angles
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3 learning outcomes – click to view
Samples: Angles on a straight line. Challenge puzzle - angles. Exterior Angles. Angles on a Straight Line.
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Angles on a straight line
- Activities: 2 course, 1 extra
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Challenge puzzle - angles
- Activities: 1 course, 0 extra
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Exterior Angles
- Activities: 0 course, 1 extra
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3 learning outcomes – click to view
KS2.Y6.G.PD – Geometry - position and direction
Pupils should be taught to:
KS2.Y6.G.PD.1 – Describe positions on the full coordinate grid (all 4 quadrants)
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1 learning outcomes – click to view
Samples: Cartesian Plane - Identify location. Cartesian Plane - Identify coordinates. Cartesian planes - lines and shapes.
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Cartesian Planes
- Activities: 3 course, 5 extra
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1 learning outcomes – click to view
KS2.Y6.G.PD.2 – Draw and translate simple shapes on the coordinate plane, and reflect them in the axes
KS2.Y6.G.S – Statistics
Pupils should be taught to:
KS2.Y6.G.S.1 – Interpret and construct pie charts and line graphs and use these to solve problems
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3 learning outcomes – click to view
Samples: Column graphs. Line graphs. Line and Pie Graphs - Financial Literacy. Interpreting column graphs - 6. Line graphs.
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Column graphs
- Activities: 3 course, 3 extra
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Line graphs
- Activities: 2 course, 0 extra
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Interpret data presented using a pie graph
- Activities: 0 course, 5 extra
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3 learning outcomes – click to view
KS2.Y6.G.S.2 – Calculate and interpret the mean as an average
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3 learning outcomes – click to view
Samples: Median, Range and Mean. Chance and Probability (as fractions). Chance from 0 to 1. Chance Fraction.
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Calculate mean, median, mode and range.
- Activities: 1 course, 0 extra
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Chance and Probability (as fractions)
- Activities: 2 course, 4 extra
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Recognise that probabilities range from 0 to 1.
- Activities: 1 course, 0 extra
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3 learning outcomes – click to view