Framework Referencing - June 2002
A working document
Year 1 (Level 1 and start on level 2) |
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Objective | Program | Pack |
Know by heart all pairs of numbers with a total of 10 (K) | TenSprint | Numeracy |
Use everyday language to describe position, direct and movement | Maze | Movement |
Year 2 (Consolidation of level 2 and start on level 3) |
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Objective | Program | Pack |
Understand that more than 2 numbers can be added. Begin to add three single digit numbers mentally | TenSprint | Numeracy |
Compare two given two digit numbers, say which is more or less and give a number which lies in between | Guess (less than 100) Box (0 - 100) | Sense of Number |
Year 3 (Revision of level 2 and start on level 3) |
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Objective | Program | Pack |
Recognise two-digit and three-digit multiples of 2, 5 or 10, and three-digit multiples of 50 and 100. | Numbers, Multiples | Properties of Number |
Order whole numbers to at least 1000 (K) | Guess (less than 1000) Box (0 - 1000) | Sense of Number |
Begin to find remainders after simple division | Maximum Remainder (Practice) | Enriching Number |
Identify and sketch lines of symmetry in simple shapes, and recognise shapes with no lines of symmetry (K) | Add a Square Remove a Square | Symmetry and Transformations |
Sketch the reflection of a simple shape in a mirror line along one edge. | Mirror | Symmetry and Transformations |
Recognise unit fractions and use them to find fractions of shape.(K) | Matching Fractions (Level 1) | Numeracy |
Year 4 (Consolidation of level 3 and start on level 4) |
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Objective | Program | Pack |
Solve mathematical problems or puzzles, recognise and explain patterns and relationships, generalise and predict. Suggest extensions asking "What if...?" | Boat, Tadpoles | Mathematical Puzzles |
Make and investigate a general statement about familiar numbers or shapes by finding examples that satisfy it. | Inscribe (resource program) | Investigations (available June 2002) |
Give one or more numbers lying between given numbers and order a set of whole numbers less than 10000 | Guess | Sense of Number |
Estimate a proportion | NumberLines | Numeracy |
Recognise negative numbers in context (e.g. on a number line) | BoxN, GuessN | Sense of Number |
Recognise simple fractions that are several parts of a whole, recognise the equivalence of simple fractions. | Towers, Wall | Sense of Number |
Find remainders after division (K) | Maximum Remainder | Enrichng Number |
Recognise the equivalence of simple fractions (K) | Matching Fractions (Level 1) | Numeracy |
Order simple fractions | Ordering Fractions (Level 1) | Numeracy |
Use known number fact and place value to add or subtract mentally. | Minimax | Sense of Number |
Add 3 or 4 small numbers | AddsUpTo, Magic | Numeracy |
Recognise position | 3inaline | Co-ordinates |
Use the 8 compass directions N, S, E, W, NE, NW, SW, SE | Pilot (Level 1) | Movement |
Classify polygons using criteria such as: symmetry properties (K) | Add a Square Remove a Square | Symmetry and Transformations |
Sketch the reflection of a simple shape in a mirror line parallel to one side (all sides parallel or perpendicular to the mirror line). | Transform - Reflections | Symmetry and Transformations |
Year 5 (Revision of level 3, but mainly level 4) |
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Objective | Program | Pack |
Choose and use appropriate number operations to solve problems, | Minimax | Sense of Number |
Solve mathematical problems or puzzles, recognise and explain patterns and relationships, generalise and predict. Suggest extensions asking "What if...?" | Boat, Hopslide, Tadpoles | Mathematical Puzzles |
Make general statements about odd or even numbers | Numbers | Properties of Number |
Recognise multiples of 6, 7, 8, 9, up to the 10th multiple. | Numbers | Properties of Number |
Order a given set of positive and negative integers(K) | BoxN (-1000 - +1000) | Sense of Number |
Use decimal notation for tenths and hundredths (K) | BoxD ((0 - 10 1d.p. and 0 - 10 2d.p.) GuessD (0 - 10 1d.p. and 0 - 10 2d.p.) | Sense of Number |
Know by heart all multiplication facts up to 10 x 10. | Money Share | Ratio |
Solve simple problems using ideas of ratio and proportion ('one for every... ' and ' one in every...') | Money Share, Paint Mix (Level 1), Ratio Match (Level 1) | Ratio |
Use known number facts and place value for mental addition and subtraction | Darts | Numeracy |
Use doubling or halving starting from known facts. | Darts | Numeracy |
Read and plot co-ordinates in the first quadrant | Elephant (Level 1) Rhino (Level 1) Lines | Co-ordinates |
Understand and use angle measure in degrees. Estimate acute and obtuse angles | Angle 90°, Angle 360° | Angle Estimation |
Recognise where a shape will be after a reflection in a mirror line parallel to one side (sides not all parallel or perpendicular to the mirror line). | Transform - Reflection Mirror - Mirror Draw | Symmetry and Transformations |
Classify triangle (isosceles, equilateral, scalene) | Inscribe - 3 of a Kind | Investigations (available June 2002) |
Recognise where a shape will be after a translation. | Transform - Translation | Symmetry and Transformations |
Year 6 (Consolidation of level 4 and start on level 5) |
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Objective | Program | Pack |
Solve mathematical problems or puzzles, recognise and explain patterns and relationships, generalise and predict. Suggest extensions asking "What if...?" | Boat, Hopslide, Jumping, Reverse, Tadpoles | Mathematical Puzzles |
Recognise prime numbers to at least 20. | Numbers | Sense of Number |
Order fractions such as 2/3, 3/4, 5/6, | Tower (Level 2) Ordering Fractions | Sense of Number Numeracy |
Make general statements about odd or even numbers. | Identify, Numbers | Properties Of Number |
Recognise multiples up to 10 x 10. | Identify, Numbers Inscribe - Resource program | Properties Of Number Investigations (available June 2002) |
Recognise square numbers to at least 12 x 12. | Identify, Numbers | Properties Of Number |
Recognise prime numbers to at least 20. | Identify, Numbers | Properties Of Number |
Solve simple problems involving ratio and proportion.(K) | NumberLine, Money Share, Paint Mix, Ratio Match | Numeracy Ratio |
Give a decimal fraction lying between two others (e.g. between 3.4 and 3.5) | Magnify, GuessD NumberLinesD (Level 1) | Sense of Number Numeracy |
Use known number facts and place value to consolidate mental addition and subtraction | Darts | Numeracy |
Use known number facts and place value to consolidate mental multiplication and division | Darts | Numeracy |
Order a mixed set of numbers with up to 3d.p. | BoxD, Magnify | Sense of Number |
Make and investigate a general statement about familiar numbers or shapes by finding examples that satisfy it. Develop from explaining a generalised relationship in words to expressing it in a formula using letters as symbols. | Points, Trellis | Investigations (available June 2002) |
Calculate the perimeter and area of simple compound shapes that can be split into rectangles (K) | Spirals - Squares Inside and Triangles Inside | Investigations (available June 2002) |
Read and plot co-ordinates in all four quadrants | Elephant, Rhino | Co-ordinates |
Recognise where a shape will be after reflection: in a mirror line touching the shape at a point (side of shape not necessarily parallel or perpendicular to the mirror line). | Transform - Reflection Mirror - Mirror Draw Mirror - Mirror Line | Symmetry and Transformations |
Recognise where a shape will be after reflection: in two mirror lines at right-angles (side of shape all parallel or perpendicular to the mirror line). | Transform - Reflection Rangoli | Symmetry and Transformations |
Recognise and estimate angles | Angle 90°, Angle 360°, Snooker | Angle Estimation |
Classify quadrilaterals | Inscribe - 3 of a Kind, Star Challenge | Investigations (available June 2002) |
Recognise where a shape will be after a rotation through 90° about one of its vertices. | Transform - Rotation Centre Point (Level 1) | Symmetry and Transformations |
Year 7 Revision of Level 4, but mainly level 5 |
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Objective | Program | Pack |
Identify the necessary information to solve a problem; represent problems mathematically, making use of symbols, words, diagrams, tables and graphs. Break a complex calculation into smaller steps, choosing and using appropriate and efficient operations, methods... (K) Present and interpret solutions in the context of the original problem; explain and justify methods and conclusions, (K) orally and in writing. Suggest extensions by asking "What if...?" or "Why?"; begin to generalise... | Boat, Frogs, Hanoi, Hats, Hopslide, Jugs, Jumping, Master, Nim, Reverse, Tadpoles Magic Inscribe - 3 of a Kind, Star Challenge, Points | Mathematical Puzzles Numeracy Investigations (available June 2002) |
Recognise and use multiples, factors, .., highest common factor and lowest common multiple in simple cases, and primes (less than 100) | Define, Identify, Numbers, Factor Inscribe - 3 of a Kind, StarChallenge | Properties Of Number Investigations (available June 2002) |
Recognise the first few triangular numbers, squares of numbers to 12 x 12... | Define, Identify, Numbers | Properties Of Number |
Understand the relationship between ratio and proportion; use ratio notation, ... divide a quantity into two parts in a given ratio; solve simple problems about ratio and proportion using informal strategies. | Money Share, Paint Mix, Ratio Match | Ratio |
Understand and use decimal notation and place value : multiplying and dividing integers and decimals by 10, 100 and 1000 and explain the effect | Tenners | Numeracy |
Compare and order decimals in different contexts | BoxD (0 - 1 3d.p.) GuessD ( 0 - 1 3d.p.) | Sense of Number |
Understand negative numbers as position on a number line. | BoxN (0 - 10) GuessN (-100 -+100) | Sense of Number |
Recognise the equivalence of percentages, fractions and decimals | Equivalent Pairs | Enriching Number |
Use fraction notation to describe parts of shapes | Matching Fractions | Numeracy |
Calculate simple percentages, fractions and decimals. | Make that Number (Level 1) | Enriching Number |
Understand addition, subtraction, multiplication and division as they apply to whole numbers | Minimax | Sense of Number |
Generate and describe simple algebra sequences | Frogs, Boat Identify | Mathematical Puzzles Properties of Number |
Use correct vocabulary ... shapes | Inscribe - 3 of a Kind, StarChallenge | Investigations (available June 2002) |
Use 2-D representations to visualise 3-D | 3-D Maze | Movement |
Generate sequences from practical context and describe the general term in simple cases | Frogs, Boat Trellis | Mathematical Puzzles Investigations (available June 2002) |
Understand and use the language associated with ..., translations, ... | Racegame | Movement |
Use conventions and notation for 2-D co-ordinates in all four quadrants | Elephant (Level 2) Rhino Locate | Co-ordinates |
Use angle measure: distinguish between estimate the size of acute, obtuse and reflex angles | Angle 90°, Angle 360°, Snooker | Angle Estimation |
Recognise and estimate angles | Angle 90°, Angle 360°, Snooker | Angle Estimation |
Know and use the formula for the area of a rectangle; calculate the perimeter and area of shapes made from rectangles | Spirals - Squares Inside, Triangles Inside | Investigations (available June 2002) |
Year 7 Revision of Level 4, but mainly level 5 (Cont) | ||
Objective | Program | Pack |
Understand and use the language and notation associated with reflection, translations and rotations | Transform - Reflections Transform - Rotation Transform - Translation Tiles | Symmetry and Transformations |
Recognise and visualise the transformation and symmetry of 2-D shapes: reflection in given mirror lines and line symmetry. | Add a Square Remove a Square Mirror - Mirror Line Mirror - Mirror Image Rangoli - Challenge Transform - Reflections | Symmetry and Transformations |
Recognise and visualise the transformation and symmetry of 2-D shapes: rotation about a given point and rotation symmetry | Centre Point - Level 1, 2 and 3 Transform - Rotation | Symmetry and Transformations |
Explore these (rotations, reflection and translation) transformations and symmetries using ICT | Transform - Reflections Transform - Rotation Transform - Transformation Tiles | Symmetry and Transformations |
Year 8 (Consolidation of Level 5, and start on level 6) |
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Objective | Program | Pack |
Solve more demanding problems and investigate in a range of contexts | 3-D Maze, Queens | Movement |
Identify the necessary information to solve a problem; represent problems in algebraic, geometric or graphical form.(K) Solve more complex problems by breaking them into smaller steps... Present and interpret solutions, justifying inferences and explaining reasoning...(K) Suggest extensions by asking "What if...?" or "Why?"; begin to generalise... | Boat, Frogs, Hanoi, Hats, Hopslide, Jugs, Jumping, Master, Nim, Reverse, Tadpoles Queens Spirals - Guess Spiral, Infinite? | Mathematical Puzzles Movement Investigations (available June 2002) |
Order decimals | BoxD (0 - 1 3d.p.), GuessD (0 - 1 3d.p.), Magnify | Sense of Number |
Use equivalence of fractions decimals and percentages to compare proportions (K) | Make that Number (Level 2) | Enriching Number |
Add, subtract, multiply and divide integers | Darts NumberLines (Levels 3 - 5) | Numeracy |
Recognise and use multiples, factors (divisors), common factor, highest common factor, lowest common multiple and primes | Trellis | Investigations (available June 2002) |
Consolidate understanding of the relationship between ratio and proportion; reduce a ratio to its simplest form, ... divide a quantity into two ... parts in a given ratio ... (K) | Money Share, Paint Mix, Ratio Buster, Ratio Match | Ratio |
Express simple functions in symbols; represent mappings expressed algebraically | Points | Investigations (available June 2002) |
Plot the graphs of linear functions where y is given explicitly in terms of x. Recognise that equations of the form y=mx + c correspond to straight line graphs. | Plotter (y = mx, Find the Line ) | Graphing |
Transform 2-D shapes by simple combinations of rations, reflections and translations, on paper and using ICT. | Transform Tiles | Symmetry and Transformations |
Enlarge 2-D shapes, given a centre of enlargement and a positive whole-number scale factor (K) explore enlargement using ICT. | Transform - Enlargement | Symmetry and Transformations |
Year 9 (Revision of Level 5, but mainly level 6 objectives for able pupils at level 7 with some on level 8) |
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Objective | Program | Pack |
Represent problems and synthesise information in algebraic, geometric or graphical form; move from one form to another to get a different perspective on the problem. Solve substantial problems by breaking them into simpler tasks Present a precise, reasoned argument, making use of symbols, diagrams and graphs and related explanatory text...(K) Suggest extensions by asking "What if...?" or "Why?"; begin to generalise... | Hanoi, Hats Vectmeet | Mathematical Puzzles Movement |
Use proportional reasoning to solve a problem, and choose the correct numbers to take as 100%, or as a whole; ... interpret and use ratio in a range of contexts, including solving word problems. | Ratio Buster | Ratio |
Generate terms of a sequence using term-to-term and position-to-term definitions of a sequence, on paper and using ICT(K) | Points, Trellis | Investigations (available June 2002) |
Investigate the gradients of parallel lines (EX) | Plotter (Parallel Lines) | Graphing |
Solve linear inequalities in one variable | Regions (Guess Inequalities Level 1 and Level 3) | Graphing |
Begin to solve inequalities in two variables (EX) | Regions (Guess Inequalities Level 2 and Level 4) | Graphing |
Given values for m and c, find the gradient of lines given by equations of the form y = mx + c (K) | Plotter (Find the Line, Lineover, Point and Lines, y = mx) | Graphing |
Visualise and use 2-D representation of 3-D objects | 3-D Maze | Movement |
Use units of measurement to calculate ... and solve problems in a variety of contexts ... | Ratio Buster | Ratio |
Transform 2-D shapes by combinations of translations, rotation and reflections on paper and using ICT. | Transform | Symmetry and Transformations |
Know that translations, rotations and reflections preserve length and angle and map object on to congruent images. (K) | Transform | Symmetry and Transformations |
Enlarge 2-D shapes, given a centre of enlargement and a whole number scale factor, on paper and using ICT. | Transform - Enlargement | Symmetry and Transformations |
Extend to enlarging 2-D shapes, given a fractional scale factor; recognise the similarity of the resulting shape (EX) | Transform - Enlargement | Symmetry and Transformations |
Find the locus of a point that moves according to a simple rule, both by reasoning and by using ICT | Elephant Vectmeet | Co-ordinates Movement |