S3 Pathways for learning in Maths Pathway 1 (Lower) Pathway 2 (Middle) Pathway 3 (Upper) Targets Complete coverage of level 3 experiences and outcomes in Mathematics Cover level 4 experiences and outcomes that relate to lifeskills Complete Maths or Lifeskills Maths at National 3 or 4 by end of S4 Targets Complete coverage of level 4 experiences and outcomes in Mathematics Develop skills at the fourth level and be working at a level equivalent to National 4 by the end of S3 Be in a position to attempt National 5 Maths in S4, possibly with a view to repeating or being presented for the Nat 5 Maths exam in S5 Targets Be secure at the fourth level by the end of S3 Have been challenged to work beyond the fourth level by the end of S3 Pass National 5 Maths in S4 1 Skills related to measurement Select appropriate units Use appropriate units Equivalence of units 2 Skills related to calculation BODMAS (using basic calculators) Negative numbers (with and without calculators) Squares and square roots (using scientific calculators) 1 Skills related to measurement Estimating Tolerance Accuracy (Rounding, including sig. fig.) Scientific notation 2 Skills related to calculation Substitution of positive and negative numbers into formulae and expressions Squares & square roots Cubes & cube roots Fraction, decimal and percentage calculations Calculator skills (powers, roots, brackets etc.) Summer holidays 1 Skills related to measurement Estimating Tolerance Accuracy (Rounding, including sig. fig.) Scientific notation Approximately 1½ weeks 2 Skills related to calculation Squares & square roots Cubes & cube roots Fraction, decimal and percentage calculations Calculator skills (powers, roots, brackets etc.)
3 Time 12-hour and 24-hour clock times Time intervals Time management (timetables) Practical activities (stopwatches) Simple speed, distance time calculations 4 Scale drawings, maps and plans Giving directions Interpreting directions Simple scale drawings 3 Speed, Distance & Time Time as a fraction and decimal fraction Consistency of units, including converting units for speed Calculations for distance, speed and time Distance-time graphs 4 Scale drawings, maps and plans Recap on bearings Recap on different forms of scale Recap on calculations involving scale Make calculations using scale drawings (recap on S1/2 work may be required) 3 Speed, Distance & Time Time as a fraction and decimal fraction Consistency of units, including converting units for speed Calculations for distance, speed and time Distance-time graphs Velocity-time/distance graphs 4 Scale drawings, maps and plans Make calculations using scale drawings (lay foundation for understanding triangle calculations, multi-stage problems with bearings etc.) Investigate drawing triangles (aim for pupils to understand the information required to make a triangle unique) 5 Chance and uncertainty Simple evaluation of risk Logic diagrams (tree diagrams, tables of permutations, flowcharts etc.) 5 Chance and uncertainty Recap on calculating simple probability Logic diagrams (tree diagrams, tables of permutations, flowcharts etc.) Calculate probability from information in a table or diagram Relative Frequency & making predictions Approximately 1½ weeks 5 Chance and uncertainty Recap on calculating simple probability Logic diagrams (tree diagrams, tables of permutations, flowcharts etc.) Calculate probability from information in a table or diagram Combined probabilities, P(A or B) Combined probabilities, P(A and B) Relative Frequency & making predictions Approximately 1 week
6 Algebraic expressions Recap collecting like terms Recap multiplying terms Simplifying expressions Substitution into simple formulae Multiplying brackets (by a single term) 7 Lengths and Perimeter Perimeter of simple 2D shapes Problems involving length and perimeter 6 Brackets and factors Recap multiplying brackets from S2 Factorise sum/difference using numerical common factors Factorise sum/difference using algebraic common factors 7 Pythagoras Theorem Know relationship between sides in a right-angled triangle, a 2 + b 2 = c 2 Calculate hypotenuse Calculate shorter side Apply to problems in context Distance between 2 points (by plotting points) 6 Brackets and factors Multiplying binomials Factorise sum/difference using numerical common factors Factorise sum/difference using algebraic common factors Extension to level 5 Approximately 1½ weeks 7 Pythagoras Theorem Know relationship between sides in a right-angled triangle, a 2 + b 2 = c 2 Calculate hypotenuse Calculate shorter side Apply to problems in context Distance between 2 points (distance formula) Using Pythagoras twice Using Pythagoras in 3D shapes Assessment at level 3 on: 1. Skills related to measurement 2. Skills related to calculation 3. Time 4. Scale drawings, maps and plans 5. Chance and uncertainty 6. Algebraic expressions 7. Lengths and Perimeter Assessment at level 4 on: 1. Skills related to measurement 2. Skills related to calculation 3. Speed, Distance & Time 4. Scale drawings, maps and plans 5. Chance and uncertainty 6. Brackets and factors 7. Pythagoras Theorem October Holiday Assessment at level 4 with level 5 extension on: 1. Skills related to measurement 2. Skills related to calculation 3. Speed, Distance & Time 4. Scale drawings, maps and plans 5. Chance and uncertainty 6. Brackets and factors 7. Pythagoras Theorem
8 Money Revise percentage calculations Basic pay Pay slips Benefits and allowances Bills Best Buy Borrowing (HP, comparing loans) Budgeting Savings 8 Money Revise percentage calculations Backward percentage calculations Salary, monthly pay, weekly wage Gross pay calculation (include overtime, commission, bonuses etc.) Deductions Net pay and pay slips Savings (including compound interest, simple examples) Borrowing (Hire Purchase) 8 Money Revise compound percentage calculations Extend calculation skills to include multiplier method for percentage increase and decrease Revise backward percentage calculations Salary, monthly pay, weekly wage Gross pay calculation (include overtime, commission, bonuses etc.) Deductions Net pay and pay slips Appreciation and depreciation Savings (include compound interest) Borrowing (Hire Purchase) 9 Shape Area & Volume Area of square and rectangle, triangle Volume of cuboid Tessellations and Tiling Extend/Create patterns Formulae for linear number patterns Similar Shapes Enlargement and reduction using a scale factor Trigonometry in right-angled triangles Using the Sine ratio (to calculate the length of an opposite side and angles) Using the Cosine ratio Using the Tangent ratio SOH-CAH-TOA 10 Trigonometry in right-angled triangles Using the Sine ratio (to calculate the length of an opposite side and angles) Using the Cosine ratio Using the Tangent ratio SOH-CAH-TOA Calculating a denominator Extension to level 5 10 Ratio Equivalent ratio Real-life problems involving ratio (mixing paint, cooking recipes etc.) Simple applications of direct proportion 12 Equations and Inequalities Revise Solve equations of the form ax + b = cx + d Solve inequalities of the same form Applying equations and inequations to problems in context. 12 Equations and Inequalities Solve equations of the form ax + b = cx + d Solve inequalities of the same form Applying equations and inequations to problems in context. Inequalities that involve reversing the sign Approximately 1 week
End of level 3 Assessment: End of level 4 Assessment: End of level 4 Assessment: Term 3 Term 3 Christmas Holiday Term 4 Start National 4 Mathematics or National 3 Lifeskills Mathematics Start National 5 Mathematics or National 4 Mathematics Start National 5 Mathematics
Term 4 Preparation for fallback qualifications National 3 Lifeskills Mathematics in S4, National 2 Lifeskills Mathematics units could be banked: Number and Number Processes Shape, Space and Data Money Time Measurement National 4 Mathematics in S4, National 3 Lifeskills Mathematics units could be banked: Shape, Space & Measures Manage Money & Data Numeracy Pupils may be asked to sit the relevant SQA unit tests under formal test conditions. Preparation for fallback qualifications Maths or Lifeskills Maths at National 4 in S4, National 3 Lifeskills Mathematics units could be banked: Shape, Space & Measures Manage Money & Data Numeracy National 5 Mathematics in S4, National 4 Mathematics units should be banked: Numeracy (essential) Expressions and Formulae Relationships Added Value (essential) The fallback position is less clear from National 5 to National 4 because the units are not hierarchical. It is therefore essential that all pupils who are going to attempt National 5 Mathematics sit and pass both the Numeracy and Added Value units at National 4. These are SQA unit tests and will be carried out under formal test conditions. Change of Timetable Preparation for fallback qualifications National 5 Mathematics in S4, National 4 Mathematics units should be banked: Numeracy (essential) Expressions and Formulae Relationships Added Value (essential) The fallback position is less clear from National 5 to National 4 because the units are not hierarchical. It is therefore essential that all pupils who are going to attempt National 5 Mathematics sit and pass both the Numeracy and Added Value units at National 4. These are SQA unit tests and will be carried out under formal test conditions. National 3 Lifeskills Mathematics National 4 Mathematics National 5 Mathematics