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FACULTY OF MATHEMATICS AND NUMERACY – BRIDGE OF DON ACADEMY Summary: National 4 course Term 3a 3a 3a 3a 3a 3b 3b 3b 3b 3c 3b 3c 3c 3c 3d 3d 3d 3d 4a 4a 4a 4a 4b 4b 4b 4b 4b 4b Evidence Task Content Sig figs, Negatives, Scientific notation Mean, mode etc Pythagoras Equations and brackets Fractions of n, ratio, speed and time Money: wages, interest, tax, exchange Probability Freq tables, scattergraphs, stem-and-leaf Factors and factorising Area and perimeter Formulae and sequences Symmetry Volume and Surface Area Gradient of a line Scale drawing Trig (SohCahToa) Money: Profit and loss (inc. n/m = x%), HP Reading and interpreting graphs Proportion and variation NU assessment Drawing a line given equation Similarity Angles and shape properties Trig revision and practice Area and volume revision and practice Fractions and %s revision and practice Algebra revision and practice AV exam Unit Test Ques. 1 2 r6 r10 e1 e3 e13 e14 r3 3 e12 e15 r13 4 5 e7 e8 e2 e4 e5 r4 r5 6 e6 e10 e11 7 r11 r12 8 r1 r2 r7 r8 r9 Pages 2 to 4 5 6 7 8 and 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 Resources The main resources will be: “Maths in Action National 4” published by Nelson Thornes and “CfE Maths Fourth Level Pupil Book” published by Leckie and Leckie. Throughout each and every topic please bear in mind that the following should be addressed: Expressions and Formulae and Relationships Reasoning Skills: 1. Interpreting a situation where mathematics can be used and identifying a valid strategy. Can be attached to any Assessment Standard in the other Outcomes to require analysis of a situation. 2. Explaining a solution and relating it to context. Can be attached to any other Assessment Standard to require explanation of the solution given. PAGE 1 OF 28 FACULTY OF MATHEMATICS AND NUMERACY – BRIDGE OF DON ACADEMY S3 Term 1 Topic Significant Figures Syllabus Area (National 4 Course Unit Support Notes) NU 1.2 Selecting and carrying out calculations (involving whole numbers, fractions, decimals, percentages, ratio and proportion): round answers to the nearest significant figure or two decimal places. Resources L&L4: Ch 1 Notes Topic N20: Rounding II [N5E1.3] a) Appreciate the difference between zero as a place holder and a value (e.g. the hundreds digit in 6000 and 6030). b) Round off an integer value to a given number of significant figures. c) Round of any real number to a given number of significant figures. d) Be aware of how to choose an appropriate level of accuracy for a problem. In addition, pupils should: Be aware of suitable degrees of accuracy. Know to always write down a more accurate answer before rounding off. PAGE 2 OF 28 FACULTY OF MATHEMATICS AND NUMERACY – BRIDGE OF DON ACADEMY S3 Term 1 Topic Syllabus Area (National 4 Course Unit Support Notes) Negative NU 1.2 Selecting and carrying out calculations (involving Numbers whole numbers, fractions, decimals, percentages, ratio and proportion): add and subtract whole numbers including negative numbers. NU 1.3 Reading measurements using a straightforward scale on an instrument: use measuring instruments with straightforward scales to measure temperature. Resources L&L4: Ch 3 Notes Topic N18: Direct Proportion [308a, N3M1.4] a) Use direct proportion. b) Draw a graph for direct proportion and recognise direct proportion from a graph. c) Find products that offer “best value” (e.g. 300ml for £4 or 500ml for £5.50). Topic N19: Ratio [308a] {n4n7} {n5n2a} a) Simplify a ratio. b) Share a quantity out in a given ratio. Topic G02: Reading a Scale {n4n9} {n5n2b} a) Interpret and read a scale that has subdivisions representing whole numbers (e.g. 0 and 10 labelled with ten subdivisions between them). b) Interpret and read a scale that has subdivisions representing multiples of whole numbers (e.g. 0 and 10 labelled with five subdivisions between them). c) Interpret and read a scale that has subdivisions representing decimal fractions of numbers (e.g. 0 and 1 labelled with ten subdivisions between them, 0 and 1 labelled with five subdivisions between them etc.). Topic N13: Negatives [304a] {n4n8} a) Use a number line to add/subtract whole numbers to/from integers (e.g. 5 – 8 = –3). b) Able to add/subtract integers to/from integers (e.g. 7 + (–2) = 7 – 2 = 5). Make sure they use brackets so that no two operators are touching (e.g. 5 3 5 (3) ). c) Know how to multiply an integer by a whole number. Topic N24: Negatives II a) Multiply any integer by any other integer. b) Divide any integer by any other integer. c) Calculate using any of the four basic operations with any Real numbers d) Calculate a n where a R and n N . In addition, pupils should: Be familiar with a wide variety of different contexts. Interpret their calculations in the context of the problem. Make decisions based on their calculations. PAGE 3 OF 28 FACULTY OF MATHEMATICS AND NUMERACY – BRIDGE OF DON ACADEMY S3 Term 1 Topic Syllabus Area (National 4 Course Unit Support Notes) Scientific [Extra] Express large numbers in the form n 10m . Notation Resources L&L4: Ch 5 Notes Topic N21: Standard Form I [N5E1.2] {n5e2b} a) Know that “standard form” is the proper name for this piece of maths but that in the SQA Maths tests/exams it will be referred to as “Scientific Notation” b) Represent x using standard form (where x 1 ). c) Convert a number given in standard form into a fully written out number. d) Perform calculations with values given in standard form (with and without a calculator). In addition, pupils should: Be familiar with contextualised cases (e.g. molecular weights, astronomical units). PAGE 4 OF 28 FACULTY OF MATHEMATICS AND NUMERACY – BRIDGE OF DON ACADEMY S3 Term 1 Topic Syllabus Area (National 4 Course Unit Support Notes) Statistics I EF 3.2 Determining statistics of a data set: mean, median, mode, range. EF 3.3 Interpreting calculated Statistics: constructing Pie chart, (percentages and degrees), Bar graph, Line graph. Resources MiAN4: Ch 5 L&L4: Ch 33 Notes Topic I05: Graphs and Charts II [221a, 321a, N3M2.3, N3N2.1, N3N2.2, N4E3.4, N4N2.1] {n3m6b} {n4n12} {n5n1abc} a) Draw pictograms, bar graphs, simple pie charts and line graphs. b) Use and interpret combined bar charts (one section on top of another) and dual bar charts (two bar charts on one diagram e.g. boys and girls columns next to each other). Topic I07: Analysing Data II [320b, 420b, N4E3.2, N4N2.2] {n4e13} a) Revise mean. b) Calculate median, mode and range. c) Identify and deal with misleading data (e.g. when one piece of data causes mean and median to be very different or when a conclusion is unjustified as the data has been misinterpreted). d) Draw conclusions when presented with two (or more) sets of data using mean, median, mode and range. Topic I08: Graphs and Charts III [320a, 321a, 420a, N4E3.4, N4N2.1, N4N2.2] {n4e14} {n5n1d, n5n3d} a) Construct pie charts. b) Construct stem-and-leaf diagrams (including back-to-back). c) Gather data in an ungrouped frequency table and use this to calculate mean. d) Gather data in a grouped frequency table. e) Know the difference between discrete and continuous data (and which graphs charts are suitable for each). In addition, pupils should: Be aware of misleading statistics and diagrams. Be able to compare two (or more) diagrams and make decisions based on the information. Know statistical language and be able to relate it into ‘everyday-speak’ when stating a conclusion. PAGE 5 OF 28 FACULTY OF MATHEMATICS AND NUMERACY – BRIDGE OF DON ACADEMY S3 Term 1 Topic Syllabus Area (National 4 Course Unit Support Notes) Pythagoras RL 2.1 Using Pythagoras’ theorem: given measurements, given coordinates. Resources MiAN4: Ch 8 L&L4: Ch 25 Notes Topic G12: Pythagoras I [312a, 416a, N4R2.1] {n4r6, n4r10} a) Investigate the relationship between the sides of a right-angled triangle to discover the Theorem of Pythagoras. b) Use the Theorem of Pythagoras to calculate the hypotenuse of a right-angled triangle. c) Find out about Pythagoras, the man. d) Use the Theorem of Pythagoras to calculate one of the shorter sides of a right-angled triangle. In addition, pupils should: Know how to interpret a coordinate diagram and use Pythagoras to find the length of a line segment. Be able to apply Pythagoras to isosceles/equilateral triangles (and then find e.g. area). Be able to apply Pythagoras to compound shapes, such as a trapezium. Tasks: SEB Standard Grade Investigation: “All Ronders” PAGE 6 OF 28 FACULTY OF MATHEMATICS AND NUMERACY – BRIDGE OF DON ACADEMY S3 Term 1 Topic Syllabus Area (National 4 Course Unit Support Notes) Equations EF 1.1 Using the distributive law in an expression with a and numerical common factor to produce a sum of terms: 3(4x ± Brackets 2), 5(a ± 2c) EF 1.3 Simplifying an expression which has more than one variable: 3a + 4b – a + 6b RL 1. 2 1.2 Solving linear equations: ax + b = c, ax + b = cx + d where a, b, c and d are integers Resources MiAN4: Ch 1, 7 L&L4: Ch 22, 24 Notes Topic A02: Expressions I (simplifying – avoiding negative algebraic terms in solution) [314a, N4E1.3] {n4e3} a) Tidy up expressions with an algebraic term (e.g. a a a a 4 a 4a ). b) Tidy up expressions with an algebraic term and arithmetic term (e.g. b b 5 2 2b 3 ). c) Tidy up expressions with algebraic terms (e.g. 2c 3d c d c 4d ). d) Tidy up expressions with algebraic terms and arithmetic term (e.g. 3e 9 f e 4 5 f 2e 6 f 13 ). Topic A07: Expressions III [314a, N4E1.1] {n4e1} a) Evaluate expressions where an algebraic term is assigned a negative value (e.g. evaluate 3x + 2y when x = –3 and y = 5). b) Simplify expressions involving brackets (e.g. 3(2b – 7) = 6b – 21). c) Evaluate expressions involving algebraic fractions (e.g. when x = 2 and y = 7, find the 3y 5 y 4x values of (i) and (ii) ). 2x 3 Topic A08: Equations III [414a, 415a, N5R1.2] {n4r3} a) Solve equations to give negative solutions (e.g. 3a + 10 = 4). b) Solve equations involving brackets (e.g. 2(3x + 1) = 20). c) Solve equations that have rational solutions (e.g. 3y – 1 = 7). d) Solve equations that have letters on both sides and/or brackets, with negative/rational solutions (e.g. 5(2n – 3) = 3n + 8). In addition, pupils should: Create an equation form a text or diagram. PAGE 7 OF 28 FACULTY OF MATHEMATICS AND NUMERACY – BRIDGE OF DON ACADEMY S3 Term 1 Topic Syllabus Area (National 4 Course Unit Support Notes) Fractions of NU 1.2 Selecting and carrying out calculations (involving a Quantity whole numbers, fractions, decimals, percentages, ratio and proportion): convert equivalences between common fractions, decimals and percentages; find simple percentages and fractions of shapes and quantities, eg 50%, 10%, 20% and 25%, 33%; ½, ⅓, ¼, 1/10, 1/n. Resources L&L4: Ch 6 Topic N02: Fractions I and Percentages I [207b, 207c, 307b, 207a, 307a, N3N1.2N4N1.2] a) Equivalent fractions (focussing on 1 s to 1 s , 1 s and 1 s ). 2 6 10 100 35 b) Fractions of a quantity (including e.g. of £9 but not mentioning percentages). 100 20 of £3 ). c) Percentages of quantities (treating them as fractions e.g. 20% of £3 100 In addition, pupils should: Know how to calculate percentages without a calculator. Be aware of a wide variety of context where these skills can be used. Make judgements based on their calculations. PAGE 8 OF 28 Notes FACULTY OF MATHEMATICS AND NUMERACY – BRIDGE OF DON ACADEMY S3 Term 1 Topic Ratio Syllabus Area (National 4 Course Unit Support Notes) NU 1.2 Selecting and carrying out calculations (involving whole numbers, fractions, decimals, percentages, ratio and proportion): calculate ratio and direct proportion, calculate rate eg miles per hour or number of texts per month. Resources L&L4: Ch8 Notes Topic N18: Direct Proportion [308a, N3M1.4] a) Use direct proportion. b) Draw a graph for direct proportion and recognise direct proportion from a graph. c) Find products that offer “best value” (e.g. 300ml for £4 or 500ml for £5.50). Topic N19: Ratio [308a] {n4n7} {n5n2a} a) Simplify a ratio. b) Share a quantity out in a given ratio. In addition, pupils should: Know how to calculate proportion using a ‘non-unitary’ method without a calculator (e.g. 80 pencils cost £7.20 so 10 pencils cost 90p and 10 pencils cost £9). Be aware of a wide variety of context where these skills can be used. Make judgements based on their calculations. PAGE 9 OF 28 FACULTY OF MATHEMATICS AND NUMERACY – BRIDGE OF DON ACADEMY S3 Term 1 Topic Time, Speed and Distance Syllabus Area (National 4 Course Unit Support Notes) NU 1.2 Selecting and carrying out calculations (involving whole numbers, fractions, decimals, percentages, ratio and proportion): calculate rate eg miles per hour or number of texts per month, calculate distance given speed and time, calculate time intervals using the 12- and 24-hour clock. Resources L&L4: Ch 12, 13 Notes Topic N17: Speed, Distance and Time [310a, N4N1.2] {n4n6} a) Revise calculation of time intervals (e.g. 05:45 to 10:20) and time conversions (e.g. 1 hour 30 minutes = 1 1 hours = 1 5 hours). Keep time conversions to simple fractions of an 2 hour. b) Understand the idea of average speed. c) Know the relationships between speed, distance and time and use this triangle: . d) Read simple information from Distance-Time graphs. e) Create simple Distance-Time graphs. In addition, pupils should: Know how to express time (e.g. hours and minutes) as a decimal hours (e.g. 5min 24sec = 5∙4 min). Know how to convert decimal time into ‘proper’ time (e.g. 3∙2 hours = 3 hours 12 minutes). Know that the steeper a line on a distance-time graph is then the greater the speed. PAGE 10 OF 28 FACULTY OF MATHEMATICS AND NUMERACY – BRIDGE OF DON ACADEMY S3 Term 2 Topic Money I Syllabus Area (National 4 Course Unit Support Notes) Wages, simple interest, tax, exchange rates. NU 1.1 Selecting and using appropriate numerical notation and units: money (pounds and pence) Resources MiAN4: Ch L&L4: Ch 10, 11 Notes Topic N14: Money and Percentages [303b, 307a, 309a, 309b, N3M1.3] {n3m4} {n4n1, n4n3, n4n13} a) Revise decimal skills (add, subtract, multiply and divide) in the context of money. b) Discuss banking: What is interest? Why do banks pay/charge interest? Why does it vary from bank to bank, year to year? What does percent mean? [stress that percent is a fraction]. c) Know how to calculate simple interest for one year or whole number multiples of years. d) Know how to use exchange rates. Topic N15: Money II (Deductions) {n3n4b, n3n5} a) Know the meaning of the terms: gross pay, net pay, income tax, national insurance, superannuation, overtime, bonus, profit and loss. b) Calculate net pay given gross pay and deductions. c) Calculate Value Added Tax (as a percentage of value) and add to price of items. In addition, pupils should: Know how to find out the interest paid by a bank for savings and research to find good deals. Be able to search for jobs (newspaper and/or internet) and interpret the advert to work out the weekly/monthly pay. Know about the reasons for different types of pay (e.g. wage, salary, commission). Have calculated over-time using different rates (e.g. time-and-a-half, time-and-a quarter). Be aware that there is “tax allowance”, different tax rates. Have seen how income tax and national insurance are calculated (e.g. using the online calculator: http://www.thesalarycalculator.co.uk/salary.php). Have an awareness of why we pay income tax, national insurance and VAT. Tasks: SEB Standard Grade Investigation: “Bank Charges” PAGE 11 OF 28 FACULTY OF MATHEMATICS AND NUMERACY – BRIDGE OF DON ACADEMY S3 Term 2 Topic Syllabus Area (National 4 Course Unit Support Notes) Probability NU 2.3 Making and explaining decisions based on probability: recognise patterns and trends and use these to state the probability of an event happening, make predictions and use these predictions to make decisions Resources MiAN4: Ch 11 L&L4: Ch 35 Notes Topic I06: Probability I [222a, N3N2.3, N4E3.5, N4N2.3] {n4n16. n4n17, n4e15} a) Calculate probability given relevant information (as a fraction or a decimal between 0 and 1). b) Conduct a simple experiment or survey to determine or check a probability (e.g. coin toss). Topic I09: Probability II [322a, N4E3.5, N4N2.3] {n5n4} a) Use tree diagrams and organised lists to identify all possible outcomes and calculate probability of specific results. b) Calculate probability and use this to make predictions. In addition, pupils should: Be able to compare probabilities and make an informed choice based on this. PAGE 12 OF 28 FACULTY OF MATHEMATICS AND NUMERACY – BRIDGE OF DON ACADEMY S3 Term 2 Topic Statistics II Syllabus Area (National 4 Course Unit Support Notes) EF 3.1 Constructing a frequency table: Using ungrouped data. EF 3.4 Representing data in a diagram: constructing Pie chart (percentages and degrees), Bar graph and Line graph. RL 4.1 Constructing a scattergraph: Given a set of data. RL 4.2 Drawing and applying a best-fitting straight line: The line should have roughly the same number of data points on either side; Use the line of best fit to estimate one variable given the other. NU 2.2 Making and explaining decisions based on the interpretation of data from straightforward graphical forms: make decisions based on observations of patterns and trends in data; make decisions based on calculations involving data; make decisions based on reading scales in straightforward graphical forms; offer reasons for the decisions made based on the interpretation of data. Resources MiAN4: Ch 6 L&L4: Ch 32, 33, 34 Notes Topic I02: Data I [220b, N3M2.1, N4E3.1, N4N2.2] {n3m6a} {n4e12} a) Gather data through experiment or survey. b) Order data (e.g. put it into a frequency table). Topic I10: Graphs and Charts IV [N4R4.1, N4R4.2, N5A4.2] {n4r13} {n5n3ab} a) (Refer to G04) Plot points using suitable axes to create a scattergraph. b) Draw a ‘line of best fit’ on a scattergraph (visual approximation). c) Use the ‘line of best fit’ to make estimates and predictions. In addition, pupils should: Complete a frequency table with grouped data. Compare data sets from analysis or diagram and make decisions/judgements based on findings. Be able to understand statistical language. Be able to translate statistical language into layman’s’ terms when coming to conclusion. PAGE 13 OF 28 FACULTY OF MATHEMATICS AND NUMERACY – BRIDGE OF DON ACADEMY S3 Term 2 Topic Syllabus Area (National 4 Course Unit Support Notes) Factors and EF 1.2 Factorising a sum of terms with a numerical common Factorising factor: eg 7x ± 21 = 7(3x ± 7), 9 ± 27x = 9(3 ± 3x). Resources MiAN4: Ch 1 L&L4: Ch23 Notes Topic A10: Factorising I (Common Factors) [N4E1.2] {n4e2} a) (See N09) Look at common factors of numbers and algebraic terms (e.g. 12 and 4n). b) Factorise a linear algebraic expression (e.g. 4n + 12 = 4(n + 3)). c) Factorise a ‘linear’ algebraic expression involving more than one algebraic term (e.g. 15 + 5x – 20y = 5(3 + x – 4y)). d) Factorise an algebraic term involving a ‘squared’ term (e.g. 6x2 + 3x = 3x(2x + 1)). PAGE 14 OF 28 FACULTY OF MATHEMATICS AND NUMERACY – BRIDGE OF DON ACADEMY S3 Term 2 Topic Syllabus Area (National 4 Course Unit Support Notes) EF 2.1 Calculating the circumference and area of a circle: Given radius or Length, diameter. Perimeter EF 2.2 Calculating the area of a parallelogram, kite, trapezium: Composite and Area shapes by splitting into triangles. NU 1.3 Reading measurements using a straightforward scale on an instrument: use measuring instruments with straightforward scales to measure length, weight, volume, read scales to the nearest marked, unnumbered division with a functional degree of accuracy NU 1.4 Interpreting the measurements and the results of calculations to make decisions: use appropriate checking methods, eg check sums and estimation; interpret results of measurements involving time, length, volume; recognise the inter-relationship between units in the same family, eg mm/cm, cm/m and ml/l; use vocabulary associated with measurement to make comparisons for length, volume. Resources MiAN4: Ch 2 L&L4: Ch 14, 15, 26 Notes Topic G03: Measurement II (Length) [211a, 211b, N3S1.1, N4N1.3] {n3n3, n3s4a} {n4n5, n4n11a} a) Use a ruler to measure a length in cm or mm. b) Convert metric units of length (e.g. 56mm = 56cm). c) Use metre sticks, tape measures and trundle wheels to measure large lengths (e.g. length and breadth of classroom). d) Calculate perimeter of a compound shape. Topic G07: Measurement II (Basic Area and Volume) [211c, N3S1.1, N3S1.2, N4E2.2] {n3s2, n3s4b} a) Calculate area of a rectangle ( A l b ). b) Calculate area of a triangle ( A 1 of b h ). 2 c) Calculate area of compound shapes. d) Calculate volume of a cuboid ( V l b h ). e) Convert cm3 in millilitres or litres. Topic G14: Measurement IV (Areas) [N4E2.2] {n4e8} a) Calculate the area of a kite/rhombus by splitting them up into triangles. b) Calculate the area of a trapezium by splitting it into constituent parts (e.g. two triangles and a rectangle). c) Calculate the area of a parallelogram by splitting it into constituent parts (e.g. two triangles and a rectangle). 1 d) Calculate the area of a kite/rhombus using the formula Area = lb . 2 e) Understand why a parallelogram’s area can be calculated using Area = bh and use this to calculate the area of parallelograms. In addition, pupils should: Be able to use these skills in a variety of situations and context. Be aware of imperial units and have some idea of the magnitude of each (e.g. pint, lb). See that imperial measurements can be converted to metric. Have practical experience of calculating areas, length and volumes (e.g. area of the classroom). PAGE 15 OF 28 FACULTY OF MATHEMATICS AND NUMERACY – BRIDGE OF DON ACADEMY S3 Term 2 Topic Syllabus Area (National 4 Course Unit Support Notes) Formulae EF 1.4 Evaluating an expression or a formulae which has and more than one variable: Evaluate linear expressions for given Sequences variables (eg w=1, t=3, k=5 find 4w + 6t – 3k). EF 1.5 Extending a straightforward number or diagrammatic pattern: eg 4, 7, 10, 13,… and 4, 9, 16, 25,… and well known sequences. EF 1.6 Determining a formula from information or a diagrammatic pattern: Evaluate the formula for a given variable. RL 1.3 Changing the subject of a formula: Change the subject of the formulae: G = x+a, T = xc, E = wx + k. Resources MiAN4: Ch 1 L&L4: Ch 18 Notes Topic A03: Expressions II (evaluating – for examples below a 1, b 2, c 3 ) [315b, N4E1.4] {n4e4a} a) Expressions with an algebraic term (e.g. a 5 1 4 5 ) where algebraic term has no coefficient. b) Expressions with one algebraic term (e.g. 2 a 5 2 1 4 6 progressing quickly to 3b 1 3 2 1 5 ). c) Expressions with two algebraic terms (e.g. a b 1 2 3 ) where the algebraic terms have no coefficients. d) Expressions with two algebraic terms (e.g. 7a 2b 7 1 2 2 3 ). e) Expressions with two algebraic terms and an arithmetic term (e.g. 7a 2b 5 7 1 2 2 5 8 ). Topic A05: Formulae I [315b, N3S2.2, N4E1.4] {n4e4b} a) Substitute values into a given basic formulae (e.g. Area l b 7 9 63cm2 ). Topic A09: Formulae II [313a, NFE1.5, N4E1.6] {n4e5} {n5n3c} a) Substitute values into a formula involving brackets. b) Create a formula for a simple scenario. c) Create an nth term formula for a sequence. In addition, pupils should: Know the importance of setting the working out properly. Be able to create a table/sequence from diagrams/pictures and extend the pattern. Be able to create an expression from a diagram. Be aware that final answers can be algebraic expressions (and know that these are different from equations). PAGE 16 OF 28 FACULTY OF MATHEMATICS AND NUMERACY – BRIDGE OF DON ACADEMY S3 Term 3 Topic Syllabus Area (National 4 Course Unit Support Notes) Symmetry EF 2.6 Using rotational symmetry: with straightforward linear shapes. Topic G06: Symmetry [219a, 319a, N4E2.6] {n4e11} a) Reflect in a horizontal or vertical line. b) Rotate by 90 or 180 . In addition, pupils should: Be able to complete reflections/rotations on a diagram. Use the property of symmetry when finding angles/lengths/areas. PAGE 17 OF 28 Resources MiAN4: Ch 4 L&L4: Ch 31 Notes FACULTY OF MATHEMATICS AND NUMERACY – BRIDGE OF DON ACADEMY S3 Term 3 Topic Syllabus Area (National 4 Course Unit Support Notes) Volume EF 2.3 Investigating the surface of a prism: Know face, and Surface vertex, edge; Draw nets; Calculate surface area. Area EF 2.4 Calculating the volume of a prism: Triangular prism, cylinder, other prisms given the area of the base. NU 1.2 Selecting and carrying out calculations (involving whole numbers, fractions, decimals, percentages, ratio and proportion): calculate volume (cube and cuboid), area (rectangle and square) and perimeter (shapes with straight lines). NU 1.3 Reading measurements using a straightforward scale on an instrument: use measuring instruments with straightforward scales to measure length, volume; read scales to the nearest marked, unnumbered division with a functional degree of accuracy. NU 1.4 Interpreting the measurements and the results of calculations to make decisions: use appropriate checking methods, eg check sums and estimation; interpret results of measurements involving time, length, volume; recognise the inter-relationship between units in the same family, eg mm/cm, cm/m and ml/l; use vocabulary associated with measurement to make comparisons for length, volume. Resources MiAN4: Ch 2 L&L4: Ch 15, 16 Notes Topic G16: Measurement VI (Volume of a Prism) [N4E2.4, N5E3.3] {n4e10} a) (Refer to G06) Understand that for a cuboid Volume = lbh = Ah. b) (Refer to G06) Know for a triangular prism that V = Ah where A = (area of an end) and h = (distance between ends). c) Extend this to the circle and the cylinder. Calculate volume of a cylinder using V r 2 h . d) Find the volume of any prism using V = Ah (possibly where A is already calculated). Topic G15: Measurement V (Surface Area) [N4E2.3] {n4e9} a) (Refer to G01) Sketch the net of a cuboid, triangular prism and cylinder. b) (Refer to G06, G08) Calculate the area of a rectangle, triangle and circle. c) Calculate the area of the faces of a cuboid and find the total surface area. d) Sketch the net of a triangular prism and find the surface area. e) Sketch the net of a cylinder (and understand that the length of the curved surface is the circumference of the circular end) and find the surface area. In addition, pupils should: Know how to draw a net of cuboid/cube and cut it out to create the 3D shape. Know how to draw a net of triangular prism and cut it out to create the 3D shape. Apply these skills to contextualised problems. Tasks: SEB Standard Grade Investigation: “Which Container?” SEB Standard Grade Investigation: “Wooden Display Boxes” PAGE 18 OF 28 FACULTY OF MATHEMATICS AND NUMERACY – BRIDGE OF DON ACADEMY S3 Term 3 Topic Syllabus Area (National 4 Course Unit Support Notes) Gradient of EF 2.5 Investigating the gradient of a straight line: vertical a Line distance over horizontal distance; positive and negative gradients; parallel lines have equal gradient. Resources MiAN4: Ch 3 L&L4: Ch 19, 20 Notes Topic G17: Gradient I [N4E2.5, N5E3.1] {n4e6} a) Understand the term gradient referring to steepness. Know that a horizontal surface has “zero” gradient and that a vertical surface has an infinite gradient (and is therefore undefined). horizontal b) Know to calculate gradient using the formula: gradient . vertical c) Understand that on a graph we can have negative gradients (sloping downwards). d) Appreciate that parallel lines have equal gradients. In addition, pupils should: Be able to apply these skills to contextualised problems. PAGE 19 OF 28 FACULTY OF MATHEMATICS AND NUMERACY – BRIDGE OF DON ACADEMY S3 Term 4 Topic Scale Drawing Syllabus Area (National 4 Course Unit Support Notes) NU 1.3 Reading measurements using a straightforward scale on an instrument: use measuring instruments with straightforward scales to measure length; read scales to the nearest marked, unnumbered division with a functional degree of accuracy. NU 1.4 Interpreting the measurements and the results of calculations to make decisions: use appropriate checking methods, eg check sums and estimation; interpret results of measurements involving length; recognise the interrelationship between units in the same family, eg mm/cm, cm/m; use vocabulary associated with measurement to make comparisons for length. Resources L&L4: Ch 15 Notes Topic G11: Scale [317b, 317c, N3S2.3, N3S2.4, N4R2.2] {n3s3b} {n4r7} a) Able to enlarge and reduce given a scale factor. b) Able to calculate a scale factor. c) Create scale drawings, given a suitable scale, and use these to answer problems. d) Know the points of an 8-point compass. e) Know how to measure bearings and how to draw them on a scale drawing. f) Able to read a basic map and use it to calculate distances and directions/bearings. In addition, pupils should: Gather required measurements to create a scale drawing of a real-life problem (e.g. finding the height of the school). Be able to apply these skills to contextualised problems. PAGE 20 OF 28 FACULTY OF MATHEMATICS AND NUMERACY – BRIDGE OF DON ACADEMY S3 Term 4 Topic Trig Syllabus Area (National 4 Course Unit Support Notes) RL 3.1 Calculating a side in a right-angled triangle: Given a side and an angle. RL 3.2 Calculating an angle in a right-angled triangle: Given two sides. Resources MiAN4: Ch 10 L&L4: Ch 25 Notes Topic G20: Trigonometry I (Soh Cah Toa) [N4R3.1, N4R3.2] {n4r11, n4r12} a) Know how to label the sides of a right-angled triangle relative to an angle: opposite, adjacent and hypotenuse. b) Investigate the ratio of sides of mathematically similar right-angled triangles. c) Know the terms sine (sin), cosine (cos) and tangent (tan). Able to identify which one is appropriate (Soh Cah Toa) and find the ratio with respect an angle using a calculator (e.g. sin(30)). d) Use basic trig to find an unknown length on a right-angled triangle, given an angle and one other side. e) Use basic trig to find an angle in a right-angled triangle, given the length of any two sides. In addition, pupils should: Gather required measurements to create a scale drawing of a real-life problem (e.g. finding the height of the school). Be able to apply these skills to contextualised problems. PAGE 21 OF 28 FACULTY OF MATHEMATICS AND NUMERACY – BRIDGE OF DON ACADEMY S3 Term 4 Topic Money II Syllabus Area (National 4 Course Unit Support Notes) Profit and Loss (including m/n = x%), Hire Purchase NU 1.1 Selecting and using appropriate numerical notation and units: money (pounds and pence). NU 1.2 Selecting and carrying out calculations (involving whole numbers, fractions, decimals, percentages, ratio and proportion): round answers to the nearest significant figure or two decimal places; find simple percentages and fractions of shapes and quantities, eg 50%, 10%, 20% and 25%, 33%; ½, ⅓, ¼, 1/10, 1/n; calculate percentage increase and decrease; convert equivalences between common fractions, decimals and percentages. NU 1.5 Explaining decisions based on the results of calculations: give reasons for decisions based on the results of calculations. Resources L&L4: Ch 6, 11 Notes Topic N22: Money III (Hire Purchase and Loans) [N3M1.4] {n3m5} {n5n2e} a) Calculate and apply discount. b) Calculate HP cost (given deposit amount or when deposit is a percentage of cash price). c) Compare overall HP costs and reason to which is the better buy. d) Look at personal loans and compare with HP/finance options offered by companies. Topic N27: Amounts Expressed as a Percentage [N5A3.1] {n5n2d} a) Know how to express one amount as a fraction of another (e.g. bought for £10, sold for £12 2 1 of buying price). so profit = 12 6 b) Express one amount as a percentage of another (using contexts such as profit/loss, scores from tests, errors, tolerances, depreciation/appreciation). In addition, pupils should: Gather required information to perform these calculations for a real-life problem (e.g. (a) finding the net annual pay for a joiner. (b) comparing finance options to buy a specific TV. (c) calculating the percentage profit on a sale). Be able to apply these skills to wide variety of contextualised problems. PAGE 22 OF 28 FACULTY OF MATHEMATICS AND NUMERACY – BRIDGE OF DON ACADEMY S3 Term 4 Topic Syllabus Area (National 4 Course Unit Support Notes) Statistics III Reading and interpreting Graphs NU 2.1 Extracting and interpretation data from at least two different straightforward graphical forms: Straightforward graphical forms should include a table with at least four categories of information; a chart where the values are given or where the scale is obvious, eg pie; a graph where the scale is obvious, eg bar, pie, scatter or line graph; a diagram, eg stem and leaf, map or plan. NU 2.2 Making and explaining decisions based on the interpretation of data from straightforward graphical forms: make decisions based on observations of patterns and trends in data: make decisions based on calculations involving data; make decisions based on reading scales in straightforward graphical forms; offer reasons for the decisions made based on the interpretation of data. Resources MiAN4: Ch 5, 6 L&L4: Ch 34 Notes Topic I05: Graphs and Charts II [221a, 321a, N3M2.3, N3N2.1, N3N2.2, N4E3.4, N4N2.1] {n3m6b} {n4n12} {n5n1abc} a) Draw pictograms, bar graphs, simple pie charts and line graphs. b) Use and interpret combined bar charts (one section on top of another) and dual bar charts (two bar charts on one diagram e.g. boys and girls columns next to each other). Topic I08: Graphs and Charts III [320a, 321a, 420a, N4E3.4, N4N2.1, N4N2.2] {n4e14} {n5n1d, n5n3d} a) Construct pie charts. b) Construct stem-and-leaf diagrams (including back-to-back). c) Gather data in an ungrouped frequency table and use this to calculate mean. d) Gather data in an grouped frequency table. e) Know the difference between discrete and continuous data (and which graphs charts are suitable for each). Topic I10: Graphs and Charts IV [N4R4.1, N4R4.2, N5A4.2] {n4r13} {n5n3ab} a) (Refer to G04) Plot points using suitable axes to create a scattergraph. b) Draw a ‘line of best fit’ on a scattergraph (visual approximation). c) Use the ‘line of best fit’ to make estimates and predictions. In addition, pupils should: Gather required data to draw a scattergraph for two different groups and make a comparison (e.g. age and height from two year groups). Be able to apply these skills to contextualised problems. Use information gathered to draw two different types of charts/diagrams for two different groups of data and use these to present and justify a conclusion. PAGE 23 OF 28 FACULTY OF MATHEMATICS AND NUMERACY – BRIDGE OF DON ACADEMY S4 Term 1 Topic Proportion and Variation Syllabus Area (National 4 Course Unit Support Notes) NU 1.2 Extracting and interpretation data from at least two different straightforward graphical forms: calculate rate: eg miles per hour or number of texts per month; calculate ratio and direct proportion Resources L&L4: Ch 8 Notes Topic N18: Direct Proportion [308a, N3M1.4] a) Use direct proportion. b) Draw a graph for direct proportion and recognise direct proportion from a graph. c) Find products that offer “best value” (e.g. 300ml for £4 or 500ml for £5.50). Topic N19: Ratio [308a] {n4n7} {n5n2a} a) Simplify a ratio. b) Share a quantity out in a given ratio. In addition, pupils should: Be able to see how these skills apply in different subject areas across the school (e.g. proportion in Home Economics). Research and use these skills to find the best deal for buying a particular product (e.g. a real life scenario for Topic N18c). Be able to apply these skills to contextualised problems. PAGE 24 OF 28 FACULTY OF MATHEMATICS AND NUMERACY – BRIDGE OF DON ACADEMY S4 Term 1 Topic Drawing Graphs of Straight Line Syllabus Area (National 4 Course Unit Support Notes) RL 1.1 Drawing and recognising a graph of a linear equation: Draw using a table of values or chosen values of x; For y = mx +c, know the meaning of m and c; Recognise and use y = a, x = b. Resources MiAN4: Ch 3 L&L4: Ch 21 Notes Topic A11: Graphs of Linear Equations [N4R1.1] {n4r1, n4r2} a) (Referring to A09c) Take a “formula” and create a table of values/coordinates, plot the points and draw the graph. Emphasize that the line is a collection of all the points generated by the “formula” (including those between the coordinates originally plotted). b) Given any Linear Equation (of the form y = mx + c) they can create a table of values (at least three points) and draw the graph. c) Given any Linear Equation (in any form) they can create a table of values (at least three points) and draw the graph. d) Reference should be made to the steepness of the graph (m) and the y-intercept (c). e) Sketch the graph of a linear equation given in the form y = mx + c. In addition, pupils should: Appreciate the term “linear” and see the association with sequences. Know that linear means that there are no powers (larger than 1) on the variables. Realise that their line is only part of the line given by the equation. See that m is the gradient and appreciate what it means when m > 0, m = 0 and m < 0. See that c is the gradient and appreciate what it means when c > 0, c = 0 and c < 0. See how this ties in with a scattergraph and a line of best fit. PAGE 25 OF 28 FACULTY OF MATHEMATICS AND NUMERACY – BRIDGE OF DON ACADEMY S4 Term 1 Topic Similarity Syllabus Area (National 4 Course Unit Support Notes) RL 2.2 Using a scale factor to enlarge or reduce a shape: Linear, non-rectangular shape. Resources L&L4: Ch 28 Topic G11: Scale [317b, 317c, N3S2.3, N3S2.4, N4R2.2] {n3s3b} {n4r7} a) Able to enlarge and reduce given a scale factor. b) Able to calculate a scale factor. c) Create scale drawings, given a suitable scale, and use these to answer problems. d) Know the points of an 8-point compass. e) Know how to measure bearings and how to draw them on a scale drawing. f) Able to read a basic map and use it to calculate distances and directions/bearings. In addition, pupils should: Be able to apply these skills to contextualised problems. PAGE 26 OF 28 Notes FACULTY OF MATHEMATICS AND NUMERACY – BRIDGE OF DON ACADEMY S4 Term 2 Topic Angles and Shape Properties Syllabus Area (National 4 Course Unit Support Notes) RL 2.3 Using properties of shapes: Triangles, quadrilaterals and Circles using: angle in a semi-circle; relationship between tangent and radius; combinations of angle properties. Resources MiAN4: Ch 9 L&L4: Ch 27 Notes Topic G19: Circle Geometry [N4R2.3, N5R3.2] {n4r9} {n5r14} a) (Refer to G03 and G09) Able to use the properties of alternate angles, corresponding angles, vertically opposite angles, complementary angles, supplementary angles and sum of angles in a triangle. b) Investigate, understand and use the property of that a triangle formed by a diameter and two chords in a semi-circle will be a right angled triangle (angle in a semi-circle). c) Know what a “tangent to a circle” is and that it is perpendicular to the radius at point of contact. d) Know that if a chord is bisected by a radius then they are perpendicular (and vice versa). In addition, pupils should: Be able to apply these skills to contextualised problems (e.g. bearings, angles in a polygon). Tasks: SEB Standard Grade Investigation: “Presentation Pack of Golf Balls” PAGE 27 OF 28 FACULTY OF MATHEMATICS AND NUMERACY – BRIDGE OF DON ACADEMY PAGE 28 OF 28