# National 5 Mathematics – Scotland

### Scotland National 5 Mathematics

# | TOPIC | TITLE |
---|---|---|

1 | Initial Assessment | Initial Assessment |

2 | Multiplication and division | Multiplying 4-digit numbers by 3-digit numbers |

3 | Multiplication and division | Multiplying 4-digit numbers by 4-digit number |

4 | Decimals | Multiplying decimals by 10, 100 and 1000 |

5 | Multiplication and division | Repeated subtraction with divisors greater than 20 with… |

6 | Multiplication and division | Repeated subtraction with divisors less than 35 with so… |

7 | Multiplication and division | Repeated subtraction with divisors less than 55 with di… |

8 | Multiplication and division | Repeated subtraction with divisors greater than 50 with… |

9 | Multiplication and division | Using divide, multiply and subtraction in the bring dow… |

10 | Decimals | Dividing decimals by 10, 100 and 1000 |

11 | Simplifying | Directed numbers: addition and subtraction. |

12 | Simplifying | Directed numbers: multiplication and division. |

13 | Bidmas | Using Order of Operation procedures (BIDMAS) with Fract… |

14 | Multiplication and division | Multiples and factors of whole numbers |

15 | Multiples and factors | Highest common factor. |

16 | Multiples and factors | Factors by grouping. |

17 | Decimals | Rounding decimals |

18 | Decimals | Decimals to three decimal places |

19 | Decimals | Adding decimals with a different number of decimal plac… |

20 | Decimals | Subtracting decimals with a different number of places |

21 | Decimals | Multiplying decimals by whole numbers |

22 | Decimals | Multiplication of decimals by decimals to two decimal p… |

23 | Decimals | Dividing decimal fractions by whole numbers |

24 | Decimals | Dividing numbers by a decimal fraction |

25 | Fractions | Adding and subtracting fractions with different denomin… |

26 | Fractions | Multiplying fractions by whole numbers |

27 | Fractions | Fractions of whole numbers |

28 | Fractions | Multiplying fractions |

29 | Fractions | Multiplying mixed numbers (mixed numerals) |

30 | Fractions | Finding reciprocals of fractions and mixed numbers (mix… |

31 | Fractions | Dividing fractions |

32 | Fractions | Dividing mixed numbers (mixed numerals) |

33 | Indices | Adding indices when multiplying terms with the same bas… |

34 | Indices | Subtracting indices when dividing terms with the same b… |

35 | Indices | Multiplying indices when raising a power to a power |

36 | Indices | Multiplying indices when raising to more than one term |

37 | Indices | Terms raised to the power of zero |

38 | Indices | Negative Indices |

39 | Indices | Fractional indices |

40 | Indices | Complex fractions as indices |

41 | Percentages | Calculating Percentages and Fractions of Quantities |

42 | Percentages | Introduction to percentages, including relating common … |

43 | Percentages | Changing fractions and decimals to percentages using te… |

44 | Percentages | Changing percentages to fractions and decimals |

45 | Percentages | One quantity as a percentage of another |

46 | Percentages | Compound interest |

47 | Approximation | Significant figures |

48 | Speed | Average speed |

49 | Standard form | Scientific notation with larger numbers |

50 | Standard form | Scientific notation with small numbers |

51 | Standard form | Changing scientific notation to numerals |

52 | Surds | Introducing surds |

53 | Surds | Some rules for the operations with surds |

54 | Surds | Simplifying surds |

55 | Surds | Creating entire surds |

56 | Surds | Adding and subtracting like surds |

57 | Surds | Expanding surds |

58 | Surds | Conjugate binomials with surds |

59 | Surds | Rationalising the denominator |

60 | Surds | Rationalising binomial denominators |

61 | Problem solving | Compare and convert formal units of measurement |

62 | Capacity | Estimate, measure and compare the capacity of container… |

63 | Problem solving | Introducing the rules for finding the area of a rectang… |

64 | Problem solving | Finding the area of a triangle and other composite shap… |

65 | Problem solving | Area of a trapezium. |

66 | Problem solving | Area of a rhombus. |

67 | Problem solving | Area of a circle. |

68 | Problem solving | Area of regular polygons and composite figures. |

69 | Surface area | Surface area of a cube/rectangular prism. |

70 | Surface area | Surface area of a triangular/trapezoidal prism. |

71 | Surface area | Surface area of a cylinder and sphere. |

72 | Surface area | Surface area of pyramids |

73 | Surface area | Surface area of cones |

74 | Surface area | Surface area of composite solids |

75 | Volume | Introducing the formula for volume. |

76 | Volume | Using the cubic metre to measure volume. |

77 | Volume | Solving Problems about Volume – Part 1. |

78 | Volume | Solving Problems about Volume – Part 2. |

79 | Volume | Finding the volume of prisms |

80 | Volume | Volume of a cylinder and sphere. |

81 | Volume | Volume of pyramids and cones. |

82 | Volume | Composite solids. |

83 | Problem solving | Problems with length. |

84 | Problem solving | Problems with mass. |

85 | Problem solving | Problems with area. |

86 | Problem solving | Problems with volume/capacity. |

87 | Triangles | Using the prefix to determine polygons |

88 | 3D shapes | Recognise and name prisms according to spatial properti… |

89 | 3D shapes | Recognise and name pyramids according to spatial proper… |

90 | 3D shapes | Recognise nets for prisms, pyramids, cubes and cones |

91 | 3D shapes | Viewing 3-D shapes. |

92 | 3D shapes | Constructing models. |

93 | Angles | Adjacent angles |

94 | Angles | Complementary and supplementary angles |

95 | Angles | Vertically opposite angles |

96 | Angles | Angles at a Point. |

97 | Angles | Parallel Lines. |

98 | Angles | Additional questions involving parallel lines |

99 | Angles | Angle sum of a triangle |

100 | Angles | Exterior angle theorem |

101 | Angles | To determine angle labelling rules, naming angles accor… |

102 | Angles | More difficult exercises involving parallel lines |

103 | Angles | Angles of regular polygons |

104 | Angles | Complementary angle results. |

105 | Angles | Bearings – the compass. |

106 | Angles | Theorem – Equal arcs on circles of equal radii subtend … |

107 | Angles | Theorem – The perpendicular from the centre of a circle… |

108 | Angles | Theorem – Equal chords in equal circles are equidistant… |

109 | Angles | Theorem – The angle at the centre of a circle is double… |

110 | Angles | Theorem – Angles in the same segment of a circle are eq… |

111 | Angles | Theorem – The angle of a semi-circle is a right angle. |

112 | Angles | Theorem – The opposite angles of a cyclic quadrilateral… |

113 | Angles | Theorem – The exterior angle at a vertex of a cyclic qu… |

114 | Angles | Theorem – The tangent to a circle is perpendicular to t… |

115 | Angles | Theorem – Tangents to a circle from an external point a… |

116 | Angles | Theorem – The angle between a tangent and a chord throu… |

117 | Angles | Theorem – The products of the intercepts of two interse… |

118 | Angles | Theorem – The square of the length of the tangent from … |

119 | Angles | Theorem – If the opposite angles in a quadrilateral are… |

120 | Angles | Theorem – If an interval subtends equal angles at two p… |

121 | Angles | Theorem – When circles touch, the line of the centres p… |

122 | Angles | Theorem – Any three non-collinear points lie on a uniqu… |

123 | Construction | Geometric constructions |

124 | Construction | To identify collinear points, coplanar lines and points… |

125 | Construction | Angle bisector construction and its properties (Stage 2… |

126 | Construction | Circumcentre and incentre (Stage 2) |

127 | Construction | Orthocentre and centroids (Stage 2) |

128 | Construction | Constructions and loci – single condition |

129 | Construction | Constructions and loci – multiple conditions |

130 | Similar shapes | Similar triangles |

131 | Similar shapes | Using similar triangles to calculate lengths |

132 | Similar shapes | Special triangles |

133 | Transformations | Use grids to enlarge/reduce 2D shapes |

134 | Transformations | Special transformations – reflections, rotations and en… |

135 | Transformations | Transformations – reflections |

136 | Transformations | Geometry transformations without matrices: reflection (… |

137 | Transformations | Geometry transformations without matrices: translation … |

138 | Transformations | Geometry transformations without matrices: rotation (St… |

139 | Transformations | Geometry transformations without matrices: dilation or … |

140 | Transformations | The definition and concept of combined transformations … |

141 | Triangles | Recognise and name triangles |

142 | Triangles | Congruent triangles, Test 1 and 2 |

143 | Triangles | Congruent triangles, Test 3 and 4 |

144 | Triangles | Proofs and congruent triangles. |

145 | Triangles | Examples involving overlapping triangles |

146 | Pythagoras | Find the hypotenuse |

147 | Pythagoras | Pythagorean triples |

148 | Pythagoras | Find the hypotenuse Part 2 |

149 | Pythagoras | Calculating a leg of a right-angled triangle |

150 | Trigonometry | Graphing the trigonometric ratios – I Sine curve. |

151 | Trigonometry | Graphing the trigonometric ratios – II Cosine curve. |

152 | Trigonometry | Graphing the trigonometric ratios – III Tangent curve. |

153 | Trigonometry | Graphing the trigonometric ratios – IV Reciprocal ratio… |

154 | Trigonometry | Trigonometric ratios. |

155 | Trigonometry | Using the calculator. |

156 | Trigonometry | Using the trigonometric ratios to find unknown length. … |

157 | Trigonometry | Using the trigonometric ratios to find unknown length. … |

158 | Trigonometry | Using the trigonometric ratios to find unknown length. … |

159 | Trigonometry | Unknown in the denominator. [Case 4]. |

160 | Trigonometry | Angles of elevation and depression. |

161 | Trigonometry | Trigonometric ratios in practical situations. |

162 | Trigonometry | Using the calculator to find an angle given a trigonome… |

163 | Trigonometry | Using the trigonometric ratios to find an angle in a ri… |

164 | Trigonometry | Trigonometric ratios of 30., 45. and 60. – exact ratios… |

165 | Trigonometry | The cosine rule to find an unknown side. [Case 1 SAS]. |

166 | Trigonometry | The cosine rule to find an unknown angle. [Case 2 SSS]. |

167 | Trigonometry | The sine rule to find an unknown side. Case 1. |

168 | Trigonometry | The sine rule to find an unknown angle. Case 2. |

169 | Trigonometry | The area formula |

170 | Trigonometry | Reciprocal ratios. |

171 | Trigonometry | Angles of any magnitude |

172 | Trigonometry | Trigonometric ratios of 0°, 90°, 180°, 270° and 360° |

173 | Co-ordinate Geometry | Triangle inequality theorem |

174 | Coordinate geometry | Distance formula. |

175 | Coordinate geometry | Mid-point formula |

176 | Coordinate geometry | Gradient |

177 | Coordinate geometry | Gradient formula. |

178 | Coordinate geometry | The straight line. |

179 | Coordinate geometry | Lines through the origin. |

180 | Coordinate geometry | General form of a line and the x and y Intercepts. |

181 | Series and sequences | General sequences. |

182 | Series and sequences | Finding Tn given Sn. |

183 | Simplifying | Algebraic expressions. |

184 | Simplifying | Simplifying Algebraic expressions: combining addition a… |

185 | Simplifying | Simplifying algebraic expressions: multiplication |

186 | Simplifying | Simplifying algebraic expressions: division |

187 | Simplifying | Expanding algebraic expressions: multiplication |

188 | Simplifying | Expanding algebraic expressions: negative multiplier |

189 | Simplifying | Expanding and simplifying algebraic expressions |

190 | Simplifying | Simplifying algebraic fractions using the index laws. |

191 | Simplifying | Algebraic fractions resulting in negative indices. |

192 | Simplifying | Cancelling binomial factors in algebraic fractions. |

193 | Simplifying | Products in simplification of algebraic expressions |

194 | Simplifying | Algebraic Expressions – Larger expansions. |

195 | Simplifying | Simplifying algebraic fractions. |

196 | Graphs | Quadratic polynomials of the form y = ax. + bx + c. |

197 | Graphs | Graphing perfect squares: y=(a-x) squared |

198 | Graphs | Solve by graphing |

199 | Graphs | Graphing cubic curves |

200 | Problem solving | Problem solving strategies |

201 | Equations | Solving equations containing addition and subtraction |

202 | Equations | Solving equations containing multiplication and divisio… |

203 | Equations | Solving two step equations |

204 | Equations | Solving equations containing binomial expressions |

205 | Equations | Equations involving grouping symbols. |

206 | Equations | Equations involving fractions. |

207 | Equations | Simultaneous equations |

208 | Equations | Elimination method |

209 | Equations | Elimination method part 2 |

210 | Equations | Applications of simultaneous equations |

211 | Factorising | Expansions leading to the difference of two squares |

212 | Factorising | Common factor and the difference of two squares |

213 | Factorising | Factorising quadratic trinomials [monic] – Case 2. |

214 | Factorising | Factorising quadratic trinomials [monic] – Case 3. |

215 | Factorising | Factorising quadratic trinomials [monic] – Case 4. |

216 | Factorising | Factorisation of non-monic quadratic trinomials |

217 | Factorising | Factorisation of non-monic quadratic trinomials – moon … |

218 | Simplifying | Substitution into algebraic expressions. |

219 | Formulae | Equations resulting from substitution into formulae. |

220 | Formulae | Changing the subject of the formula. |

221 | Factorising | Simplifying easy algebraic fractions. |

222 | Factorising | Factorisation of algebraic fractions including binomial… |

223 | Inequalities | Solving Inequalities. |

224 | Inequalities | Inequalities on the number plane. |

225 | Roots | Difference of two squares |

226 | Roots | Quadratic trinomials [monic] – Case 1. |

227 | Roots | Introduction to quadratic equations. |

228 | Roots | Quadratic equations with factorisation. |

229 | Roots | Solving quadratic equations. |

230 | Roots | Completing the square |

231 | Roots | Solving quadratic equations by completing the square |

232 | Roots | The quadratic formula |

233 | Roots | Problem solving with quadratic equations |

234 | Roots | Solving simultaneous quadratic equations graphically |

235 | Matrices | Vectors |

236 | Scatter diagrams | The range. |

237 | Probability | The mode |

238 | Probability | The mean |

239 | Probability | The median |

240 | Probability | Calculating the median from a frequency distribution |

241 | Averages | Calculating mean, mode and median from grouped data |

242 | Averages | Range as a measure of dispersion |

243 | Averages | Measures of spread |

244 | Averages | Standard deviation applications |

245 | Averages | Measures of spread: the interquartile range |

246 | Pie charts | Pie and bar graphs. |

247 | Scatter diagrams | Scatter Diagrams |

248 | Scatter diagrams | Stem and Leaf Plots along with Box and Whisker Plots |

249 | Probability | Cumulative frequency |

250 | Scatter diagrams | Frequency histograms and polygons |

251 | Pie charts | Line graphs. |

252 | Scatter diagrams | Frequency distribution table |

253 | Scatter diagrams | Relative frequency |

254 | Probability | Probability of Simple Events |

255 | Probability | Rolling a pair of dice |

256 | Probability | Experimental probability |

257 | Probability | Tree diagrams – not depending on previous outcomes |

258 | Probability | Tree diagrams – depending on previous outcomes |

259 | End of Course Assessment | End of Course Assessment |