# Level 3: S3 Mathematics – Scotland

### Scotland Level 3: S3 Mathematics

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

1 | Initial Assessment | Initial Assessment |

2 | Problem solving | Problems with numbers. |

3 | Problem solving | Problems involving money |

4 | Fractions | Comparing and ordering fractions |

5 | Fractions | Comparing and ordering fractions greater than (>) 1 |

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

7 | Fractions | Multiplying fractions by whole numbers |

8 | Fractions | Fractions of whole numbers |

9 | Fractions | Multiplying fractions |

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

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

12 | Fractions | Dividing fractions |

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

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

15 | Decimals | Rounding decimals |

16 | Decimals | Decimals to three decimal places |

17 | Approximation | Significant figures |

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

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

20 | Decimals | Multiplying decimals by whole numbers |

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

22 | Decimals | Dividing decimal fractions by whole numbers |

23 | Decimals | Dividing numbers by a decimal fraction |

24 | Percentages | Calculating Percentages and Fractions of Quantities |

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

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

27 | Percentages | Changing percentages to fractions and decimals |

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

29 | Percentages | Compound interest |

30 | Standard form | Scientific notation with larger numbers |

31 | Standard form | Scientific notation with small numbers |

32 | Standard form | Changing scientific notation to numerals |

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

34 | Multiples and factors | Highest common factor. |

35 | Multiples and factors | Factors by grouping. |

36 | Speed | Average speed |

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

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

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

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

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

42 | Indices | Negative Indices |

43 | Indices | Fractional indices |

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

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

46 | Problem solving | Larger areas: square metre, hectare, square kilometre. |

47 | Problem solving | Comparing and ordering areas. |

48 | Problem solving | Area of a trapezium. |

49 | Problem solving | Area of a rhombus. |

50 | Problem solving | Area of a circle. |

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

52 | Volume | Introduction to volume. using the cubic centimetre as a… |

53 | Volume | Using the cubic centimetre to measure volume. |

54 | Volume | Introducing the formula for volume. |

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

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

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

58 | Volume | Finding the volume of prisms |

59 | Problem solving | Problems with length. |

60 | Problem solving | Problems with mass. |

61 | Problem solving | Problems with area. |

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

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

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

65 | Angles | Adjacent angles |

66 | Angles | Complementary and supplementary angles |

67 | Angles | Vertically opposite angles |

68 | Angles | Angles at a Point. |

69 | Angles | Parallel Lines. |

70 | Angles | Additional questions involving parallel lines |

71 | Angles | Angle sum of a triangle |

72 | Angles | Exterior angle theorem |

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

74 | Angles | More difficult exercises involving parallel lines |

75 | Series and sequences | Further difficult exercises involving formal reasoning |

76 | Angles | Angles of regular polygons |

77 | Angles | Complementary angle results. |

78 | Angles | Bearings – the compass. |

79 | Triangles | Recognise and name triangles |

80 | Quadrilaterals | Midsegments of Triangles |

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

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

83 | Triangles | Spatial properties of quadrilaterals |

84 | Pythagoras | Find the hypotenuse |

85 | Pythagoras | Pythagorean triples |

86 | Pythagoras | Find the hypotenuse Part 2 |

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

88 | Pythagoras | Proofs of Pythagoras theorem |

89 | Construction | Geometric constructions |

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

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

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

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

94 | Construction | Constructions and loci – single condition |

95 | Construction | Constructions and loci – multiple conditions |

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

97 | Transformations | Transformations – reflections |

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

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

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

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

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

103 | Trigonometry | Trigonometric ratios. |

104 | Trigonometry | Using the calculator. |

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

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

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

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

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

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

111 | Series and sequences | General sequences. |

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

113 | Simplifying | Algebraic expressions. |

114 | Simplifying | Substitution into algebraic expressions. |

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

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

117 | Simplifying | Simplifying algebraic expressions: multiplication |

118 | Simplifying | Simplifying algebraic expressions: division |

119 | Simplifying | Expanding algebraic expressions: multiplication |

120 | Simplifying | Expanding algebraic expressions: negative multiplier |

121 | Simplifying | Expanding and simplifying algebraic expressions |

122 | Inequalities | Simplifying absolute values |

123 | Equations | Solving equations containing addition and subtraction |

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

125 | Equations | Solving two step equations |

126 | Equations | Solving equations containing binomial expressions |

127 | Equations | Equations involving grouping symbols. |

128 | Equations | Equations involving fractions. |

129 | Inequalities | Solving for the variable |

130 | Equations | Simultaneous equations |

131 | Equations | Elimination method |

132 | Equations | Elimination method part 2 |

133 | Equations | Applications of simultaneous equations |

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

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

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

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

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

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

140 | Inequalities | Solving Inequalities. |

141 | Inequalities | Inequalities on the number plane. |

142 | Inequalities | Solving and graphing inequalities |

143 | Scatter diagrams | The range. |

144 | Probability | The mode |

145 | Probability | The mean |

146 | Probability | The median |

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

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

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

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

151 | Pie charts | Bar Charts |

152 | Probability | Cumulative frequency |

153 | Scatter diagrams | Frequency histograms and polygons |

154 | Pie charts | Line graphs. |

155 | Pie charts | Pie and bar graphs. |

156 | Scatter diagrams | Scatter Diagrams |

157 | Scatter diagrams | Frequency distribution table |

158 | Scatter diagrams | Relative frequency |

159 | Probability | Probability of Simple Events |

160 | Probability | Rolling a pair of dice |

161 | Probability | Experimental probability |

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

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

164 | End of Course Assessment | End of Course Assessment |