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### 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.
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
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.
230 Roots Completing the square
231 Roots Solving quadratic equations by completing the square
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
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