At a glance
The course in numbers
How to read it. One row is one 45-minute lesson; its pack holds the plan, worksheet and quiz. The week column counts 3 lessons a week until you change the control above; the sheet you download uses the same numbers. Each topic ends at an assessment point, its question bank, which you can assign in the app for a marked score. The learning intention is the first idea of each lesson in the students' own pages; the traps are the examiner traps those pages pre-empt.
The topics in syllabus order
Weeks 1 to 30Topic 1Number
Weeks 1 to 7| Week | Ref | Lesson | Learning intention |
|---|---|---|---|
| 1 | 1.1 | Types of number: primes, factors, multiples, rational and irrational | In the lab, pick two numbers and watch their multiples light up on the 1 to 100 grid; then switch to factors and step through the sieve until only the primes are left. |
| 1 | 1.2 | Sets, set notation and Venn diagrams | In the lab, set the universal set \(\xi = \{1, \dots, n\}\), choose a rule for A and for B, and watch each number drop into its region of the Venn diagram. |
| 1 | 1.3 | Squares, cubes and roots | In the lab, slide \(n\) and watch the square grow as \(n^{2}\) unit squares; then switch to roots, type a number and see which two squares it lies between. |
| 2 | 1.4 | Fractions, decimals and percentages | In the lab, set the numerator and the denominator and read the same value as a fraction in its simplest form, a decimal and a percentage. |
| 2 | 1.5 | Ordering quantities and inequality symbols | In the lab, enter each fraction as numerator and denominator and read off its decimal. |
| 2 | 1.6 | The four operations: fractions, negatives and order of operations | In the lab, set a starting number and a second number and step along the number line: adding a negative moves left, subtracting a negative moves right. |
| 3 | 1.7 | Indices: the laws of indices | In the lab, choose a base \(a\) and the powers \(m\) and \(n\), and watch the factors line up: multiplying joins the two strings of factors, dividing cancels them in pairs. |
| 3 | 1.8 | Standard form | Type a number into the lab and watch the decimal point hop until exactly one non-zero digit sits in front of it. |
| 3 | 1.9 | Rounding and estimation | In the lab, press Next number, choose decimal places, significant figures or a nearest power of ten, and decide which way it rounds before the lab shows you. |
| 4 | 1.10 | Limits of accuracy: upper and lower bounds | In the lab, set the rounded value and the accuracy, then drag the true value along the line. |
| 4 | 1.11 | Ratio and proportion | In the lab, choose Simplify and drag the sliders: the blocks regroup until no common factor is left. |
| 4 | 1.12 | Rates, average speed and best value | Open the lab on Average speed and change the distance and time sliders for each leg. |
| 5 | 1.13 | Percentages: change, reverse percentages | In the lab, choose Percentage of and drag the percentage slider along the double number line: the top shows the percentage, the bottom shows the amount. |
| 5 | 1.13 | Simple and compound interest | In the lab, choose Simple and compound and set the rate and number of years. |
| 5 | 1.14 | Using a calculator efficiently | A calculator follows the order of operations exactly. |
| 6 | 1.15 | Time: 12- and 24-hour clock, time calculations | Open the lab on 12 and 24 hour clock and drag the time round a full day. |
| 6 | 1.16 | Money and currency conversion | Bills, change and wages are a chain of simple steps. |
| 6 | 1.17 | Exponential growth and decay | Open the lab on Population growth, then Depreciation. |
| 7 | 1.18 | Surds: simplifying and rationalising | In the lab, choose Simplify and move the slider through numbers such as 20, 72 and 200. |
| 7 | Assessment point | Topic question bank, 114 multiple-choice questions: print or review, or assign in the app for a marked score. |
Examiner traps to pre-empt:
- 1 is not a prime number, and 2 is the only even prime.
- \(72 = 8 \times 9\) is true, but it is not a product of PRIMES: 8 and 9 both split further.
- Do not mix the rules.
Topic 2Algebra and graphs
Weeks 7 to 14| Week | Ref | Lesson | Learning intention |
|---|---|---|---|
| 7 | 2.1 | Algebraic notation and substitution | Open the lab on Substitution, pick a formula and drag the sliders for each letter. |
| 7 | 2.2 | Expanding brackets and simplifying | In the lab choose One bracket and set the number outside to a negative value, say \(-3\). |
| 8 | 2.2 | Factorising expressions | In the lab choose Common factor and press Next step to see the highest common factor of the numbers, then of each letter, come out in front. |
| 8 | 2.3 | Algebraic fractions | In the lab choose Cancel and press Next step. |
| 8 | 2.4 | Indices II: algebraic and fractional indices | In the lab pick a rule and move the sliders for \(m\) and \(n\). |
| 9 | 2.5 | Forming and solving linear equations | In the lab pick an equation and press Next step one move at a time. |
| 9 | 2.5 | Changing the subject of a formula | In the lab choose a formula and press Next step. |
| 9 | 2.5 | Simultaneous equations | In the lab choose Two lines and set the sliders to the equations \(2x + y = 7\) and \(x - y = 2\). |
| 10 | 2.5 | Solving quadratic equations | In the lab set \(a = 1\), \(b = -5\), \(c = 6\) and look at where the curve crosses the \(x\)-axis: at 2 and 3. |
| 10 | 2.2 | Completing the square | In the lab set \(b\) to 6 and press Make the square. |
| 10 | 2.6 | Linear inequalities and the number line | Set an inequality in the lab and watch the number line: the circle at each end fills in or empties as you switch between \(<\) and \(\le\). |
| 11 | 2.6 | Inequalities as regions on a graph | In the lab, type an inequality such as \(y < 2x + 1\). |
| 11 | 2.7 | Sequences and the nth term | In the lab, set a first term and a common difference and watch the terms build up as bars. |
| 11 | 2.7 | Quadratic, cubic and exponential sequences | In the lab, choose a quadratic sequence and watch the lab stack the first and second differences under the terms. |
| 12 | 2.8 | Direct and inverse proportion | In the lab, pick a type of proportion (\(y \propto x\), \(y \propto x^2\),...) and set \(k\). |
| 12 | 2.9 | Conversion, distance-time and speed-time graphs | In the lab's conversion tab, choose a pair of units (miles and kilometres, pounds and dollars, Celsius and Fahrenheit). |
| 12 | 2.10 | Graphs of functions: tables, plotting and tangents | In the lab, pick a function and fill the table one \(x\) at a time. |
| 13 | 2.10 | Solving equations graphically | Open the solving tab in the lab. |
| 13 | 2.11 | Sketching curves: roots, intercepts and turning points | In the lab's sketching tab, change the coefficients and watch the key features move: the intercepts, the line of symmetry and the turning point. |
| 13 | 2.12 | Differentiation: gradient functions | In the lab, drag P and Q onto the curve and read the gradient of the chord PQ. |
| 14 | 2.12 | Stationary points | In the lab's stationary points tab, slide the point along the curve and watch the tangent. |
| 14 | 2.13 | Functions: notation, inverse and composite | In the lab's functions tab, type inputs into the function machine and watch the mapping diagram fill in, each arrow joining an input to its output. |
| 14 | Assessment point | Topic question bank, 132 multiple-choice questions: print or review, or assign in the app for a marked score. |
Examiner traps to pre-empt:
- \(n(n + 1)\) is the product of two consecutive numbers, but not necessarily even ones.
- \(2x^{2}\) means \(2 \times x^{2}\), not \((2x)^{2}\).
- Money answers need two decimal places: $127.5 should be written $127.50.
Topic 3Coordinate geometry
Weeks 14 to 16| Week | Ref | Lesson | Learning intention |
|---|---|---|---|
| 14 | 3.2 | Coordinates and drawing linear graphs | In the lab, set the gradient to 2 and the intercept to \(-1\). |
| 15 | 3.3 | Gradient of a straight line | Drag the two points in the lab and watch the gradient triangle. |
| 15 | 3.4 | Length and midpoint of a line segment | In the lab, drag the end points and watch the right-angled triangle under the segment. |
| 15 | 3.5 | The equation of a straight line | In the lab, set \(m\) and \(c\) with the sliders. |
| 16 | 3.6 | Parallel lines | In the lab, drag the point that the second line must pass through. |
| 16 | 3.7 | Perpendicular lines and bisectors | In the lab, rotate the first line and watch the perpendicular line turn with it, always at \(90^\circ\). |
| 16 | Assessment point | Topic question bank, 36 multiple-choice questions: print or review, or assign in the app for a marked score. |
Examiner traps to pre-empt:
- Writing the coordinates the wrong way round. \((x, y)\) is always across first, then up: 'along the corridor, then up the stairs'. \((-1, 3)\) and \((3, -1)\) are in different quadrants.
- Sign slips with negative \(x\): \(-2 \times (-1)\) is \(+2\), not \(-2\).
- Mixing up \(x = 3\) and \(y = 3\).
Topic 4Geometry
Weeks 16 to 19| Week | Ref | Lesson | Learning intention |
|---|---|---|---|
| 16 | 4.1 | Geometrical terms: shapes, solids and nets | Open the lab and drag the arm of the angle slowly from 0° all the way round to 360°. |
| 17 | 4.2 | Ruler and compasses constructions | Every construction starts with accurate measuring. |
| 17 | 4.3 | Scale drawings and bearings | In the lab, choose a scale and draw the plan of a room. |
| 17 | 4.4 | Similar shapes | Use the lab to enlarge a shape by different scale factors. |
| 18 | 4.4 | Areas and volumes of similar shapes | In the lab, enlarge a solid and watch three readouts: length, surface area and volume. |
| 18 | 4.5 | Line and rotational symmetry | In the lab, place a mirror line on each shape and reflect it. |
| 18 | 4.6 | Angles: lines, parallel lines and triangles | In the angle facts tab, drag the lines and watch the angle readouts. |
| 19 | 4.6 | Angles in polygons | In the polygons tab, change the number of sides and watch the polygon split into triangles from one vertex. |
| 19 | 4.7 | Circle theorems I: semicircles and tangents | In the semicircle tab, drag point C around the circle. |
| 19 | 4.8 | Circle theorems II: centre, segments, cyclic quadrilaterals | In the angle-at-centre tab, drag C around the major arc and watch angle ACB stay at exactly half of angle AOB. |
| 19 | Assessment point | Topic question bank, 60 multiple-choice questions: print or review, or assign in the app for a marked score. |
Examiner traps to pre-empt:
- A reflex angle is NOT just a big obtuse angle. \(170^\circ\) is obtuse; anything over \(180^\circ\) is reflex.
- A kite's equal sides are next to each other (adjacent); a parallelogram's equal sides are opposite.
- Do not count the same edge twice.
Topic 5Mensuration
Weeks 20 to 21| Week | Ref | Lesson | Learning intention |
|---|---|---|---|
| 20 | 5.1 | Units of measure and conversions | In the lab, pick a quantity, type a value and switch between units. |
| 20 | 5.2 | Area and perimeter of 2D shapes | In the lab, change the size of the rectangle and watch the area and perimeter change. |
| 20 | 5.3 | Circles, arcs and sectors | In the lab, change the radius and press Roll it to see the circumference unroll into a straight line just over 3 diameters long. |
| 21 | 5.4 | Surface area and volume: prisms and cylinders | In the lab, slide the cutting plane along the prism: every slice has the same shape and area. |
| 21 | 5.4 | Surface area and volume: cones, pyramids and spheres | In the lab, press Pour three times: it takes exactly three full pyramids (or cones) to fill the prism (or cylinder) with the same base and height. |
| 21 | 5.5 | Compound shapes and parts of shapes | In the lab, build a compound shape and watch which edges the perimeter follows: only the outside ones. |
| 21 | Assessment point | Topic question bank, 36 multiple-choice questions: print or review, or assign in the app for a marked score. |
Examiner traps to pre-empt:
- Check the answer makes sense: 3.75 km is a long walk, so the number of metres must be LARGE (3750), not 0.003 75.
- \(1\text{ m}^2\) is NOT \(100\text{ cm}^2\).
- \(1\text{ m}^3\) is 1000 litres, not 100 and not 1 million.
Topic 6Trigonometry
Weeks 22 to 25| Week | Ref | Lesson | Learning intention |
|---|---|---|---|
| 22 | 6.1 | Pythagoras' theorem | In the lab, drag the corners of the right-angled triangle and watch the three squares. |
| 22 | 6.2 | Right-angled trigonometry: SOH CAH TOA | In the lab, pick an angle and watch the three sides relabel themselves as the angle moves to the other corner. |
| 22 | 6.2 | Elevation, depression and bearings | In the lab, walk the observer towards the tower and watch the angle of elevation grow. |
| 23 | 6.3 | Exact trigonometric values | In the lab, slide the angle to \(30^\circ\), \(45^\circ\) and \(60^\circ\) and compare each decimal with its exact form: \(0.7071\ldots\) is \(\dfrac{1}{\sqrt{2}}\) and \(0.8660\ldots\) is \(\dfrac{\sqrt{3}}{2}\). |
| 23 | 6.4 | Graphs of sine, cosine and tangent | In the lab, send the point round the unit circle and watch its height draw the sine graph and its horizontal position draw the cosine graph. |
| 23 | 6.4 | Solving trigonometric equations | In the lab, drag the horizontal line \(y = k\) up and down across the graph and watch the solutions move in pairs. |
| 24 | 6.5 | The sine rule | In the lab, change the angles of the triangle and watch the three ratios \(\dfrac{a}{\sin A}\), \(\dfrac{b}{\sin B}\), \(\dfrac{c}{\sin C}\). |
| 24 | 6.5 | The cosine rule | In the lab, set two sides and open or close the angle between them. |
| 24 | 6.5 | Area of a triangle: half ab sin C | In the lab, fix two sides and swing the angle between them. |
| 25 | 6.6 | Pythagoras and trigonometry in 3D | In the lab, rotate the cuboid and switch on the base diagonal, then the space diagonal. |
| 25 | Assessment point | Topic question bank, 60 multiple-choice questions: print or review, or assign in the app for a marked score. |
Examiner traps to pre-empt:
- Adding the squares when you need a shorter side.
- For the isosceles triangle, use HALF the base.
- Rounding too early.
Topic 7Transformations and vectors
Weeks 25 to 26| Week | Ref | Lesson | Learning intention |
|---|---|---|---|
| 25 | 7.1 | Reflection and rotation | In the lab, drag the mirror line to a vertical position such as \(x = 1\), then to a horizontal one such as \(y = -1\). |
| 25 | 7.1 | Enlargement and translation | In the lab, place the centre of enlargement and set the scale factor to 2, then to \(\frac{1}{2}\). |
| 26 | 7.2 | Vectors in two dimensions | In the lab, drag the head and the tail of the vector. |
| 26 | 7.3 | Magnitude of a vector | In the lab, drag the head of the vector and watch the right-angled triangle beneath it. |
| 26 | 7.4 | Vector geometry | In the lab, drag the points \(A\) and \(B\). |
| 26 | Assessment point | Topic question bank, 30 multiple-choice questions: print or review, or assign in the app for a marked score. |
Examiner traps to pre-empt:
- Mixing up \(x = k\) and \(y = k\).
- Turning the wrong way.
- Naming two transformations, such as 'a reflection and then a translation', or leaving out the centre or direction.
Topic 8Probability
Weeks 27 to 28| Week | Ref | Lesson | Learning intention |
|---|---|---|---|
| 27 | 8.1 | Introduction to probability | In the lab, choose how many counters of each colour go in the bag, then pick an event. |
| 27 | 8.2 | Relative and expected frequencies | In the lab, pick an outcome to count and add trials 1, 10, 100 or 1000 at a time. |
| 27 | 8.3 | Combined events: sample spaces and Venn diagrams | In the lab, choose two dice and the rule for combining them (add, multiply, difference), then pick an event. |
| 28 | 8.3 | Tree diagrams | In the lab, set up a bag of counters and build the tree one pick at a time. |
| 28 | 8.4 | Conditional probability | In the lab, pick a 'given that' condition and watch the table: everything outside the chosen row or column fades out. |
| 28 | Assessment point | Topic question bank, 30 multiple-choice questions: print or review, or assign in the app for a marked score. |
Examiner traps to pre-empt:
- A probability bigger than 1 or below 0 is always wrong.
- The rule \(1 - p\) only works for an event and its opposite.
- In a Venn diagram, "likes coffee" includes the overlap.
Topic 9Statistics
Weeks 28 to 30| Week | Ref | Lesson | Learning intention |
|---|---|---|---|
| 28 | 9.2 | Classifying and interpreting data | Open the lab and look at the frequency table: each value is listed once with how often it occurs. |
| 29 | 9.3 | Averages, range and interquartile range | In the lab, drag one dot far to the right and watch the four measures. |
| 29 | 9.3 | Averages from frequency tables | Open the lab's frequency table of goals scored. |
| 29 | 9.4 | Statistical charts and diagrams | In the lab's charts tab, change the numbers of each fruit and watch the bar chart, the pictogram and the pie chart all redraw from the same table. |
| 30 | 9.5 | Scatter diagrams and correlation | In the lab, pick a data set and drag any cross. |
| 30 | 9.6 | Cumulative frequency diagrams | In the lab, add up the frequencies as you go to fill the cumulative frequency column. |
| 30 | 9.7 | Histograms with unequal class widths | In the lab's histogram tab, tick 'show the mistake: height = frequency' and see how the wide 30 to 50 class towers over the others. |
| 30 | Assessment point | Topic question bank, 42 multiple-choice questions: print or review, or assign in the app for a marked score. |
Examiner traps to pre-empt:
- Always check that the frequencies add up to the total number of data values.
- Read the words after 'of'. 'What fraction of the girls...' divides by the girls' total, not by the grand total of 60.
- With times, a LOWER mean is better (faster).
Also for this course
Beyond the scheme
Lesson packs90 packs: plan, worksheet, quiz
Question bankBuild a test from every course
PlannerBlock out the term
Classes and gradebookAssign the banks, track everyone
Student syllabus pageIGCSE Maths 0580
Original work by the TheLucidSTEM team. Week numbers assume 3 lessons a week unless you change the control; the download carries the numbers shown.