A selection of questions to practise converting between equivalent fractions that include opportunities for some problem solving, the use of a variety of mathematical terminology and some deeper thinking about the topic.
Some questions to delve a little deeper into the understanding of probability and tree diagrams. The first two are fairly standard (I)GCSE fare but subsequent questions become more complex with questions 5 and 6 requiring the solution of quadratic equations if an algebraic approach is used. Suitable for KS4 students who are ready for something a little more challenging than the standard GCSE style question. Answers included.
A set of questions to practise the concept of y=mx + c including finding equations of lines with various clues (including just two points on the line). Simple start but some harder questions later. Also some questions to provoke deeper thinking towards the end. I like to ask the class to come up with their own 'True, False, Sometimes True' style questions as a useful and challenging extension. This can result in some excellent discussion amongst the class. No knowledge of perpendicular lines needed.
A worksheet/activity in which the pupils begin to use long division to find simple recurring decimals from fractions. The questions develop in complexity and challenge the pupil to examine the patterns in the decimal representations of the sevenths. The final task is to categorize denominators to try to discover a rule for which denominators produce terminating decimals and which produce recurring decimals.
An attempt to make algebraic substitution a little more interesting! Students must use the formulae to crack the code and then solve the anagrams. I wrote this for Key Stage 3 but it would be well suited for KS4 too. Stress the importance of careful calculation - one error early on and everything could be wrong! Collaboration between students and checking/discussion of answers might be useful as they work through this. Answers included.
A worksheet designed to get pupils thinking about percentage problems. After a simple start the questions become more difficult and often involve several steps. Some questions towards the end start to require an understanding of the 'reverse percentage' style of question. Answers included. Suitable for able KS3 students and GCSE .
A set of 12 questions that allow students to explore this topic in more depth. It includes some more challenging styles of questions that require students to apply and develop problem-solving skills. Ideal for higher achieving students that are ready for some extension following an introduction to this topic. Answers are included.
A selection of questions aimed at identifying and finding perpendicular lines. The questions include finding points of intersection and areas of triangles formed and lead on to some more complex problems intended to foster a deeper understanding of the topic. Appropriate for able KS4 students learning this for the first time or, possibly, a revision resource for A-level.
An attempt to make algebraic substitution a little more interesting! This version includes use of negative and decimal values. Students must use the formulae to crack the code and then solve the anagrams. I wrote this for Key Stage 3 but it would be well suited for KS4 too. Stress the importance of careful calculation - one error early on and everything could be wrong! Collaboration between students and checking/discussion of answers might be useful as they work through this. Answers included.
A selection of questions which involve the student finding the equations of quadratic functions given various clues. The questions get harder as the student progresses leading to finding cubic functions and requiring the use of systems of equations (in 2, 3 and 4 variables). Use of graphic calculators or similar applications is encouraged to check answers. Suitable for able GCSE/Additional Maths students or Sixth Form maths students.
A short collection of questions to practise and reinforce calculation of means and medians from lists of data and frequency distributions. I've also included problems to provoke some deeper thinking about these measures and provide a little more challenge. Nothing too complicated but it might be useful for a summary or revision purposes.
Useful for Additional Maths or Sixth Form students to practise using the unit circle to find trig ratios of various angles in a practical manner. The sheet also includes opportunities to convert between radians and degrees and to recall exact values of trig ratios.
Students are asked to find the sums of convergent geometric series (although this term is not used in the questions). The aim is that, by investigating what happens to the sum as increasing numbers of terms are added, the students can discover the limit for the sum (again, this terminology is not used). I wrote it with able Year 7 pupils in mind to extend the topic of fractions and encourage investigatory approaches to learning but it would be appropriate for many KS3 or KS4 pupils (and could be used as an investigation to introduce convergent geometric series in KS5). Some questions involve the use of algebra for generalising and, while some students may have limited experience with this, it may serve as a useful introduction to the use of algebra to describe patterns. I have tried to push the need for clear record-keeping and observation and asked the students to comment on any interesting patterns or surprises.
A worksheet of 5 pages which takes student through the steps of solving linear simultaneous equations by elimination. The first 4 pairs of equations have detailed steps and hints. After that there are further problems (some worded) with no hints for additional practice. There are also two extension questions asking students to consider what is happening when faced with a pair of equations with an infinite number of solutions and a pair with no solution. Answers are included. I used this for the second lesson with a Year 8 class after I had demonstrated the elimination method in the first lesson but it became clear that some students were not sure about the process.
A set of tasks which lead the student through finding the height then area of an isosceles triangle, onto the areas of a variety of regular polygons and ultimately deriving a formula for this. Knowledge of right-angled triangle trigonometry required. It's a useful extension for this topic and requires good algebra manipulation skills. I have tried to remove the scaffolding as the tasks progress and have included opportunities for thinking about the connections between circles and regular polygons with large numbers of sides. Suitable as an extension activity for very able Year 9 or able GCSE students.
This series of 8 steps starts by leading students to the discovery of how to find a linear rule for a sequence. This is then developed to second, third and fourth order rules. As the steps progress I have removed more and more scaffolding to enable the students room to discover and think. The final three steps challenge the students to discover the formulae for the sums of the first n integers, square numbers and cube numbers. A knowledge of simultaneous equations in two variables is required, this needs to be extended into three and perhaps four if students progress. I have used it with great success with able Year 10 students. It encouraged enquiry and gave the class lots of good algebra practice.
Four tasks which require students to sketch straight lines, use pairs of simultaneous equations to find the points of intersection and then calculate the area of the triangle formed. Good practice and extension of these topics for an able Year 9 group or GCSE class. Presented without too much scaffolding but with an optional hint for question 4 which requires more thought and care. Could be used as an extension or a homework assignment. Possible extensions include 4 lines intersecting to form an irregular quadrilateral. Answers included.
