Bespoke is the national newsletter from the central Maths Hub team.
This website has 3 different puzzle styles on it- each is broken down into Explorer, Puzzler and Master.
The Mobiles puzzles focus on algebraic thinking and reasoning within a visually attractive and engaging format. The problems do get quite complex, but students can illustrate their thinking on screen by drawing and making notes with the pen function.
The Who Am I puzzles focus on properties of number, ranging from odd and even numbers through to harder divisibility laws, squares and cubes. These puzzles are currently under construction.
The Mystery Grid starts off basically as a Sudoku puzzle, although their complexity increases, with the introduction of inequalities, larger grids and in the Master Section, complex grids involving all 4 operatons. It is a real challenge for students with limited reasoning skills, but it is also very engaging- a Year 7 bottom set student went home and played on it for two hours after we did it in lesson!
This can be used by teachers and students to generate questions on a variety of topics, split into Bronze, Silver and Gold difficulty. It is particularly useful for those students who like to do lots of independent practice and learning at home to follow up what they have done in lessons.
This very useful website has fully interactive algebra tiles, bar modelling, Cuisenaire Rods and Dienes blocks, which are great for whole class discussions or independent computer work. Colours, lengths and number of ‘parts’ can all be edited. The website also has differentiated questions and AFL check-up for use in the classroom.
YouTube- Essence of Calculus Playlist (search on Youtube ‘Essence of Calculus Playlist’)
This playlist has videos that cover everything from the paradox of the derivative through to higher order derivatives and Taylor Series. Students could watch it before a lesson on a certain topic, as they explain topics in a thought-provoking way. As differentiation from first principles begins to appear on the new A-Level, this level of understanding and thought process has never been more important. Most videos are 15-20 minutes long
Videos in order:
1. The Essence of Calculus
2. The paradox of the derivative
3. Derivative formulae through geometry
4. Visualising the chain rule and the product rule
5. Derivatives of exponentials
6. Implicit differentiation- what’s going on here
8. Integration and the Fundamental Theorem of Calculus
9. What does area have to do with slope?
10. Higher order derivatives
11. Taylor Series
Sheffield Royal Institution Mathematics Masterclasses
for Year 9 students in 2018
The Royal Institution is pleased to announce the running of the 2017 Sheffield Secondary Mathematics Masterclasses. Schools are invited to nominate up to four students to attend the Saturday morning Royal Institution Mathematics Masterclasses at Sheffield Hallam University and the University of Sheffield. The series will run from Saturday 12 May until Saturday 30 June (excluding 26 May and 2 June); therefore we need to ask for your nominations before Friday 4 May 2018
RI Masterclasses are run in series of six Saturday morning workshops designed to inspire and engage young people to think more deeply about the wonders and applications of mathematics, giving them the chance to explore a range of topics beyond the school curriculum. Students nominated should be interested and enthusiastic about mathematics, as well as being from among the most mathematically able students currently in Year 9 at your school (though not necessarily as measured by exam success). Masterclasses are free for the students.
You can find at the bootm of this webpage an information sheet about the classes for students and parents, a student details form and a nomination form. The nomination procedure is:
- Duplicate the information for parents sheet and student details form to give to your chosen students;
- Collect their completed student details forms;
- Complete your nomination form, with students in priority order (if more students are nominated than can be accommodated, we will involve as many schools as possible, allocating places in order of priority);
- Return the nomination form and scanned copies of the completed student details forms for all nominated students via email to the address below.
Please note that students are expected to attend the entire series of six sessions. If your chosen student(s) cannot commit to the series, please offer the opportunity to other students instead. The demand for places is usually far greater than the number available, so please place your nominations in priority order. Student absence without a justifiable excuse may result in the loss of their place to a student on the waiting list.
To confirm the place I must receive scanned signed copy of the student details forms for all nominated students.
If you cannot scan the forms, please return the nomination form by post. The postal address is: Heather Holt, UK Student Recruitment, Surrey 5401, Sheffield Hallam University, Howard Street, Sheffield, S1 1WB. If you wish to get parents to send their forms directly to me then please pass on my details.
Teachers are not required to attend the Masterclasses with their students but we would be grateful if a teacher from each nominating school could come along and help at one or two sessions – please see overleaf for more details. If you or one of your colleagues would be able to come and support one of more of the workshops, please let me know.
I look forward to receiving your completed nomination and student forms.
2018 Sheffield Royal Institution Mathematics Masterclasses
Information for teachers
About the Masterclasses
Royal Institution Mathematics Masterclasses are designed to encourage, inspire and engage young people in the art and practice of mathematics. The highly interactive sessions introduce students to aspects or applications of maths which may not usually be covered in the school curriculum, and open young people’s eyes to the excitement, beauty and real-world value of mathematics.
Where possible, every school in and around Sheffield will be asked to nominate a few students to attend the whole Masterclass series – this is six Saturday morning sessions. Though every effort is made to accommodate all student nominations, the series is likely to be over-subscribed so not all nominated students will gain a place.
Who to nominate
The classes are designed to highlight the variety of applications of mathematics; they are hands-on workshops with real theoretical depth, allowing students to explore the mathematics within each topic. Participants need enthusiasm and persistence as well as mathematical ability; it will be a rare student who understands all the material completely at a first hearing and participants will need a determination to explore.
We ask schools to nominate a few of their brightest and most enthusiastic students to attend the Masterclasses. These will not necessarily be the students who do best at exams – these will be the students who are always willing to question and want to explore and understand things in more detail. Whilst we aim to establish an enjoyable working atmosphere, the students who derive the greatest benefit are those who are most attentive and hard working.
Saturday 12 May – Sheffield Hallam University, Owen Building
Saturday 19 May – Sheffield Hallam University, Owen Building
Break for Half Term
Saturday 9 June - University of Sheffield, Hicks Building
Saturday 16 June – University of Sheffield, Hicks Building
Saturday 23 June – Sheffield Hallam University, Owen Building
Saturday 30 June – University of Sheffield, Hicks Building
The Masterclasses will run from 10am until 12:30pm, starting promptly. There will be a short break during the session, and students are asked to bring a drink and a small snack.
We welcome teacher helpers to give assistance during the Masterclass sessions. Helpers support the students with activities and may be able to pick up ideas from the Masterclass for use in their own teaching. Please let us know (on the nomination form) the names and contact details of any of your staff who would like to help in this way.
The information on the student details form will enable us to contact them if they have been successful in gaining a place on the series. We will ask them to complete an additional details form online to ensure we have all the information we need to run the Masterclasses effectively and safely. We must have parental consent in order to contact them and for the students to attend the series. The consent statement on the form also enables you to pass the student’s details to us.
Students will be notified if they have a place on the Masterclass series and will be expected to attend every session. We will also email you to let you know which of your students have gained a place, and will ask you to please ensure the students and their parents/guardians complete the online registration.
Parents are asked to let us know if a session has to be missed for any reason - failure to do so may result in the loss of place in favour of a student on the waiting list. Some students may have a prior commitment on one of the Saturdays – if we are informed of this it will not be a problem to accept them, however if they are due to miss more than one session we would ask you to offer the place to a different student.
Operational Research (O.R.) is the science of better decision making.
O.R. enables individuals and organisations to clarify problems, define courses of action, improve operations and make informed decisions through analytics.
and so much more ..
Ideas that focus on using technology to support looking at different mathematical structures, to support or reveal a deeper understanding..
The resources described by Pete Sides at the White Rose Maths Hub conference on bar modelling can be found here.
Power point presentation.
PDF of presentation at White Rose Bar Model conference, Salford (Feb 2017).
10 Bar random sums <10 illustrated on a bar model (any part of the number sentence can be hidden)
NB comparative bars & subtraction are also available on the same file
Fraction as a number a mixture of random and self-input fractions showing equivalence in different denominations and mixed number & vulgar fractions
NB- Values of parts or ratios can be selected to be shown or not
10 Bar interactive model of x+y=10 as a bar and as a line graph
x-squared interactive model of y=x2 shown as bars and as a point on graph
Circle thoerems: a series of simple geogebra files to allow interactive investigation of theorems
Representing the structure behind mathematics can help develop an understanding of arithmetic and/or algebra. This can also be linked with multiple representations of a concept as each of the illustrations below can be shown in alternative ways including number lines, sets & arrays of counters amongst others.
These are intended to provoke discussion amongst colleagues rather than to be used without thought or reflection with learners but SYMH would be happy to hear of colleagues' thoughts on these and if they have used any or similar models with learners to good effect.
You can also find here a series of resources that can be used with colleagues to discuss conceptual development and structures underlying some of the common techniques taught in number and algebra.
Click on each below link to download PDF
The UKMT Individual Maths Challenges are lively, intriguing multiple choice question papers, which are designed to stimulate interest in maths in large numbers of pupils. The three levels cover the secondary school range 11-18 and together they attract over 600,000 entries from over 4,000 schools and colleges. Link to official website
The Junior and Intermediate Challenges are aimed at pupils in the relevant year groups. The Junior challenge is for pupils at year 8 (England) or below and the intermediate challenge is for year 11 and below. The Senior Challenge is aimed at pupils aged 16-19 studying maths and not yet at University.
The Maths Challenge question papers are taken in school on the date shown above and returned to the UKMT for marking. The Senior Challenge takes 90 minutes and the Intermediate and Junior Challenges are an hour long.
The papers contain 25 multiple choice questions. Of these, the first 15 are more accessible whilst the final 10 will provide more food for thought. Gold, silver and bronze certificates are awarded to 40% of participants nationally in the Junior and Intermediate Challenges, and 60% of participants nationally in the Senior Challenge. The most successful participants at each level are invited to enter follow-on rounds; Kangaroos (multiple choice questions) or Olympiads requiring full written answers.
Locally some school integrate past questions into their lessons or homework to challenge pupils and prepare them for the style of questions. Below are links to PPTs containing some Junior level questions from previous years. They have been organise loosely into topic areas but often UKMT questions challenge pupils to consider maths in a non-standard way.
Just a few images that some may find helpful when describing calculations with negatives
Multiplying involves the concept of an "enlargement" operation.
Then the distinction between the multiplying effect of 1 (stays the same) and -1 (flips it over)
Which also works on negatives
...and so we can multiply by any sized positive or negative number.
Now I know I haven't included "taking away" negatives but my explanation takes more than one image to explain - but consider 5 - (-2). Since we know that 5 = 7-2, then 5 - (-2) can be written as (7-2) - (-2). Using this argument alongside appropriate diagrams with learners has proven to be succesful.