Tag Archives: Statistics

5 Resources for Maths GCSE(9-1)

Hello and welcome to the Transum Mathematics newsletter for February 2017. It is being written a little earlier than normal to make up for the fact that there was no January newsletter and that I will be travelling later in the month at the time when I would otherwise be writing this.

This month’s puzzle is about a restrained flea that jumps one foot at a time either north, south, east or west. At how many different places could he end up after 8 jumps?

Flea

While you think about that I would like to tell you of five resources on the Transum website that have been updated recently. Although they are perfect for the UK’s GCSE exam preparation they could also be used in different ways for younger learners.

  1. Weekly Workouts. These question papers (5 more have just been added) are designed for students on the Mathematics GCSE(9-1) Foundation level courses who are hoping to achieve one of the higher grades available. Each Weekly Workout contains 7 exam-style questions. The first six can be answered online but the seventh requires the student to draw something that needs the teacher to check. Each Workout can also be printed onto one A4 page.
  2. Practice Papers. These printable papers are designed to challenge students on the Mathematics GCSE(9-1) Higher level courses. Each question is similar to a question on one of the specimen papers produced by the exam boards for the 2017 exams. Full worked solutions are available for each question for Transum subscribers.
  3. Revision Tips. This is a page of suggestions and links to resources for anyone preparing for a mathematics exam. There are links to self-marking exercises on all the basic school mathematics concepts along with puzzles, games and investigations all designed to support revision.
  4. Syllabus Checklists. This part of the Transum Mathematics website contains a growing list of objective checklists for various common mathematics exams. Students can go through each objective and classify them as easy, OK or help! They can then print the objectives they have classified as requiring help and fill in the space for notes as their understanding develops.
  5. Exam Presentation. Save this for a week before the exam. It contains the tips and tricks that students might find useful when doing their last-minute preparation. You, as a subscriber, can download the PowerPoint version of the presentation so that it can be customised to suit your situation.

In addition to the items mentioned above, many other pages on the Transum Mathematics website have been updated or changed. A Starter called Tindice provides a quick, fun (when you know the answer) Starter to a busy Maths lesson but it can also be used to initiate an investigation into the sum and product of odd and even numbers.

I often help older students with their understanding of significance testing in statistics. In particular the chi-squared test is often clouded with strange precedents and terminology. A very short presentation called Significance has been developed to simplify the concept and to get the student to analyse the data provided by the Optical Illusions survey. As a subscriber you can see the results of the significance testing in real time. The students can use their GDCs to find the connections themselves. The presentation focusses on the big picture idea and leaves you as the teacher to fill in any gaps.

The Transum website was particularly busy in the weeks leading up to Christmas. Some of the ChristMaths activities had been updated and clearly people all over the world were enjoying them. If you missed out this year why don’t you send yourself a time-delated email (to arrive on the 1st December) reminding you of the URL. An email to yourself can be flagged as ‘Delay Delivery’ in many email programmes such as Outlook.

The answer to this month’s puzzle can be found by considering the following:

Think of the flea on a coordinate grid starting at the origin. If the flea only jumps in one direction it would end up at either (0,8), (8,0), (0,-8) or (-8,0).

Now consider the possible points in the first quadrant, (x,y) where x is the number of jumps east minus the number of jumps west and y is the number of jumps north minus the number of jumps south. It is probably a good idea to sketch these points on some graph paper and you will see the pattern created by the locations. Multiply the number of points in the first quadrant by four and add the ‘return-to-origin’ possibility to find the total.

The answer is 81 different places.

That’s all for now

John

P.S. If a got 50 pence for every time I failed a maths exam I’d have about £6.30 now.

7 New Resources for the Maths Classroom

Happy Christmas and welcome to the December 2016 edition of the Transum Mathematics newsletter. We will begin with the puzzle for this month: How many positive two-digit numbers are there whose square and cube both end in the same digit? The answer is at the end of this newsletter.

While you think about that, here are the seven new resources that have appeared on the Transum website since the last newsletter.

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  1. First Impressions

I was given the idea to create this fun data collecting application by Year 13 students working on projects including the chi-squared test. It was proving difficult and time consuming for them to collect their own data in sufficient quantities in order to meaningfully apply statistical tests. First Impressions asks the pupil for their initial perceptions of optical illusions. When the activity has been completed (it takes less than two minutes) the pupil is presented with the data collected from all of the other people who have also used this app. This data can then be used by the pupil for all sorts of graphs, charts and statistical analysis. Give it a go and share your ideas.

  1. Weekly Workout

With questions similar to those on the specimen papers produced by the exam boards for the forthcoming Maths CGSE(9-1), the Weekly Workouts provide half-hour revision papers for Foundation students aspiring to achieve the higher grades. The first six questions can be answered online just like the other Transum online exercises but the seventh question on each paper requires more drawing and is best done on paper with feedback from the teacher. The number of Weekly Workouts for Foundation level pupils is growing week by week. You have probably already seen the twenty Practice Papers for Higher students haven’t you?

  1. Brainbox

This number arranging puzzle was devised by Les Page and adapted as a Transum Mathematics interactive numeracy puzzle. There are twelve levels (and a few hidden bonus levels) arranged in increasing order of difficulty and there are efficient solving strategies that you will probably soon discover for yourself. Perfect for Year 5 pupils up to pensioners.

  1. Plinko Probability

This simulation describes the motion of a ball falling through a Quincunx (Galton Board) made out of pegs. In the intro tab, a ball has an equal probability of going to the left or right of the peg. The pupil can choose to send 1, 10 or all the balls though the board (up to a maximum of hundred) and watch how the balls fall into the different containers at the bottom of the board. A nice introduction to the normal distribution.

  1. Trigonometry Advanced

A self-marking exercise on the sine rule, cosine rule and the sine formula for finding the area of a triangle. The questions are carefully arranged in increasing order of difficulty preparing pupils for the linked exam-style questions.

  1. Triangle Solver

This new, powerful resource is a large triangle to project on to your whiteboard. Drag the vertices to make the triangle roughly the shape you want then type in three measurements, a mixture of sides and angles, then within the blink of an eye the other measurements magically appear. The triangle is solved!

This Solver is not only intended to be used with standard trigonometry or Pythagoras questions but also as a resource for students learning the basic construction skills with a rulers and pair of compasses. It also works well for a class practicing drawing angles using a protractor.

The teacher could manipulate the triangle to show a base of say 13cm. Either side of this base angles of 50° and 70° are shown. The class is then challenged to make an accurate drawing of the triangle and their accuracy can be measured against the actual values the Triangle Solver produces when everyone has finished their drawings.

Similarly a triangle with only the three sides given can be projected for a class practicing ruler and compass constructions. This time it is fun to compare the measured angles of the finished triangle with the ones the Triangle Solver calculates.

  1. ChristMaths Activities

Not strictly a new resource but certainly an updated one. Don’t be tempted to stray from Mathematics when planning those festive, end-of-term lessons when there are so many Yuletide treats in this collection.

The answer to this month’s puzzle is:

  • The nine two digit numbers that end in a zero;
  • The nine two digit numbers that end in a one;
  • The nine two digit numbers that end in a five;
  • The nine two digit numbers that end in a six;

These added together give a total of 36.

Enjoy the Christmas holiday and enjoy the ChristMaths activities,

John

P.S. Calendars, their days are numbered.