Monty Hall's a Goat
by Ian Fisher
Every summer we update the worksheets and website with the work we have done over the past 12 months. This gives me time for reflection on the year and to look back at our achievements.
Writing for 10ticks is extremely rewarding; there are no constraints on what we do. We do it because we love it. We do it because we know it will make your life easier and motivate your students into finding mathematics fascinating. We can put time and effort into crafting a successful worksheet for the benefit of time starved teachers. In this blog I will look over some of the worksheet ideas produced for our new edition.
As a quick digression, the worksheet seems to have become an unpopular bedfellow for the teacher over the last decade. It has been given bad press because of the hastily prepared sheet of work, possibly hand written, with reams of questions and no progression, photocopied and given out to a class as a last minute homework, and just for the sake of tick-boxing the homework given box. I have heard of head teachers banning the use of worksheets in their schools. Should we now call our worksheets a digital maths resource, so that we are not tagged with the label? This short-sightedness is the equivalent of saying, “ I have seen a bad text book, so we will not use text books in our school”. Ludicrous.
Yes, I believe practice is an important element to learning. Our consolidation worksheets have sets of questions to allow time for this, along with structured, graduated progressions. More able pupils may work on odd numbers, or down columns, and those that need consolidation can work through more. The worksheets have been likened to a lesson plan in their progression. Our texts are successful because of this .... but there is much, much more to 10ticks than just consolidation questions. Variety is just as important. That is why we have games, puzzles, investigations, Action Maths, Calculated Colourings etc, all linked to specific mathematical concepts, so the teacher can focus on delivering a skill in a variety of ways. It has been shown that this wide variety of delivery mechanisms actually helps teacher development by thinking about pedagogy. I could go on, but a short digression has now become a long rant, so enough.
This year we have added over 270 worksheets to the 10ticks collection and I want to highlight one or two of my favourites. We do have a new Search tool that will help you navigate through this vast, rich resource.
As a side note, for those of you referencing 10ticks into schemes of work, use the comment field, as this doesn’t change from year to year. Page numbers and Years will, depending on the whim of the government at the time.
Frequency Trees (search M16.162 then onwards) is a brand new area. We have developed this from scratch. It is a graduated series of worksheets, linking frequency trees with two way tables and probabilities. The progressions are easy to follow, allowing for instant student success.
The Monty Hall Problem (search M16.113) is a very famous problem that can be solved easily by running a trial with the whole class. Will you win a car or a goat?
Roman Numeral Matchstick Puzzles (search M16.64) is a delightful page of puzzles that involve moving matchsticks around to solve questions in Roman numerals format. Great fun.
The last question of the sheet, Sec D 6)., is obviously a trick question, which can be answered gleefully by spinning the sheet around 180 degrees.
BIDMAS Snake (search M16.78) is a question that hit the news this year. It is a question that was given to third graders (8 year olds) in Bao Loc, Vietnam. See how your class fares.
There is alot of introductory algebra in the update. Stars and Circles (Algebra) (search M16.253) is a typical start to algebra, replacing a star and circle with numbers to solve the questions. Also look at Balancing Shapes (search M16.86) for a starter to solving equations. Algebraic Expression Diagrams (search M16.95) is a visualisation method for algebra. It is consistent with the way multiplication is taught using grids.
Algebraic Pyramids (starting Algebra) (search M16.255) looks at number pyramids, and finding generalisations for different pyramid sizes. We do this by using polygon shapes, rather than numbers, to see how many of each polygon appear in the top block. You should find a generalisation for the 3-block base, 4-block base and 5-block base, before guessing what it will be for a 6-block base. To find a link between the generalisations it may be wise to cover Pascal’s triangle immediately before this topic.
OK, I could go on, but won’t. There is a plethora of enrichment material this year: puzzles, games and investigations, so go and explore these new materials. My apologies to those worksheets that didn’t get a mention by name - I hope you weren’t offended.