by Ian Fisher
Every summer I like to add my thoughts for the year and to mention some of my favourite worksheets that have been added to the ever growing 10ticks collection. Hundreds of worksheets have been added this year, and picking out my favourites is like picking my favourite child, sometimes not that difficult a task!
Our aim is to help teachers, by creating a one-stop shop for you. Instead of having to spend hours trawling around the internet, wasting your valuable time, everything you need is here, in one place. With 10ticks you also know that you can rely on the quality of the materials.
For the last few years mathematics educationalists have been focused on the Mastery approach and problem solving. Many people think of 10ticks as being simply consolidation worksheets (which is a large part of the Mastery approach!). I believe that this outdated thinking doesn’t do 10ticks justice. You need to explore 10ticks a little more, and seek out investigations/problems solving/puzzles etc to see how they can deliver lessons (and Mastery) for you. Subscribers should also look out for Worksheet of the Week that is sent out by email every Monday. Hopefully you will find some great ideas to use with your students.
Secondary school teachers should look at our resources from Year 2 onwards, as much of them could be appropriate for your lower ability KS3 students. Our materials are mapped to the ambitious primary National Curriculum, Reception to Year 6. The remaining materials are grouped by year for secondary, Year 7 to Year 11. To make this easier to understand for GCSE students, Foundation Tier ends with Year 9 and the extra materials needed for the Higher Tier are in Years 10 and 11.
So Pop Pickers, here is a countdown of my top 10 favourite resources added this summer:
Number 10Paper Chain Hoops (Multiplication 11 and 12) 1
This is used with Paper Chain Hoops (Multiplication 11 and 12) 2. Students can colour the paper chain links or you can print them on coloured paper. If printed on different coloured paper, mix and match the links to make a more brightly coloured paper chain. Find the next paper chain link by finding the answer to the multiplication at the end of another link.
There are many other paper chain sheets. Search ‘paper chain’ to find other examples.
Target Year 4
This worksheet features the rewriting of calculations so they are in the form 2n. These emphasise the rules of indices that should already be known. Students finish by recording these laws, using information from the calculations they have rewritten, along with any previous knowledge.
Target Year 10
This worksheet, along with Spidering Substitutions 2, looks at substituting in to quite complex equations. The equations are built along pathways of smaller equations, so students can see the BIDMAS element of the substitution. In Substitution Tables the pathways are replaced by tables, and fractional and negative numbers are used in the substitutions.
Target Year 7
A series of worksheets that focuses on areas of circles/rings in terms of π starting with Concentric Circles and Shading Concentric Circles. It progresses to thirds and quarters of circles, and to finding equivalent areas with Concentric Circle Parts and Matching Concentric Circle Areas. The final sheet, Archery Targets, investigates the areas of different archery targets, as well as redesigning the target as a square with same area as the circle.
Target Year 9
The worksheet looks at zooming in on a number line. The number line starts between two consecutive whole numbers, then zooms in between two tenths. The tenths’ number line is shown below the first number line. It is then zoomed in again, to a new number line, showing hundredths. A number (thousandths) marked on this third number line has to be identified.
The Zoom Out (Thousandths) worksheet has a similar layout. Here the information given is thousandths, and students work outwards to find the missing information. Students should then make their own sets of questions with Make Your Own Zoom (Thousandths).
There are Zoom In and Zoom out cards for tenths and hundredths. Use the search facility to find these.
Target Year 5
Finding the perimeters and areas will involve Pythagoras and trigonometry, as well as the traditional perimeter and area formulae. On each of the two blank cards students have to draw a shape that, when ordered, become the middle perimeter and middle area. This is deceptively difficult, as the creation of each card affects the other, in terms of ordering. It is a great way to get students revising perimeter and area topics. One answer is given, but many are possible. Get students to check each other’s...again reinforcing the topic.
Target Year 10
Two squares are divided in different ways. What fraction of the original square are the parts? What is this as a percentage of the original square? Students will start exploring fraction/percentage equivalents as well as special awareness, such as what is half of a quarter? This can be explored further, by students making their own divisions using Splitting a Square (Make Your Own).
Target Year 6 or Year 7
This is a problem solving exercise, involving ordering groups of objects by sharing apples into boxes. Cut-outs are provided so that pupils can do the problem physically and record their answers. Some pupils may attempt this without the cut-outs. What are the constraints that having greatest to least put on the answers? Hint: Why isn’t 13, 1, 1 an answer? Once the rules are clear off you go! There are 12 solutions. You may want to challenge some pupils to find them all.
Target Year Reception or Year 1
The first of this set of worksheets is a made up number system using random symbols. Students should recognise the format of the numbering to rebuild the 100 grid.
This is a fantastic set of worksheets, featuring different number systems. Many real number systems are built in the same way, but use different symbols.
Hundred Square (Eastern Arabic), Hundred Square (Bengali), Hundred Square (Perso-Arabic), Hundred Square (Lao) use one system and Hundred Square (Chinese) and Hundred Square (Malayalam) use the other system. Look at other number systems, such as Suzhou numerals. How do they fit in? What about Devanagari, Gujarati, Bengali, Oriya, Telugu, Tamil, Burmese or Thai?
The Muddled Numbers worksheet looks at different scripts. Which is which, and what do they represent?
Target Year 7
Ok, so the Winter Olympics take place every 4 years, but you can still use this activity annually in the curling season. Here are two different ways of working with the equation of a circle.
In the curling question, with the centre of the concentric circles being the origin, find the equation of each of the rings. The origin is then moved about, so how does the equation change?
In the Olympic rings question, students construct three of the rings, given their equations. They then have to draw the missing two rings and find their equations.
Target Year 11
I hope you enjoy using the resources with your classes as much as we have enjoyed creating them. If you have ideas that you would like us to convert into a worksheet, please do email us and let us know.
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....
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