# Secondary Maths Collection – Alan Catley’s Tarsias

Resources | Published 4 August, 2011

#### TES Secondary maths resource collections

Collection Author: Craig Barton - Maths AST and creator of www.mrbartonmaths.com (TES Name: mrbartonmaths)

As well as being a fantastic Autograph Trainer, Alan has also become a dab-hand with Tarsia over the last few years. What I really like about Alan’s Tarsia activities is the amount of thought that goes into their design to ensure that the students get the most out of them, often combining them with images and Autograph files. Alan has kindly donated some of his favourite Tarsia activities here, and written about how they might be used in the classroom.

“I was introduced to ‘jigsaw’ activities through the ” Logarithms” activity which appeared in the Standards Unit ‘box’ called Improving Learning in Mathematics (long before Tarsia was available!). This jigsaw activity proved highly successful in creating discussion between students despite the fact that it was basically a text book exercise in a different format. Following this success with this ‘consolidation’ Tarsia other approaches were developed and trialled with students. The really important issue with Tarsia is for the teacher to think very carefully about why an activity has been created and how it is to be used. Here are a few specific examples”

Fractional indices

• This is designed for use when the focus of a lesson is to introduce the concept of the logarithm. The idea is to re-visit negative and fractional indices by asking students to solve the puzzle, discussing issues as they arise. Once completed the concept of the logarithm can be introduced and students can be asked to re-write each match in the puzzle as a log expression.

Lines + circles (images)

• This activity involving images of lines intersecting circles and corresponding pairs of simultaneous equations can be used in a variety of ways. One example is to introduce the basic concept of the equation of a circle with the assumption that the linear equation is fully understood! In my experience it may well result in a quick revision of y=mx+c ! (I have an interactive Powerpoint for this which gets the whole class engaged in an arm waving ‘graphaerobics’ session). The Tarsia can be extended to solving to find intersection points using Algebra … confirmed by checking on Autograph). Please note that idea for this Tarsia came from just one of the many electronic activities available from Bring on the Maths – ideally this is projected to the front board whilst the Tarsia challenge is on the desks!)

• Further use of images showing graphs of functions plus their corresponding gradient graphs. These are matched to the function but the student then has to provide the derivative. Careful choice of functions here – lots very similar to ensure that the student has to think rather than be able to spot by guessing if the numbers used were very different. Also some use dy/dx and others f’(x) notation.

C1 exam revision (Tang + Norm)

• A specific topic that traditionally causes problems so lots of past exam questions turned into a Tarsia ‘follow me’ activity.

Factor Theorem

• A great way of introducing the Factor Theorem but it took a long time to ensure that this is a unique solution! i.e. (x-1) is only a factor of one of the given functions etc. A wonderful group activity used in conjunction with a paused slow plot of y = 2x³ + x² – 4x – 3 on Autograph (at approx x = -2) “where does this graph cut the x-axis?” etc. The group will have to share the work out which means they discuss and share each other’s answers but the more they do the easier the puzzle gets. The ‘Start’ is a trivial one deliberately!

Binomial Expansions

• Basically a series of past exam questions but the first time this was used I gave all three terms. This was a disaster as the students were able to spot the matches by only finding the first two terms when the most difficult job is finding the third term. Changed to just giving the third term and it became a huge success as a consolidation activity.

Iterations - algebra
Iterations – Roots between
Iterations – Find x

• These three activities basically cover most of the skills required to answer questions on this topic. Credit for these ideas goes to the Bring on the Maths activities on this topic but most of the questions in the three activities come from past papers. Perhaps a bit of Tarsia ‘overkill’ on one topic but it works really well.

Partial Fractions

• The idea here is to introduce the concept of algebraic partial fraction by first of splitting the fraction 3/28 into its partial fractions but note that there are lots of wrong answers (all ‘feasible’ initially) that have been placed around the edge of the puzzle. Once the correct numerical answer has been found the concept of only the simplest algebraic partial fraction can be introduced. They should then be able to find a few in the puzzle and will hopefully get inquisitive about the other more difficult cases. This can then lead on to discussion about how to find the A, B etc. values (algebraically versus constant controller on Autograph?!)

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