# Pythagoras with mixed ability Year 9 class

Discussion in 'Mathematics' started by dan79, Jun 26, 2011.

1. ### dan79

Hello all,
I am new to this site so forgive me if this is posted in the wrong section.
I have just completed my maths pgce and have an interview next week with a lesson brief of teaching pythagoras to Year 9 mixed ability in a 25 minute lesson. I have only taught this topic as an introduction with higher ability Year 8 in the past. I was thinking of a lesson that involves pre-prepared triangles and sqaures that pupils have to piece together, rather like a jigsaw, then measure and record on a pre-prepared table. They then have to look for relationships between the areas of the squares and record. My main question is how best to differentiate this task for mixed ability? Also, could this lesson be perceived as not challenging enough for the higher ability pupils and if so how best to address this? Any ideas or comments gratefully accepted!
Dan

2. ### Betamale

Dan, this is the right place.
Ok the topic is ~ level 7 in the main so depending on what they call mixed ability many <u>may</u> struggle to access it fully and certainly will in such a short space of time
IMO:
Starter must establish 2 things
(i) Can pupils square and square root numbers without flapping
(ii) Can they recongise what RA triangle is and understand the names of sides even if it means you put the words on the board and they mathc them up (dont waste time on this)
Make this clear in a lesson plan as without it you may as well teach them bascket weaving in mandarin.
Main
Introduce the formulae and do the basic triples as a group (leaving some for the kids to do themselves) after this interactive session where you probe for conjectures.
Differentiation within this can either be
(i) Getting pupils to work with harder calculations
and/or
(ii) finding a shorter side without telling the higher ability kids and allowing them to find out what to do.
A series of 10 minutes of differentiated quetions on the board or a sheet with the levels of each will suffice.
Plenary
An example of which is wrong and why based on you showing examples 2/3 which are right and one wrong based on key learning points. (take an old exam paper and answer a couple well and one badly)
This is a very hard topic for many so clearly state in your planning that this forms part of a 3 or so hour plan as if you introduce too much you will lose them

3. ### Mathsteach2Established commenter

I am not a maths teacher but I have taught lots of maths - willing to be shot down by qualified maths teachers!

That seems an awful amount to cover in 25 minutes, Betamale. Let's make some assumptions, the group is 25 boys and girls who will mostly be more interested in each other than Pythagoras' Theorem. Small group work is essential with any mixed ability class, especially when you do not know them. I suggest five groups of five, boys and girls in every group.

As an NQT you should have elementary drama skills to get the class to arrange themselves into these groups, each group seated facing each other around a table. Provide each group with sets of shapes which will show Pythagoras by the addition of the respective areas of the shapes.

Each group elects a leader and a spokesperson. The spokesperson will describe to the whole class what happened in their group during the plenary.

Timing: `Introduction of self, Pythagoras (not in detail, top students should know it) and small group work tasks. (Elect leader, spokesperson, solve jigsaw, return classroom to the arrangement for plenary. Five minutes.

Arrange seating and small groups using elementary drama. Distribute jigsaws. Five minutes. (This could be shortened by having the seating arranged before the class enters, giving more time for group work and plenary.)

Small group work tasks. Ten minutes.

Plenary. One minute each group. HW: draw diagram of their jigsaw solution. Dismiss/tidy up the room depending on the students' next lesson.

Whew! I'm ready for a break myself!

The sets of shapes can all be identical for each group, or you could make them to be differentiated, i.e one set is harder to solve than another. The groups will not be differentiated (you do not know them) but a bright student leading his/her group may solve an easy set very quickly. If this happens, exchange that set with another group's set, giving the bright student's group a harder set. etc.etc. Have fun!

4. ### v.vijeyarasa

Hi Dan,
I like your suggestion of a table and I also like that the students discover the theorem for themselves rather than you just tell them the theorem. To avoid a lot of confusion, I advise you to have triangles that have integer side lengths. I would also include a non-right angled triangle so that the students can see if the theorem works also for non-right angled triangles. Your starter could be an exercise of say 3 - 4 questions:
1. 5^2
2. 6^2 + 8^2
3. squart root (6^2 + 8^2)
I suggest you use the letters a, b and c in your tables so that the students get used to these letters and also introduce the important words like hypotenuse.
For the more able students I suggest they need to find, without your assistance, one of the shorter sides when they are given the hypotenuse. This would be done after they could write down the theorem from their table of values and find the length of the hypotenuse given the 2 shorter sides.
I would also provide them with questions where the right angled triangle needs to be drawn in on the picture eg. a question where you have to find the perimeter of a trapezium and pythagoras' theorem is required to find the length of one of the sides or even a 3D Pythagoras' Theorem question like find the length of the longest pencil that will fit into a pencil case in the shape of a rectangular prism.
How long are your lessons? I hope this helps.

5. ### Betamale

Woeful on so many fronts its not even worth addressing each point in turn. Im sorry but this, IMO, is simply fabricated, dreadful and riddled with assumptions.

6. ### Mathsteach2Established commenter

Shoot first and ask questions afterwards - very helpful, Betamale, thank you!

Seriously though, I did acknowledge I was making some assumptions.

The make-up of the class, the ethos of the school/maths department (why do they have mixed ability maths groups in Y9?), the NQT is trained in elementary drama, top students already know Pythagoras, room furniture can be easliy arranged for small group work around a table, both boys and girls, many not really interested, the students are used to working in small groups, the NQT does not know the students to begin with. Are there any others?

I was trained in small group work ('Human Groups", Sprott) during my PGCE in 1965-6. I have used this pedagogical technique succesfully in my teaching for 40 years, science, mathematics, primary and infant. The jigsaw was used by one of our tutors during training. It is, of course, not the only technique I use.

I may not have successfully addressed the OP, that is to adequately challenge the more able in understanding and using Pythagoras' Theorem. OK, but my style is to always teach to the most able, when delivering new work. At any time I am able to stop the group work, draw the attention of the whole class and make another point, but only at the highest level.

Such presentations would not last more than five minutes each, and only use them if there are more students off-task than I can deal with by moving around, sometimes asking a student to exchange places with someone in another group, as I get to know them.

In any case, presentations from the front should never last more that 10 minutes at the most, even with the brightest in a mixed ability group. Get the students doing something, I was told in my PGCE.

If the school does not encourage small group work, then I would only use their school mathematics text book (if they have one, otherwise I would photocopy the relevent pages from my own), give a ten minute presentation to begin, then get them to work on their own in silence for the remaining 15 minutes, using the differentiated exercises which are available in good text books. I would walk around the class whilst they were working (in silence), helping here and there, perhaps occasionally drawing the attention of the whole class if I saw the need - at the highest level, of course.

In modern parlance, Betamale, I am a facilitator of learning. I have never set myself up for the whole lesson at the front of 20 to 30 young adolescents for them to make pot-shots at what I am doing.

nuff said

8. ### Mathsteach2Established commenter

Brilliant, Betamale, you are obviously not a teacher-trainer. I wish you well in your practice.

9. ### valed

You don't say!?
What is your specialism then - drama?
If any NQT put that strategy in front of me, I would be hitting the roof!

10. ### Mathsteach2Established commenter

Oh dear, I really do seem to have opened a can of worms here!

I am now retired (thank God for that, some may say) so I thought perhaps I was out of touch. However, it seems I might be in line with Ofsted, and a quick Google on mixed ability teaching shows that research into the advantages and disadvantages of both mixed ability grouping and streaming is very much alive, in countries throughout the world (with no preferences either way, it seems).

Yes, I am a trained and experienced drama teacher, but my main specialism is secondary physics. However, I have only mostly taught science and mathematics to KS4. Elementary drama techniques are useful in all subject areas, and throughout the compulsory school age-range. I gained an MEd in 1995, and contributed substantially, as a student, to the course by demonstrating the usefulness of drama in all subject areas.

The business of mixed ability teaching is my point. I ask again, what are the reasons for this school to have mixed ability classes in Y9 for mathematics, and how do they expect their reasons to be addressed and the outcomes to be successful? I think for a one-off lesson, small group work is very focussed for all abilities, and the research backs this up (and Ofsted?).

11. ### valed

Really !! ???
If there is a Firing Squad, I trust .....
... you really are digging a hole here!
Good spot of mine then!

13. ### Mathsteach2Established commenter

I like your resource, mcs123, it seems to be just a modern version of my textbook approach.

So in a 25 minute lesson, we have 10 minutes, say, on the PP, then 15 minutes on the WSs? (No time for a plenary?). With the WSs, do the students work individually, in pair groups, or larger small groups?

I presume differentiation is addressed best when the students work on their own with the WSs (in silence?), and the best get the furthest?

14. ### Mathsteach2Established commenter

I tried to para this with the edit button but the button did not work!

15. ### Mathsteach2Established commenter

Of course I do not know what you do, and my apologies for suggesting that I do! However, I was only going on what you are saying, I have given some details about myself, perhaps you could do the same?

Browsing some of your other posts here, and please do not accuse me of predatory behaviour, I notice you have an uncomfortable disposition towards circuses.

In Nuffield Science, a circus of experiments was advocated, and I successfully implemented them throughout my career, right up to when I retired in 2006.

If this exchange proceeds, perhaps we could contiinue it in a more general forum, (Secondary perhaps, or Opinion if we wish to accept the playgound exchanges). God bless.

16. ### NRICH_Alison

I quite like Tilted Squares for introducing Pythagoras. But then I would say that, wouldn't I? (Warning: the Teachers' Notes accompanying the problem have me in.)

17. ### pinkkazNew commenter

This is a really nice little demonstration on youtube (make sure it isn't blocked at your interview school though):
http://www.youtube.com/watch?v=CAkMUdeB06o

Also, there is a great smile worksheet on this (search for smile maths on google, check the activity list for pythagoras).