Inverting the Lesson - "Box Plots"

This is a lesson I have used to teach "Interpreting Box Plots", and I love it!

It’s an inverted lesson as opposed to the traditional approach of teaching box plots as I do not mention the topic, I do not teach what a box plot is; instead conditions are created where students are able to interpret the majority of the information without my input.

I think it is similar to the approach Kate Nowak @k8nowak presented  at the NCTM Regionals  "Inverting the lesson". This approach is about changing how we deliver lessons, which can typically be  I Do, We Do, You Do.

So this lesson starts off with no mention of box plots,  I do not teach what a box plot is and the parts of it...

There are three parts to the lesson. All of the resources are available here or for non-TES users here.

1. Estimate the number of dots.ppt (Original file here created by Craig Barton)

2. Box Plot spreadsheet (use this for other lessons)

3. Film task (applying our new-found knowledge)

This task was originally created by the legendary Craig Barton (@mrbartonmaths & Diagnostic Questions) here "Dotty Thinking", since then I have adapted it for teaching Box Plots.

Watch the video below for a complete description of how I use the resource.

Key Points

The lesson has 

• Simple reference points - pupils can easily identify the max and min points of the box plot and most students can recognise the median.
• The highest achieving student does not necessarily make the best guess, all pupils regardless of their current learning in mathematics can access this task.
• Not a prerequisite for a maths task but my students enjoy this lesson (they're all desperate to find out how many dots there are and what the film genre is).

What I like about this lesson:

1. It has reference points, and stick-ability.

2. It promotes student discussion and student centred.

3. It is a low entry task - all students can take part and want to take part !

4. It takes no longer to teach than the standard box plot lesson.

What other topics do we teach this way? Please share in the comments section below.

Thanks

Damian

Credits.

newyearbaby90 for the film box plot resource

Craig Barton for his brilliant resource and ideas - Thanks Craig!

Creating Cognitive Conflict

Creating “Cognitive Conflict” 

When I teach Indices I usually give this sort of worksheet. Which I think is ok, I have insisted that they must show their working and by the end I can gauge whether the student understands the concept or not.

After hearing Dr Malcolm Swan talk about “creating conflict", I wondered what that would look like in practice. I then came across this absolute cracker from Andrew Stadel (@mr_stadel)on his blog. Andrew gave them this worksheet (below) in which all the questions have been answered incorrectly. When I initially looked at this I did think this was not as powerful as a worksheet mixed with correct and incorrect answers. The richness of this activity is because all of the answers are common misconceptions and as Dylan Wiliams said: "good feedback causes thinking" I think the same applies to questions - "A good question causes thinking". 

After hearing Malcolm Swan speak about “creating conflict”, I believe this hits the spot and it places the student on the back foot and creates conflict.

For many students when they see:

Question 1, creates conflict with many students because they believe it to be correct, when I am adamant that none of the answers are correct - let the battle commence! Suddenly between the two students they start making suggestions as to what it could be. 

Another favourite of mine is question 5. This is a classic misconception that exposes students who do not have an understanding that the power of a half is the same as the square root.

One question which caused a lot of discussion among the mathematics teachers I showed this to was question 3.

Some teachers were not happy with this question, which to me means it is causing conflict with them, and therefore likely to cause discussion within the classroom.

How do I use it?

I believe the activity works best in pairs with the sheet printed and laminated with a set of post-it notes. I like students to work together so they can share solutions, argue in more logical and in reasoned ways which allows them access to mathematics and to take more ownership. It’s much more fun to try to think and reach solutions collaboratively so students don’t feel so isolated and are less likely to think of the task as a threatening business. 

The post-it notes allow me to see which students are making progress, and which students might need some support. It allows me to check their reasoning, and also to share best practice with the class.

After they have completed the activity - I then ask them to write up the correct method and answer in their exercise book. 

I write this blog and @robertkaplinsky throws this into the mix, another great idea, something else to try out.

If you have any thoughts or perhaps similar activities please share them in the comments section below.

Misconceptions / A4L / Self Marking Activities

Bored of doing test papers - try these activities!

These are activities I have used during revision lessons, revision days (or superlearning days), and homeworks.

Activity 1 - Substituting Self Marking - A paired activity

For this activity I had students working in pairs.

For this activity I would recommend that you print this out on doubled sided A3 paper (it works on A4 just as well). I like to print it on A3 paper because then it is a novelty for my students - they don't generally get treated to A3 paper. I also give the students a red pen to mark the paper, some enjoy the power of the red pen - in my instructions I tell them to mark it as if they were the teacher. I tell them to write any notes/help you would give "Stephen" and get them to grade it - in anyway they see fit.  Pupils are to discuss and ensure they are both happy with every question because they will be asked to justify any marks docked or given.

Feedback
The students enjoyed it, they didn't feel they were revising or doing work! They discussed the answers and shared best practice. During this process they were using higher level thinking skills than normal and also engaging in a lot of mathematical discussion.

I used common misconceptions in writing the answers, which hopefully will highlight common errors to them?

I thoroughly enjoyed the lesson !

Would I do it again - yes! I felt it was very beneficial to them, but I would not let this become a common activity, otherwise the novelty element might be lost.
I hope you enjoy it - give it a go and tell me how it went for you.

Activity 1 - Substitution Self Mark

Activity 2,3 & 4 - Transformations Self Mark booklets

These 3 activities are similar to Activity 1 where this fictitious character "Stephen" has been working on the Rotation, Reflection and Enlargement. He has completed all 3 booklets and the pupils must mark his work and when he is wrong say why.
These activities are all 4 pages and are best printed off as a booklet on one A4 page.

Activity 2 - Rotation Self Mark
Activity 3 - Reflection Self Mark
Activity 4 - Enlargement Self Mark

If you want the original word document of these just tweet me@dwatson802 and I will send you it.

Three Acts - The Need for Speed!

I feel the need, the need for speed!

I used this activity with my GCSE group as a bit of revision on the topics of speed, converting units of measure, and re-arranging formula.

3 Acts - The Fastest Man on the Planet! 

Act 1 - The Hook!

I projected this picture -and asked if they had any questions?

The following were the 6 questions they came up with - in no particular order.

1. How long is the race?
2. What time did he take?
3. What is 34.87km/h in m/s?

4. Does he break the world record?
5. What does MR mean?
6. What is the black smudge.

I asked them what they needed to answer questions 1 - 4.  I answered question 5 as "Meeting Record" I hope I was correct - and asked the students to go away and clarify whether I was correct.. I explained what the black smudge was.

There was open discussion at this point about what distance the race was - after looking at the WR (world record) they decided it was not the 100m or 200m?  They eventually decided it must be 300m - although some were convinced this distance did not exist. This led nicely to Act 2 ->

Act 2

Give them this

Now they decided to work out how long it took Bolt to complete the 300m race and to check whether he broke the world record record?
At this point we discussed what speed was - not just the formula. I wanted them to be able to explain what being fast was ? This was really difficult for some of them as they did not like discussing it - they were happy enough to know the formula. This was a major learning point for me - when I cover the topic speed for the first time with students I must not just give them the formula - we will debate and come up with the formula from discussion and examples - practical examples.
After the discussion they worked in pairs to find the time taken by Bolt to complete the 300m race. The problem of converting the km/h to m/s was challenging and again we discussed what 34.87km/h actually meant. They then completed their calculations to work out the time taken.

*******At this point I wish I had given the students mini-whiteboards so I could see their answers - and their working. ********
Act 3
The reveal

Reflections

This activity was so much more satisfying than your typical text book which gives them all the information and they just need to substitute the values it into an equation.

The satisfaction was

1. The pupils were more engaged in the topic than they would be if the answer is just told to them or found at the back of the book
2. There was a lot of discussion - with non-specialist maths students able to input.
3. They were problem solving without being pushed or cajoaled by me.
4. They enjoyed the video - and a few whooped with delight as they got the time exactly right.

Did they learn anything? I believe they had a greater grasp of the speed equation and what it meant from their discussions. It was great to see them discussing the problem and reasoning for why the race could not be 200m long and not 400m.

Improvements : - use mini-whiteboards, ask the students to go away and come up with their own.

Will I use it again - definitely.
Try it, improve it, tell me what you think.

The goods

Act 1 - Hook Picture
Act 2 - Distance Shot
Act 3 - Video


New UPGRADE - The Dan Meyer "Bolt" Version


Thanks Dan!


LINK - http://threeacts.mrmeyer.com/download/bolt.zip


For all Dan Meyers 3 acts see https://docs.google.com/spreadsheet/ccc?key=0AjIqyKM9d7ZYdEhtR3BJMmdBWnM2YWxWYVM1UWowTEE#gid=0

Trying to use an IWB effectively in maths (Part 1)

One of my personal targets this school year is to use my interactive whiteboard (IWB) effectively. Last year I had a Promethean IWB installed in my room and I only used it as a digital whiteboard with PowerPoint. So this year I have set myself a target to use it effectively.

My progress so far!


1. I trained myself up using the ActivTips videos free on ITunesU - these were very inciteful and sparked lots of ideas - these are amazing so do check them out. I downloaded them to my Ipod and listened / watched whilst doing housework (sad but true). I have had no training on using the IWB so this has been a trial and error process.

2. I searched the web for the useful resources - which proved a massive waste of time. I searched the TES and Promethean planet but found the resources very poor. The TES has some fantastic resources but nearly every teacher classifies PowerPoints as IWB material - PowerPoints are generally not interactive so I gave up on this. I could not refine my search in the TES to find anything specifically for the IWB. Promethean planet was an even bigger disappointment - the quality of the resources was very poor. I was really disappointed with the presentation of peoples flipcharts - most of the flipcharts were not suitable to use so again this was another dead end. If you have found any good flipcharts please pass them on.

3. The positives from my search were  1 .ActivInspire activity packs and resource packs from Promethean planet and  2. The Whiteboard Blog. Danny Nicholsons blog is a fantastic website which provided me a great starting point for my lessons - his blog is full of ideas and one I always look out for in my google reader account.

After all my research I decided the main focus'  for using my IWB would be 

• To create interactive resources that would give pupils a better understanding of a topic;
• To get my pupils involved / engaged more in the lesson.

The successful flipcharts


My first resource is a starter  " Balloon activity" - this was using the idea from Danny's blog. This is  a resource that could be applied to any subject or topic.In this activity I use a random name generator to select a student to pick a balloon. The student comes up to the whiteboard and pulls a balloon - and answers the question. I used this activity with 3 classes and they all loved it - and asked for it next lesson. It is a nice easy activity to create and use - feel free to edit this one and make your own. Please share any you make with me.

 Another resource I created was a rotational symmetry demonstration flipchart. I used the rotation tool and about a point which I have hidden behind the drawings. Thanks to MEP CIMT for there questions - I used them to create this page. A visual demonstration of rotational symmetry which can be easily replicated - I then asked the students to go away and find me 3 digital examples of their own - stating the order of rotational symmetry. I will compile them and put them together as a recap for them in the near future.

Another topic I decided would be good to use the IWB for was compound shapes. I have found lower ability students struggle to picture missing dimensions in compound shapes so I created this flipchart - compound shapes

In this flipchart I have allowed all the dimensions on pages 1 and 2 to be dragged and to create a copy - this allows the students to move all the dimensions. On page 3 I have added in an idea on how to make a more difficult compound shapes clearer for students. On this page you can explode the shape by dragging out each separate shape.

In part 2 I will upload some more resources and look at some other sources of good IWB activities including Geogebra, SWF files + a few others. I will also include some failures :( 
If you have any recommendations or ideas for a good IWB resource or thoughts on any of the above please add a comment.

Lone Wolf Redesigned - Thanks Shawn Cornally!

Shawn Cornally developed this game (original game Lone Wolf) from a Dan Meyer idea, I was so impressed I decided to adapt it as a starter activity to help my students remember Square Numbers, Cube Numbers and Prime Numbers.

The rules are:

1. Choose a positive square number (or cube number or prime number dependent on the game) integer
2. You lose if you choose the same number as someone else
3. Lowest unique square (or cube or prime) number wins

How did it go?

Initially there was some concern by the pupils that this was a rubbish game (mainly because some of them did not understand the rules). But once we got started they loved it, probably because I also added a bonus for the victor of a piece of flapjack or brownie (their choice). It was great though that students suddenly were interested what a square, cube or prime number was. Whether or not they will remember what each of the numbers are remains to be seen - but hopefully they will remember.

Here is the file for those interested - try something new this week.

Plotting Quadratics Basketball Style

I am a big Dan Meyer fan, and I am always trying to teach in a more engaging fashion. I generally have to look to adapt his resources to suit the level of my students - although I am trying to push my students to their full potential. One of my favourite resources Dan has published was his "Will it hit the hoop?" - and this week I have finally managed to use it!

I used it with a group 13/14 year olds and it was fantastic. My learning intentions were as follows
1. To be able to visualise quadratic equations.
2. To be able to plot a quadratic equation.
3. To begin to recognise the impact of changing co-efficients and constants of a quadratic equation.

The students were engaged, keen to learn, eager for the result and more importantly left the lesson confident they could plot a very complicated quadratic equation.

Format of the lesson
1. Play Basketball introduction outlining learning intentions.

2. Discuss quadratic graphs and their features - visual demonstration via an interactive quadratic graph generator.
3. Give out worksheet and laminated take 1 sheet with a whiteboard pen.

Pupils use calculators to work out points and plot them on their basketball sheet. Pupils come up to the IWB and drag the basketball into the correct position. Lots of discussion at this point and pupils decide whether Dan scores a basket. I show them the video and pupils get off with completing the exercise.

4. The activity takes about 40 minutes, we then run through the answers via the videos. I only actually plotted the last 2 co-ordinates near the basket.

Amazing lesson - I loved it - they loved and most importantly they came up saying they could plot quadratic equations. Any comments welcome.

Here are the resources - a big thanks to Dan Meyer who without his videos it would not have been possible to make this lesson. Please accept my apologies for my poor grammar / punctuation etc.


Improvements

Possible lesson  improvements -

• More discussion about the equations and the effects of altering the equation.
• Digital improvements - equation and table on the same sheet as the graph.

I intend to try to get an older group of students to use Geogebra to model the basketball path and find the equations for themselves.

The goods!

https://docs.google.com/leaf?id=0BzKYiLlPmUGZNTM4ZWRkYjAtNDhmZC00OTUyLWE1MmItNDg5YTAyYWQ2M2Iz&hl=en_US