Ratio with Bar Modelling

I currently run support classes for numeracy for years 4, 6, 8, 9 and 11.

Many of the students I see struggle to remember techniques, particularly when they are seemingly abstract.

Two main bits of inspiration brought me to re-teach ratio through bar modelling

(1) Concrete - Pictorial - Abstract
Research suggests students grasps concepts best if initially they can "play" with objects, then sketch it pictorially, before moving to the abstract technique.

(2) White Rose Maths Hub
With so many examples of bar modelling on their twitter feed @WRMathsHub, I visited their website and found a few bar modelling resources, here.

Ratio with Bar Modelling
Within the first 5 minutes the students appeared confident and comfortable with the new technique, and commented that it was much easier for them to understand what was going on.

Here is a little of their finished work:

These questions in their template can be found here.

Ski Slope Learning

After reading Miss B's blog on ski slope learning (https://www.missbsresources.com/maths-resources) I decided to give it a go with a @MathsMastery problem I'd seen this week:

Ski slope learning is essentially a student friendly differentiation technique to enable all students to make progress (from the top to the bottom of the ski slope), taking whichever route they think is best for them.

Here are the different "runs" for this problem:

 

 





#10minwin Deepening Thinking Template

Following the OTP I've been looking for ways to really deepen thinking of all students, particularly with tasks that are self-differentiating.

I loved this idea from @MissDks2 ...

... so have been developing it for use with Year 7 Mastery SoL next year.

We're particularly looking at developing their questioning skills, hence the slight change to the template above

Here's the first draft, with an example of solving equations.

Template can be found here.

3 Act Lesson: Similar Shapes in Prison Break

I've long been a fan of Dan Meyer's 3 act lessons and this week have used the time to make the first of my own!

Since watching Prison Break a few years ago I remembered how much planning Michael (the lead male) has to put into getting his brother out of a high security prison... some of it has to be maths based right?

Riots, Drills and the Devil

In this episode Michael has to drill through a wall, using nothing but paper, pen (of course also his tattoo), a lightbulb and an eggbeater, to make holes at strength holding positions on the wall.

If he messes up, he'll drill through a pipe and be discovered.

Structure

I've added a little extra into the standard 3 act:

• true or false: canvas opinion on the content of the lesson and challenge expectations
  
• prequel: I expect only half the class will have seen Prison Break, so I've put in the opening credits to get everyone on the same level

Act 2 Information

The lesson closely relates to similar shapes, enlargement and trigonometry so could be used as an introduction or development in any one of these themes.

Enjoy!

Full powerpoint lesson here.
Link to resource on 101 Qs here.

See No Evil, Hear No Evil, Speak No Evil

This idea came from OCR
Get three volunteers from the class. They will sit at the front relatively far apart from each other. One of them will be blindfolded and will be ‘See no evil’, the other will have headphones on listening to music (at a reasonable volume but not enough to damage their hearing!) and be ‘Hear no evil’ and the other will not be allowed to speak and be ‘Speak no evil’. You each give them one piece of information from one square on Activity Sheet 4. You also inform ‘Speak no evil’ of what variable they need to find out. You give them a time limit of 5 minutes to communicate with each other all the pieces of information and they have to have a correct answer. This is a fun, end of topic activity that can be very entertaining to watch. The key is to use the whiteboards. The student who cannot see can speak and hear and similarly for the other students and their other senses. Students have to figure out a strategy to communicate their ideas to each other effectively. Remember they can write messages on their whiteboards which is crucial for the student who cannot hear or speak! You may want to do an example first. Students not involved should have access to the information you have given them and be encouraged to calculate the answer themselves. In fact you could make the rest of the class the judge of whether the particular group has succeeded in their task.

Thoughts
- students have to work as a team
- all students in team have to be involved for it to work
- what are other students in the class doing?
- does this have more impact than practising questions normally in groups?

Possible Adaptations
Although this might take a little while to explain the first time, it could be used again with other topics in small groups, where each of the roles (including teacher giving information) is taken by a set of 4 students, so all students are involved.

#10minwin: Speed Mathing

A lot of what we do at GCSE level is recapping knowledge that at least some students already have, so the idea behind this is

"the knowledge is in the room"

(thanks to James Wise & Simon Thompson for this!)

Each student was given some information about a unit conversion, from which they had to come up with a problem and write it on a post-it.

Students then arranged their chairs in two rows (they were surprisingly efficient at doing this!), and they had one minute to ask a question, including how to apply any conversion facts they were given.

These are a few of the question which have been collated and will form part of a procedural revision bank for later in the year.

We'll also be doing this tomorrow to recap angle rules, where each table will be given an angle fact as well as some examples and non-examples, then will speed math to share it.

The goal is a much higher engagement in the learning than recapping as a whole class.

Manglish: Comprehension in Worded Maths Questions

With the GCSE Numeracy a little over 4 months away, we're really focussing on honing Year 10's problem solving skills. Here's a lesson I did last week to work on just that.

Starter
As usual, on the board as they came in. My goal here - productive panic. Students had become a little overconfident in how prepared they are for the exam, so I needed them to feel what it would be like if the exam was tomorrow, in the panic zone.

We then reflected on feelings: too hard, panic, didn't know what a frustum was etc. This was the motivation for the lesson, they now knew why it was that we needed to revisit the IMCA model that we'd started the year with.

IMCA Model
Next they were given the template below, same question but guiding them through each aspect of IMCA. After a discussion with the English dept, some comprehension style questions were given for Information.


Methods were given to choose from, with the idea of there being some red herrings in, e.g. if the question was about circumference, area was also an option.

- PAUSE -

Students were only allowed to answer these first 2 sections, and this was done in silence. Only at this point were they allowed to collaborate to do the calculations, though most chose to carry on independently.

Here we really emphasised that before writing the answer, they should revisit the "what is the question" in the information section to make sure they were actually answering it!

Reflection
Pupils now felt more confident again, they were back in their comfort zone. I asked for feedback on the model, to which I had a fantastic response:
"I feel really confident answering these questions when there is guidance, but in an exam I could never think of this myself."
This led neatly on into the second phase... creating the scaffolding.

Phase 2
Students worked in pairs on an unseen problem (each pair had a different problem) to create scaffolding similar to what I had given them for the first phase. This enabled them to really think about what the important information was so they could ask questions about it. They were also great at being mean and choosing really similar topics for the methods section which weren't quite right!

Phase 3
Quick task, which involved swapping with another pair, and using their scaffolding for guidance.

Plenary
We agreed that they would become better at coming up with the questions if they had more practice, so that's exactly what we'll do! We also agreed that the end goal was for the template to become internal, so they were self questioning rather than peer questioning.



Resources can be found here.

Circle Theorems Pile-Up

In trying to assess as many circle theorems at once, and inspired by the Trigonometry Pile-Up, I attempted to create a double-sided scaffolding worksheet for this.

Worksheet below!

Front Side: unscaffolded worksheet for students to attempt to find the labelled angles.

Reverse Side: hints given to guide pupils in finding the labelled angles.

#10minwin - Burger Questions

I have a number of students for whom the final answer is the only thing of importance. Whilst there is no arguing with the fact that accuracy of the final result is key, I wanted to emphasise the justification and explanation of methods.

After reading a post on sandwich questions and with a penchant for burgers, have started to create worksheets in this format.

Result: with the answer already given, students have no option but to show how to get from question to answer. It also had the added bonus of highlighting misconceptions, as if the correct answer wasn't reached, then the method couldn't be correct. Plus, minimal marking required!

WWW & EBI from Pupils

I asked my Class Teacher to run a brief activity with my class when I wasn't there to ask for WWW and EBIs about my teaching. Some were really uplifting and some were things I hadn't realised I was / wasn't doing so definitely some useful points to work on. Full notes on this are here, but below I have written some of my most pressing thoughts.

So it seems that in general they like the variety of activities, particularly when they are doing group work (including when they are teaching their peers) and the silent lesson went down a treat.

Questioning

A big concern is choosing which students to ask questions to, and something I remember feeling frustrated about at school.

I want to ask the students who have their hands up, as they are so excited that they know the answer, but obviously then you’ll probably only hear from ¼ of the class throughout the entire lesson. Instead, I was advised to use the ‘hands down’ policy, which has served to get many of the pupils interested in the task, but I then received this feedback from a pupil “I don’t like it when you pick on people when they don’t know but other people are desperate to answer,” which goes back to the original problem of frustration, so I am again questioning the technique.

A possible solution to this lies in the use of whiteboards, getting students who think they know the answer to write things down on whiteboards and hold them up so that I am aware that they know it, but in the meantime use the random name generator to select a student to answer the question initially. I think this would work best if I first asked the students why they think it is important that I find out that some people don’t know the answer.

Task Explanation

A further concern is in how I am explaining my tasks – one student commented that I am “good at explaining what we need to do” yet another said “make the task more clear so people understand better.” Unfortunately I think part of the confusion may lie in the fact that they are not always concentrating when the task is being explained, but I am also aware that many of my explanations have been rushed, especially when I am excited for them to get onto the task!

Perhaps a bit more time spent on explaining with bullet points on the board, and leaving them up, might help. Alternatively, more detailed task explanations could be given to some students if they are continually struggling, but this would involve publicly identifying them, which I would like to avoid.

Relationships

My final, and most upsetting, concern, was a student who said “you talk to other people on my table more than me.” Due to a poor scribbling out on the paper, I have been able to identify the table on which this student sits and will make a concerted effort to speak to all of them equally until the relationship has been mended. However, the student who they felt I spoke more to, was the student on the table who needed more attention in general as he is one of the weaker students in the class. Arrrgh!

To the Pub!

With CA1 happily handed in this morning, it was time for another session on geometry.

We began by considering a "real-life" problem, which was presented to us by handout:

We discussed the problems in groups and thought about the different ways in which it could be solved, what you would do as the starter activity in this lesson and how you would extend the task.

Possible extensions discussed involved finding the minimum length of fence needed to separate the land; turning a quadrilateral into a triangle of the same area and then proving by induction that any shape could be turned into a triangle of equal area by using the same technique.

This problem was posed in a Japanese classroom; the full lesson can be seen on the website. The key points to take from this lesson were:

• ensuring personal reading and thinking time before group discussion
• motivation by selecting 2 students for Bando and Chiba
• students drew solutions on board before group discussion
• hint cards for differentiation
• verbal explanation of problems avoids problems with different reading times
• second problem was still a high level problem
• hint cards are not read aloud

Later in the pub we discussed the idea of reading each others' Curriculum Assignments anonymously, so I have created a folder here:

https://drive.google.com/?tab=mo&authuser=0#folders/0BxnnS5919b_XNThHc2R4MDNKNlE

Each intern will need to request permission to access this folder.

A Session on Task Design - Thank You Gabriel!

Today's session with Gabriel was incredibly helpful as it focussed on Task Design; the subject of our CA1 Assignment. Slides can be viewed here.

We began by considering interior and exterior angles in a polygon, then following the principles of needing to convince:
a) ourselves
b) a friend
c) a sceptic

We then looked at the different ways in which the task could have been designed:

It was noted that no formulation is necessarily "better" than another, but they each can be considered in terms of the outcomes desired and the students themselves.

The following ideas were discussed:

Option 1

• question suggests it should be easy to find out

Option 2

• invites investigation
• like proving your answer to a friend
• students might responds with 'no'! - but then ask why not

Option 3

• what does the word investigate mean
• difficult to lock program to ensure focus on task
• self-differentiating

Option 4

• may not get this exact formula, therefore might assume they are wrong
• when give the formula, students may not feel the need to prove it themselves
• takes away the opportunity for discovery

At the end of this session, Gabriel asked us to fill in a questionnaire to help for a section that he is writing for a book on teacher education. This prompted me to discuss the following ideas:

• considering my own proofs: think about how I am going to introduce a concept to the class; do I want to prove it beyond all doubt or do I want to leave that as an exercise for the students to do?
• possible lesson idea: introduce an idea and then have 5 minutes silent thinking about the concept - find out who is convinced and who is not then get the convinced people to prove to the 'sceptics'
• task design: think carefully about the outcomes desired from the task and how to structure it to achieve these outcomes