“From Mathematics Question – Number 17, onwards, I plan to post each question on the blog, as well, with extra comments that will then appear in the Mathematics Questions – Newsletters. So, basically, each question, plus comments, will become part of the blog and then the newsletter will appear periodically, bringing together, each time, three questions plus comments (as it does now). Hope that makes sense!”

The above didn’t materialise! Oops! What will happen is, I will be publishing the questions as normal on my website, nilsbirdtraining.com/mathematics-resources, and then the newsletter will be published in this blog.

So, here goes with Mathematics Questions – Newsletter No. 5.

In the previous blog post, I mentioned about the publication of Mathematics Question – Number 18. Now Mathematics Question – Number 19 has been published. Download it here. It is the third question in, “The skill of thinking” series. As with Mathematics Question – Number 17 and Number 18, it is written for Grades 5 to8. It asks students to think about different ways that four friends can spend time at a ten-pin bowling alley, over a six month period.

Also in the previous blog post, I mentioned about upcoming webinars and a week-long mathematics course. The dates for these have now been published:

As with all the training nilsbird training tries to provide, the fees for attending the above events are being kept low so that teachers from different economic backgrounds can attend.

The standard price for a webinar is $7 (£5.11). However, until 48 hours before the training is due to take place, it is heavily discounted to the amazing price of $2.50 (£1.82). The standard price for Developing a mathematics professional is $35 (£25.54). However, until 48 hours before the training is due to take place, it is heavily discounted to the amazing price of $10 (£7.30).

Finally, nilsbird training’s first live stream event of this Autumn will be at 16:00 GMT on Wednesday 6thOctober 2021 on it’s YouTube channel. The topics will include CPD (continuous professional development) and active learning: https://youtu.be/je0DgWZZRP0

So, apologies for another information-sharing blog. My next post will be about the mathematics questions so, hopefully, there will be something of interest for you in that. During October I would like to continue to discuss the idea of thinking skills, mentioned in the previous blog post.

A new mathematics question has been published – Mathematics Question – Number 18. Download it here.

The question is the second in a series called, “The skill of thinking”. Written for Grades 5 to 8, the question asks students to think about different ways of purchasing books; from an online store, or a physical book store. There are membership schemes and discounts for students to think about. As with Mathematics Question – Number 17, the idea of the question is not to work with complex mathematics, but to bring together related information to solve a problem.

How important are thinking skills to you as a teacher? Do we just take them for granted when working with students, or do students actually need support with developing them? There is even a Thinking Skills examination provided by Cambridge Assessment International Education (17/18 year olds).

I think there is a new topic for a future blog coming here. What are thinking skills and do we need them? Let’s see what I can do!

The webinar preparations are coming on and the dates will soon be published. Just looking at providing three webinars in October, plus a week-long mathematics course.

Don’t forget to watch out for the live stream event in October – via YouTube. The focus will be CPD and Active Learning.

Well! This post is just a brief, short post to share some new ideas for 2021/2022. Here goes!

The mathematics questions are back! Question Number 17 has been published. It’s the first in a new series called, “The skill of thinking”. Question 18 will be published on Monday 20th September 2021. All the questions can be found at here. (Don’t forget the Mathematics Questions Newsletter is now part of this blog.)

Supporting CPD/Professional Development returns with some webinars in October2021. Watch out for a blog post with all the details. The high standards shown in Standard for teachers’ professional development are what nilsbird training wants to aspire to!

Nilsbird training is embarking on a new venture – live streams via YouTube. The first will be on October 6th at 16:00 GMT. Themes will be CPD and active learning. Watch out for a blog post with all the details.

Thinking again about CPD/Professional Development, complete these three statements and let nilsbird training know what your needs are for 2021/2022:

1) Over the next year I want to learn more about … so that I can improve my students progress in the classroom. 2) Over the next year I want to improve my understanding of … so that I can improve my students progress in the classroom. 3) Over the next year I want to improve my … so that I perform more effectively as a teacher and support my personal well being.

For this post on telling the time (my last, I think, for the moment!) I’m going to look at some of the written approaches I took.

Depending on the age/ability of the students, I tried to go as far as I could with my written approaches. At the start, it was important that students knew the basics.

This information was put into practise.

As I linked in fractions with telling the time (see the previous post), appropriate questions were used.

As some students progressed, harder questions were given, mixing in fractions when appropriate.

The most able students were set the task of planning a journey involving time.

I did not shy away from asking higher-level thinking questions, such as 15 minutes is the answer, what is the question? (The students did find this question particularly hard!)

So, the end of the posts about telling the time. I hope you found them interesting. I certainly learnt a lot that I didn’t know before!

The multi-topic mathematics questions are returning next week, so the newsletters will appear again. Something to look forward to!

This new post focuses on some practical steps I took to support the students understanding of how to tell the time.

I have always been a great believer in kinesthetic learning; students actively engaged in their learning (as opposed to focusing on a particular style of learning because a student is deemed to learn best in that way). I have always felt that if you can immerse a student in an activity, it will very likely support their understanding.

With the above in mind, I tried a couple of ideas, both based around the students having to visualise the layout of a clock on a carpet. For example, for some students (either because of their age or ability) that were just learning about the clock face/I was just trying to consolidate understanding, I placed a chair/stool on the carpet and said it was the centre of a clock. I then asked them to sit/stand at particular numbers, having told them where 12 was. To do this, they had to visualise where the numbers would be. So, for example, students were asked to stand at 2, 4 8 and 10.

I then asked questions, such as, who is standing at 10? Or asked a student to go and stand where 7 would be. To make the activity slightly harder, I would remove the chair so that the students lost a point of reference.

My other idea was to ask the students to stand, individually, on a carpet; all facing in the same direction which was 12. I then gave them instructions, such as, turn through a 1/4 of an hour, clockwise, and then asked, where are you facing? Or, turn through 1/2 an hour, anticlockwise, and then asked, where are you facing?

This second activity opened up a lot of possibilities for the content of questions/extension material. For example, students could start the activity facing, for example, 4 and then be asked to turn/say where they were facing. Or the amount of turn could cover all the factors of 60 – 1/2, 1/3, 1/4, 1/5, 1/6, 1/10, 1/12, 1/15, 1/20, 1/15 and 1/60; plus multiples of these, for example, turn through 5/6, or 37/60, of an hour. (This got even harder if you asked students to turn through, for example, 3/8 of an hour, or 17/12 of an hour.)** ** We must not forget that minutes, as well as fractions of an hour, will all be part of this work as well.

The responses the students had to give to questions, such as, where they were facing, were certainly challenged, if they had to clearly describe where they were positioned after a challenging turn. So, here is a particular scenario:

Teacher: “Ok. Let’s move to the carpet.“

Teacher: “Everybody find your own space. Face the green wall. That’s 12.“

Teacher: “Turn to face 3.“

Teacher: “Ok. Turn through 3/5 of an hour anticlockwise. Where have you ended up?“

Student: “21 mins to the hour.“

Teacher: “Great. That’s correct.“

Teacher: “Can anyone describe where they are facing in a different way?“

Student: “1 min before the 8.“

Teacher: “Yep! That’s correct.“

Now, maybe you can begin to see why I said in my introduction to this series: “The journey I have made has made me realise how telling the time can be taught and all the mathematics that can actually be taught using a clock!“

Whilst trying out these practical activities, things such as fractions, were beginning to play an important role. As a result, I decided to focus on fraction understanding, as well as time, but that is another story!

When considering the use of fractions when telling the time, factors/multiples/primes, as well as the manipulation of fractions, can also play their part. So, the scenario above could become:

Teacher: “Ok. Let’s move to the carpet.“

Teacher: “Everybody find your own space. Face the green wall. That’s 12.“

Teacher: “Turn to face 3.“

Teacher: “Ok. Turn through 4/5 of an hour anticlockwise. Where have you ended up?“

Student: “27 mins past the hour.“

Teacher: “Great. That’s correct.“

Teacher: “Can anyone describe where they are facing in a different way?“

Student: “2 mins past the 5.“

Teacher: “Yep! That’s correct.“

Teacher: “Now. Turn 2/3 of an hour clockwise. Where have you ended up?“

Student: “7 mins past the hour.“

Teacher: “Can anyone describe where they are facing in a different way?“

Student: “2 mins past the 1.“

Teacher: “Yep. That’s correct.“

Teacher: “So, what do you think we have just done? What calculation have we done?“

Student: “4/5 – 2/3.“

Teacher: “Great. So, where’s the answer to this calculation? Where can we find it on our clock?“

Student: “How far we would turn anti-clockwise from 3 to where we ended up – 8 mins.“

Teacher: “Great! Can anyone say what fraction this 8 mins is? A clue is: it’s 8 mins out of 60.“

Student: “8/60. I think, cancelled down, it’s 2/15.“

Teacher: “Yep! If we did 4/5 – 2/3, we’d get 2/15.“

I agree the above is a little contrived, but I hope you get the idea!

Other topics that could be integrated with clocks are angles (not just values but names, such as, right-angle and acute), transformations (for example, if the line of reflection is from 12 to 6, what is the reflection of 4 o’clock?) and multiplication tables (Hopefully this last one will be talked about in another blog post.)

That’s it for now. My next post will talk about further written work I did with clocks.

Don’t forget, via supportforteachers.com, you can find out all about the online teacher training conference, Educating the 21^{st} Century Student, 26th to 28th August 2021.

For those of you who like regular posts, I must apologise for not being that regular at the minute! Life, as mentioned before, is always busy and so, currently, posts happen when they can! (Look out soon for the sign-up form that will enable you to be kept informed when a blog post has arrived.)

So, when you look at the cognitive difficulties that adults with dementia suffer, it sheds some light on the cognitive development of children; the clock drawing activity showing what development is/has taken place. Why has the student not drawn the numbers at the edge of the circle?

One thing I wanted to get across to the students, at the start of my teaching, is that time is continuous; it does not stop. (I feel that this is really important, as just reading a digital clock does not actually allow an understanding of this.) I also tried to get some basic facts over to the students:

Some students were able to work with these facts:

Next time (part 3) I will talk about the practical approach I used to reinforce the students’ understanding.

Don’t forget, via supportforteachers.com, you can find out all about the online teacher training conference, Educating the 21^{st} Century Student. I now have an additional workshop on Saturday 28th August, delivered by the very capable Sanjit Chimber. It’s all about maths activities for 16 to 19 year olds.

Today I’m writing my part 1 to the posts about telling the time. In my last post I introduced what I did in the Primary school and mentioned that “… putting numbers on a clock (the first challenge for the students) is harder than you might think and that’s what I’ll begin with next time!” So, more on this now!

As I started to work with the primary students I began to see the difficulties some of them had with placing numbers in the correct place round an analogue clock. (It wasn’t so much the order that the numbers had to be placed in; it was more the correct spacing between the numbers):

To enable students to have a chance of any accuracy with their clock layouts, I said, “Place the 12 and 6, 9 and 3 first; then put the other numbers in between.” This did help and some of the students took the idea on board as they created their clocks over a period of time.

Now, in doing a bit of a searching on the internet about the difficulties of drawing analogue clocks, I have discovered that, apparently, there is a drawing-clock test that is used to check for things like dementia. One article talks about clock-drawing errors, including what I have mentioned: https://neuro.psychiatryonline.org/doi/full/10.1176/appi.neuropsych.12070180

Maybe my next post (part 2) will be a little more about this drawing-clock test. We’ll see!

Don’t forget, via supportforteachers.com, you can find out all about the online teacher training conference, Educating the 21^{st} Century Student. I have some great live speakers lined up: Alison Borthwick (alisonborthwick.co.uk), Dr Alan Cross, Dr Tony Birch (bircheducation.co.uk), Sioban Parker, Stephen Atyeo and myself. Speakers who will provide pre-recorded workshops: Ann Starks, Joseph Hubbard (creationresearchuk.com) and Sheba Moyo.

Thanks for now and see you next time. David nilsbird training PS As always, you can always contact me using the details in the side bar.

A slight delay to this blog post but, fortunately, the marking season and the National Tutoring Programme support I’ve been doing in a primary school are coming to an end, so I can now concentrate on a few other things.

This blog post is titled Telling the time – an introduction. During my time at the primary school, I have tried to support student understanding of how to tell the time using an analogue clock:

Because of the covid pandemic, students in the UK missed a lot of face-to-face lessons and one of the casualties, for some primary students, was being taught how to tell the time. So, when I started my support, I made it my mission to try to teach the students how to tell the time using an analogue clock. (The journey I have made has made me realise how telling the time can be taught and all the mathematics that can actually be taught using a clock!)

Now, the thing is, some of you reading this post might question why it is important to teach students how to tell the time using an analogue clock, when they all have a phone! Well, throughout these posts on what I did I will try to explain why I think it is! (If you ask students if they can tell the time, they might, happily, tell you yes and confidently say, “It’s 1:17 pm”; getting the time from their phone! However, if you then showed them 1:17 on an analogue clock, they might not have a clue where to begin! I have a theory about whether this is a problem: being able to read digital time but not analogue. But I will say more about this in another blog post.)

I began my mission by drawing clocks on paper/creating flashcards for o’clock, half-past, quarter past and quarter to; then practising these with the students, getting them to draw their own clocks in their books. (To begin with I resorted to them drawing round something circular!)

Now, putting numbers on a clock (the first challenge for the students) is harder than you might think and that’s what I’ll begin with next time!

Don’t forget, via supportforteachers.com, you can find out all about the online teacher training conference, Educating the 21^{st} Century Student. I have some great live speakers lined up: Alison Borthwick (alisonborthwick.co.uk), Dr Alan Cross, Dr Tony Birch (bircheducation.co.uk), Sioban Parker, Stephen Atyeo and myself. Speakers who will provide pre-recorded workshops: Ann Starks, Joseph Hubbard (creationresearchuk.com) and Sheba Moyo.

Thanks and see you next time, David nilsbird training

Welcome to Mathematics Questions – Newsletter No. 4 – support for Mathematics Questions 10 to 13

Download the previous Mathematics Questions – Newsletters here

Before I dive into the newsletter, I thought I’d point out that you can still receive the Mathematics Questions – Newsletter straight to your inbox. Sign up here.

To contact me regarding anything to do with this newsletter, use the contact details shown in the side bar.