Showing posts with label KS3. Show all posts
Showing posts with label KS3. Show all posts

16 July 2023

Challenge in Year 7 Assessments

Last year I blogged about the principles behind the design of our Key Stage 3 assessments and shared some examples of challenging questions for Year 8 and Year 9. I wrote new assessments this year (to avoid the sharing of exam papers with younger siblings!). I'll share some of the more challenging Year 7 questions in this post.

This year we took a lot of our assessment questions from AQA's Key Stage 3 Assessments on All About Maths. I don't know why I've never used these before. They're excellent.

Here's the last question on our Year 7 non-calculator assessment:



This question tests reasoning skills, and fluency in substitution (i.e. understanding the notation 2p and 3q) and working with directed number (because the least possible value is a negative number). It's a precursor to working with bound calculations (the idea of 'small minus big equals small'). It's an accessible question that everyone can attempt, but few students got full marks. I expected to see long lists of trial and error attempts, but actually most students just answered -11, where they'd assumed they should use 11 for both p and q.

Here's another question that challenged Year 7:

This requires reasoning (working backwards from the mean) and knowledge of prime numbers. Many students struggled with working backwards from the mean - teaching time is so tight at Key Stage 3, we just didn't have as much time as we'd have liked to develop reasoning skills through averages puzzles.

Here's another reasoning question that some Year 7 students found tricky.


I'm confident that the vast majority of our students can add one fifth and one sixth, but many didn't get the mark for the first step because they didn't attempt it. This question requires fraction skills, proportional reasoning and the interpretation of a worded problem.

Here's an angles problem that they found more difficult than I expected them to. We'd practised similar questions from MathsPad and Don Steward in class. I'm confident that they know their angle facts, so it's the reasoning rather than the underlying knowledge that got in the way here.


Our students had a lot more success with the question below - a skill we had dedicated some time to in lessons. Forming equations to solve geometry problems is such an important problem solving skill, we do a lot of practice of this in Year 7 and 8. It also helps that it's not a wordy question.


With this next question, it was interpretation of the information given (the perimeter of the large triangle) and then understanding of what the question was asking (for the perimeter of the whole shape - which doesn't include any of the interior lines) which caused difficulty.



Finally, the last question on the calculator paper was designed to challenge our highest attainers. Many students picked up marks on the first two parts, but only two students in the whole year group showed a correct approach to the final part. This tested their knowledge of calculating a mean from a table and solving equations. I adapted this question from a Hong Kong exam paper (see Gems 168).



My Key Stage 3 assessments are here if you'd like to see the papers for Years 7 - 9. Note that I didn't write the questions myself - they are from various sources. Many of the questions are from the AQA Key Stage 3 assessments. There's lots of challenge in these assessments, but we don't accelerate beyond the topics on our schemes of work. No one got 100% in Year 8 and 9, but we did have one Year 7 student get full marks. Impressive!










28 December 2021

What Secondary Teachers Should Know About The Key Stage 2 Maths Curriculum

How confident are you that you know what your students were taught at primary school?

Look at the questions below. How many of these skills are covered by the Key Stage 2 curriculum?


I'll give you a clue: three of them are covered at primary school, the rest aren't. Do you know which ones?

For an upcoming talk I'm planning, I've been busy researching the feedback that maths departments have received from Ofsted (and 'mocksted') deep dives. One thing that I've noticed come up a few times is:

"Teachers of mathematics do not know enough about what students have learned in the past"

Secondary teachers should definitely know what's on the primary curriculum. And it's not good enough to have a 'rough idea'. Knowing the primary curriculum well helps us build a strong Key Stage 3 curriculum, and improves the effectiveness of our teaching, particularly in Year 7. 

This is easy to fix. The main problem is time. I think most secondary teachers agree that it would be good to know what's on the primary maths curriculum. But we struggle to find the time to find out. 

So I have tried to be helpful! I researched the primary curriculum from a secondary teacher's perspective (I had a pretty good knowledge of the primary curriculum already, but there were a few things I didn't know, so it was a very worthwhile activity for me). I then made a presentation summarising the key points. And then I recorded it and put it on YouTube:


 


This is only 43 minutes long, so if you want your whole department to watch it together then it should be short enough to fit in a department meeting.

The majority of the presentation is me describing the key features of the primary curriculum. In the last ten minutes I offer some advice for Key Stage 3 teaching.

The slides are here.

I hope this is helpful! Basically from reading Ofsted reports I identified a gap in maths teacher knowledge and decided to try and fix it.

This took quite a chunk of time out of my Christmas holidays, so if you find it helpful and want to say thank you, you can buy me a drink here. Cheers!





27 September 2020

5 Maths Gems #135

Welcome to my 135th gems post. This is where I share some of the latest news, ideas and resources for maths teachers.

I think we have a winner for the most intense September of all time! I can’t believe I complained about how busy I was during lockdown - September 2020 has been a whole new level of exhaustion! I’m sure many of you are in the same boat. I haven’t had time to blog, or even tweet, because I've been working until I go to bed every evening. But it’s ok, because I know September is always a killer, and I know it’s doubly difficult this year because of a global pandemic which is outside my control, and I know it will get easier. 

Anyway, on with the gems… I have ten for you again today.

1. Booklets
Thank you to Ben Sinclair (@mathsacharya) for starting to share the GCSE and A Level knowledge booklets that he uses in his teaching. These are high quality, and it's really interesting to see a booklet approach in action. Ben has borrowed lots of excellent tasks for these booklets, including plenty of Don Steward.

2. Ultimate Scheme of Work
Craig Barton (@mrbartonmaths) has launched the Eedi Ultimate Scheme of Work for Years 6 to 11. It's free to use. I've just had a play with it by selecting the White Rose Year 7 Scheme of Work. The Scheme of Work comes up in a calendar format, and I can then click into each topic to see the associated multiple choice quizzes. These quizzes can projected on the board for use during lessons, or set as quizzes for students to complete online.


I love the new feature where each quiz question displays previous results and explains a common misconception. 


3. Corbett Maths Books
If your school uses Corbett Maths 5-a-day exercises on a daily basis, it will save you a lot of time and effort if you buy the new Corbett Maths 5-a-day books instead of doing all the printing yourself. These books are available to buy here, and John Corbett explains how they work in a video here. These are great for both exam revision and for ongoing retrieval practice.

4. The Maths Masterclass Tutorials
Simon Singh is offering free weekly online maths masterclasses to increase the diversity and number of excellent mathematicians. Parents and teachers at non-selective state schools can nominate children from Year 8 to 11 to be part of this. The deadline is 9th October and there is more information here.

 

5. Backwards Fading
Chris McGrane (@ChrisMcGrane84) has shared a task on trigonometric equations that would be suitable for A level students. This is a great example of a task which uses a backwards fading approach, with self-explanation prompts.


6. Key Stage 3 Resources
Richard Tock (@ticktockmaths) shared a great lesson on adding and subtracting fractions. It features this fractions function machine task which I thought was rather nice.

Another useful task was shared by Siobhan McKenna (@ShivMcKenna55). Often students claim that 'division is much more difficult than multiplication' - this task aims to help students make sense of the connections. 
7. Indices
George Stone (@DrStoneMaths) used this task in his first A level maths lesson with his new Year 12 class. The questions are taken from variationtheory.com.

George says that highlights of the lesson included students noticing that Question 1 (a), (b) and (c) are the same and the base doesn't matter, and students getting stuck on Question 2 (e) until they noticed that 1 = (1/20)0. He also said that the challenge question blew their mind. What an engaging set of questions. I like the way that George includes an answer box on his slides - this is a really helpful technique, allowing students to check their understanding when working independently.

Another task shared by George is this set of inequalities questions for developing fluency. Students often find it quite challenging to say these statements out loud. 

8. NCETM Resources
Thanks to Debbie Morgan (@ThinkingMaths) for tweeting about the Key Stage 1 and 2 video lessons which were created by Maths Hubs and published by the NCETM during lockdown. The PowerPoints have now been shared on the NCETM website so other teachers can borrow and adapt the lessons. Thank you to the teachers who have shared these resources.

Something else worth checking out on the new NCETM website is a one hour CPD session which secondary school maths departments can use in a department meeting. This CPD encourages schools to review their Year 7 provision in the light of new DfE primary maths guidance which I blogged about in Gems 132

The new NCETM website is considerably better than the previous one! The content is now available without a login.

9. Exam Preparation
Thanks to Mr Strachan (@MrStrachanMaths) for sharing this video from Eddie Woo (@misterwootube) which models what exam preparation looks like in maths:

   

Eddie then shared a blank copy of the sheet he gives to students to support this process. I particularly like the exam review page which encourages students to consider the reasons why they lost marks.

10. Perimeter Task
Miss Konstantine (@giftedHKO) continues to share great tasks on Twitter. A recent example was this task that she used with Year 10 to help them remember to find the perimeter and not just the arc of sectors and semi circles.
Updates
I have two online presentations coming up this week. The first is after school on Thursday, when I'm doing a short talk on "Maths Teaching in 2020: Challenges and Opportunities" for the North-East Hants and Surrey Maths Hub. 

On Saturday I will be speaking about my experience of teaching Key Stage 3 at #mathsconf24. If you haven't booked yet, tickets are available here. I'm also looking forward to recording a conference podcast with Craig Barton at the end of the day.

Congratulations to the team at Just Maths and Kangaroo Maths for launching their new crossover GCSE revision book. Check out justaroo.co.uk for more information and to order.

Finally, congratulations to Jamie Frost for his nomination for the Global Teacher Prize, which has received a lot of publicity this week. I first featured drfrostmaths.com in Gems 41, back in October 2015. It won one of my Gem Awards in 2016. I have blogged about this website numerous times, but it no longer needs any introduction from me. It is incredibly popular among teachers and students, and it's great to see Jamie get the recognition he deserves for his tireless efforts. 

I'll leave you with this wonderful video from @Ayliean. If you're having a tough time at work, watch this. It will cheer you up.







30 August 2020

5 Maths Gems #134

Welcome to my 134th gems post. This is where I share some of the latest news, ideas and resources for maths teachers.

This is a double gems post! Lots of ideas and resources have been shared on Twitter in the last few weeks and - given it's the calm before the storm (i.e. the weekend before the start of what might be the craziest school year yet!) - I better post them all now, before things get too busy.

1. Games
Thank you to the wonderful @Ayliean for sharing her favourite short classroom games. They’re suitable for use with a whole class whilst the students sit down and the teacher runs the game on the board from the computer - this is good when social distancing measures are in place. I can imagine that some of these games might work well when getting to know a new tutor group. Open the file here for clickable links, and also check out the teacher guide with tips and curriculum links. 
I've just played some of these games - lots of fun!

2. New Resources
Thank you to @Miss_R_Em for sharing some some great angle reasoning worksheets on Twitter.

            
3. Quotes Display
I love this 50 Mathematical Quotations display from @nathanday314. I have added it to my Displays Page.


4. Videos
In Gems 133 I shared a video made by @McGuirea499. Mr McGuire has now made his own Youtube Channel. He's shared a number of new videos recently including a series on ratio tables. Here's an example:


@McGuirea499 has also launched the website makeemthinkmaths.com which features resources, ideas and videos.

5. Further Maths Resource
@MrsMathematica spotted a helpful resource on TES for anyone who teaches A Level Further Maths. Revision 4 Questions for AS Further Maths by Mel Murray is a set of tasks that could be used as starters for Year 2 students to revise AS content. 

A Level teachers might also be interested in @mathsaurus's new pages of A level exam questions by topic for each chapter of the Year 1 and Year 2 textbooks. All questions are from sample and 2018 papers for Edexcel, OCR A and B and AQA for the new syllabus. 

And whilst on the subject of A Level, I love this task on related binomial expressions from @360maths


6. White Rose
Those of you who follow the White Rose Scheme of Work will love @mrshawthorne7's spreadsheet for Years 7 to 9. It contains hundreds of links corresponding to the White Rose small steps, including tasks from Don Steward, ⁦‪@giftedHKO‬⁩ and ⁦‪@ChrisMcGrane84‬⁩. The link is on Charlotte's website

White Rose users will also like @BenBent05826467's work on linking UKMT questions to the White Rose scheme of work. 

7. Primary Resources
In Gems 132 I wrote about the publication of the Department for Education's of Mathematics Guidance documents for the Key Stage 1 and 2 national curriculum, and the accompanying CPD videos. 

The NCETM (@NCETM) has now shared a set of resources to accompany the ready-to-progress criteria. Written in collaboration with Nrich, the first of 79 PowerPoints can be downloaded from the NCETM's newly revamped website.

8. Vocabulary Map
@MissACMaths created a lovely map of maths vocabulary showing how it all links together.


9. Mr Carter Maths A Level
@MrCarterMaths has launched an exciting new A Level website which will be free for at least the first year.  
You can watch a video here to see how a pupil uses the site, and one here on how a teacher uses the site.

A similar site for GCSE is planned for next September.

10. Timers
I love a slick, professional PowerPoint. Thank you to @DrStoneMaths for sharing some transparent timer gifs for use in PowerPoint, based on a design by @nathanday314. They range from one minute up to ten minutes. 

On the subject of good resource layout, do have a look at this thread where @nathanday314 makes some great suggestions:

Update
For those of you who took the summer off and have missed some of my posts, here's what I've written since July:


I also updated my popular Year 7 Maths Activities post with ideas for first lessons with Year 7.

Another change to my blog was the addition of a 'buy me a drink' button! Thank you so much to the lovely people who have already used this - I am really touched by the kind messages.

Earlier this week I ran two webinars for The Mathematical Association called 'Preparing for September'. A global Zoom outage meant that the Monday afternoon session couldn't go ahead, but I was able to rearrange it for Wednesday. Thank you to everyone who joined me for one of the two webinars. The recordings can be viewed here and the slides are here.

 

Another thing I did over summer was made a resource based on the old textbook exercise below. I like the way it presents the problems in pairs: one with numbers, one with algebra. I've done this in class discussion before but not as an exercise. 
Image

I've started planning my workshop for #mathsconf24 which will be run online on Saturday 3rd October. I'll be sharing ideas for Key Stage 3. Tickets are still available!


A few weeks ago I tweeted an open invitation to Friday night's 'socially distanced maths teacher drinks' in London to celebrate the start of a new school year (and commiserate the end of the holidays!). Thank you to the ten tweeters who joined me - it's always great to meet new people, and to catch up with old friends after so long. I really missed the socialising of the summer conference season this year. 


Thank you to @MathsTeacherKYP⁩ for the giant calculator. I will lend this to students!



Here are a few things you might have missed if you've been staying away over summer:

I'll leave you with this lovely activity 'Number Pyramids' from @MathforLove, along with helpful slides made by @fawnpnguyen, which include extension tasks.
 




Those of you going back to school next week - enjoy! And good luck. See you on the other side.








30 August 2018

Year 7 Maths Activities

Craig Barton has just released his podcast Slice of Advice: First Lessons. It's packed full of good advice so do have a listen. In my contribution to this podcast, I promised that I would share some activities for first lessons (or indeed, any lesson) with Year 7. Here we are looking at activities that are accessible without being patronising, and give students the opportunity to show us what they can do (mathematically speaking) as we circulate and meet them for the first time. There are hundreds of great activities that would work well. This post features just nine examples. The pictures shown are only extracts - please click on the links for the full resource.

1. In-Betweens from Colin Foster
This is an enjoyable and highly accessible activity with a good stretch task. It will start to give you a good idea of how much your new Year 7s know about place value.
2. Rainbow Squares from Math Pickle
The idea is to find pairs of numbers that add up to square numbers (children were taught square numbers at Key Stage 2).  There is a high level of challenge as the task progresses. If anyone struggles to get started here they could be given a list of square numbers.
3. Addition Pyramids 
In Gems 84 I wrote about the time I saw this classic activity in an interview lesson. It's really simple and engaging. It looks like it may have been based on this Nrich task.
Read this post to see a similar task in action.

4.  Consecutive Chains from MathsPad
I love this - it's fun for everyone! Children first meet square and cube number in Year 5 and should be familiar with primes, factors and multiples. I think this task will be accessible to some Year 7s (perhaps after a reminder of number properties) but not all.
5. Shape Time Shape by Nrich
In this lovely task the coloured shapes stand for eleven of the numbers from 0 to 12. Each shape is a different number. Students have to work out which is which. This is an accessible and enjoyable task that gets students noticing and reasoning.
For an accessible introduction to tasks like this, check out the shape IQ puzzles here.

6. Loops by Colin Foster
This pattern spotting task is slightly more challenging, but still accessible. This is good if you want your students to start secondary school with maths that looks quite different to anything they've done before.

There are loads more lesson activities in this set of numeracy activities from Colin Foster. I particularly like 'Musical Composers' and 'Number Triangles'.

7. Number Properties Challenge from Stephen Bodman
Give students three or four random digits and they have to generate numbers with specific properties - such as 'biggest number', 'smallest odd number', 'number closest to 3000' and so on. You can download the resource from TES and it could become a regular feature of your Year 7 maths lessons.

8. Find the Factors from Iva Sallay
It's a good idea to quickly identify any students who don't know their times tables so you can provide them with support. Instead of giving them a times tables test, you could ask them to complete some Find the Factors puzzles. These multiplication based logic puzzles are fantastic. Students are given a standard multiplication grid with only a few numbers completed, and they use their knowledge of times tables to deduce the numbers around the outside. Then they can complete the rest of the grid. The difficulty levels vary from super simple to very challenging. 
9. Various Puzzles
There are numerous puzzles that involve logic and arithmetic and are suitable, and enjoyable, for Year 7s. They include Yohaku puzzles which test number sense and problem solving skills, and KenKen puzzles which help develop arithmetic fluency and reasoning skills. Other good sources of activities include Searches and Crossums from Frank Tapson, Magic Squares from Don Steward, and this page of puzzles which features Tenner Grids, Fubuki, Shape Boxes and lots more.



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After the first lesson, I'd get straight on with teaching the content of the scheme of work. We must of course be mindful of what maths our students have been taught at primary school, but take into account that they are likely to be a bit rusty after the long summer break (this applies to every year group!). If you have one main feeder school it's worth finding out if there are any particular methods (e.g. bar modelling) that your students will be familiar with.

All secondary teachers, but particularly Year 7 teachers, should know the content of the primary maths curriculum. This summary by Michael Tidd is very helpful, and perhaps worth looking at during a maths department meeting at the start of the new school year. It's also a good idea to look through the SATs papers that your new Year 7s took at the end of Year 6. To help you translate their SATs scaled score data - in 2018, a mark of 61 out of 110 (i.e. 55%) translated to a scaled score of 100, which is the Government's 'expected standard' pass mark. Of course the numbers don't tell us much, so hopefully our students will start to show us much of their mathematical knowledge and understanding over the first few weeks of Year 7. We must give them the opportunity to do so!