Archive for the ‘Number’ Category

A Journey into Manipulatives Part 1

For the first time that I can remember, I am in an appraisal process that is aimed at both my development as a teacher and as part of a department.  Three specific appraisal targets which I’m really excited to get my teeth into.  The plan is to blog about all of these, but one target at a time…

So firstly, my second target is to develop the use of manipulatives in my teaching and to share these strategies with the department. There is a particular focus with my lower prior attaining year 8 group, but not restricted to just this group.

Prior to this year, I’ve started introducing myself to the use of manipulatives with the following:

  • Attending a workshop from Johnny Hall @studymaths on the use of double sided counters, including his amazing websiteVisible Maths.png
  • Attending a workshop from Bernie Westacott @berniewestacott on the use of double sided counters
  • Attending a workshop from Peter Mattock @MrMattock about division, and the use of cuisinere rods
  • Dipping into Pete’s book Visible Maths (the negative numbers part so far) Teaching for Mastery
  • Attending a workshop on manipulatives and their representations exploring algebra tiles
  • Reading Mark McCourt’s @emathsuk book Teaching for Mastery – a huge influence on how I approached and presented
  • Attending a workshop from Dr Liz Henning on the use of manipulatives to deepen conceptual understanding (see notes here)

Double Sided Counters

Amazon Double sided counters.pngFrom these, I have made use of double sided counters when teaching negative numbers.  To begin with, I printed out some squares, with a yellow 1 on one side and and red -1 on the other side.  A bit fiddly, but did the job as I introduced negative pairs and adding and subtracting with negative numbers.  I’ve since upgraded to actual double sided counters (Amazon – 2 packs of 120, so 16 sets of 15 for classroom use).

So to the actual lessons and use of the double sided counters.  The learning plan goes like this:

  • Use of number line with negatives as starting points or ending points
  • Context questions
  • Introduce double sided countersIntroducing double sided counters
  • Zero pairThe zero pair
  • Playing with counters
  • Adding a negative and seeing resultAdding a negative
  • Quick questions
  • Subtracting a negative and seeing resultSubtracting a negative
  • Quick questions
  • Mixture of adding and subtracting negative numbers (for some groups I used these questions from

The powerpoint I made is here: Add and subtract negative numbers.  You’ll have noticed the links – there was lots of talk and playing, with demonstrations using Johnny’s site.

I am still looking to improve and refine, but so far the students appeared to make sense of what was happening.  Ideally, I would have liked more time, as always!  My year 8 group used the counters to help with the questions, whilst there was a mixture from my year 7 groups.  The higher attaining students, who had learned shortcut rules previously, wanted to just use “the rules”.  For other students, some fell back on these rules, whilst others were writing out the R and Y to help them.


Two Lessons, Two Year Groups: Translation and BIDMAS

The final #MTBoS blogging challenge is about a lesson taught this week.  I couldn’t decide between two of them, so thought I’d write about both, being two quite contrasting groups.  Firstly,  year 10 (14-15 year olds), who find maths quite challenging and haven’t had much success in their achievement over the years, but are working extremely hard and hopefully becoming more confident, learning about translation and then year 7 (11-12 year olds) learning order of operations, a group full of high achieving pupils.


Both lessons started in exactly the same way, with the brilliant Numeracy Ninjas by @maths_master William Emeny (greatmathsteachingideas). I do some sort mental arithmetic or skills practice at the start of every lesson, as not only does it set the routine for the pupils, it settles them into thinking right from the start of the lesson, and ensures their numeracy skills are regularly practised to support with the fluency when tackling tougher topics. For the year 10s, they are focussing on the first two sections, mental numeracy and timestables, whereas year 7 whizz through these two sections and focus on the key skills section. We then pick out a question that pupils struggled with to review, before launcing into the topic for the lesson.

Year 10 Translation

I knew when planning this lesson that the year 10 group studied translation last year, so they should know what it is.  However, they wouldn’t have used vectors before, so this was the focus of the lesson.


We started with a quick reminder of translation, then headed straight into what a vector was. An explanation from me, some note taking and a few vectors for the pupils to think about what they mean.
imageWe then spent a chunk of time identifying the vectors that would move the points, and then  shapes.
This was whole class questioning, and they weren’t allowed to use the words left, right, up or down, just the two numbers in the vector.  I, of course, threw in a question where there was only movement in one direction, and pupils discussed how they would give the vector for that. Then pupils had their own practice time in their books. As I circulated, I caught a couple of pupils writing their vector as a co-ordinate pair, and we stopped and discussed the different between a co-ordinates being a position and a vector being a movement, and therefore had to be written in the correct notation.

image    image

Once pupils were more secure in their vector writing, they then had a lovely translation activity from @just_maths (as a school we subscribe to Just Maths Online). We discussed the importance of identifying a vertex to complete the translation from, and to check they are completing the translation correctly, they could choose another vertex and repeat the translation.

And that’s it! I don’t really do bells and whistles in my lessons, I just aim to teach the pupils as best I can and give them the time and support to practise and hone their learning. In a few lessons time, we’ll be bringing all the learning on transformation together, where pupils will have to carry out or identify the correct transformation, including combinations.

Year 7 Order of Operations

Before I taught this, I knew that most, if not all, of this group would have been taught  about order of operations at primary school, so this would be a revision and stretch lesson.  I had to ensure they knew and understood the basics, but be ready to give them a bit of a challenge.image

I love foldables as an alternative to note taking, and I have a BIDMAS Foldable I created for this topic. I teach order of operations as BIDMAS, being careful to keep DM and AS on the same level.  The only sticking point was that pupils had been taught BODMAS previously.  We discussed what order and indices mean, and I explained why we use indices at secondary school (in the mathematical vocabularly they are excpected to know).

The skills practise involved 3 levels of questions. Pupils could choose the level to start at, and several went straight for the gold challenge, whereas others wanted a bit of practise on the more straightforward silver questions first.image

The challenge activity was a calculation square from Don Stewards Median website. I really liked this activiy, as it did make the pupils think.  Not only did they have to remember the order of operations, but they had to think about where to start and what each calculation was asking. Pupils who found the gold questions starightforward minutes ago, were feeling quite puzzled about this one.

imageWe finished the lesson with another Don Steward activiy, bracketed, from which I chose 5 equations for the pupils to decide if they were correct, or if they needed brackets in. Although mostly identified correctly, the biggie that came out of this was pupils thinking the 5 x 6 needed brackets in 2 + 5 x 6 = 32.

Unfortunatley I don’t have any photos of these pupil’s work as they have their books for revision!  The powerpoint is attached BIDMAS.

You can probably tell that I have go to places for resources and activities in my lessons. When there is so many quality resources around, thanks to the generosity of so many maths teachers sharing their work, there’s no point reinventing the wheel!  I do plan my lessons thinking of the outcome first, and then looking for activities which will enable this outcome for the pupils.

I hope you’ve enjoyed these lessons.  I’m looking forward to reading and being inspired by others in the #MTBoS challenge who have shared their lessons too.


Numeracy Picture Puzzle (Division)

Division PuzzleI came across this idea on, although I’m sure many others have also used or made something similar.  It’s quite straightforward, pupils complete 9 calculations, find the answers on the puzzle pieces, and put them in the same order as the questions to make a picture! So I made this one for the decimal division that one of my groups is currently working on.

I don’t give the scissors out until the questions have been attempted (as otherwise pupils can easily put the puzzle together!)  The bonus of having the pieces with the answers on is that pupils can self-check as they are working.  There is no reason for the cutting and putting together of the puzzle, other than it is a motivating factor to complete all the questions, giving the pupils well needed practice!

Decimal Division Puzzle

Speed Dating with Fractions, Percentages and Decimals

When preparing a resource to take and share at mathsconf4, I wanted to share something which I find valuable and seems to make a difference to pupils learning. So I chose a resource, originally from TES (complex_number) for a topic I find pupils struggle with, yet is a basis for so much mathematics: converting between fractions, decimals and percentages. The resources I use are for groups with little or no understanding of the connections between the three as they start off quite basic.

It starts with a slideshow of artwork where proportions could be viewed as a theme. IMG_0337This includes works from Piet Mondrian, Victor Vasarely, Ellsworth Kelly and Frank Stella. With a quick review of what fraction, percentage and decimal (based on a 100 square, so using £s and p to support the decimals) mean, pupils then create their own artwork on their 100 square.  They then use their art work to write the fraction, percentage and decimal of each colour used.   The advantage of using this resource has been to consolidate the connection between the fraction out of 100 to the percentage. IMG_0339 The next step is to move onto a 50 grid, 25 grid, 20 grid and 10 grid, and hence the need to change the fraction to out of 100 in order to write the percentage.   Accompanying the grids are some fraction, percentage and decimal tables, with an extra column for the fraction out of 100, for pupils to practise their conversions. IMG_0342 IMG_0343 A similar resource I’ve used is a skittle pie charts. I’ve done this by giving out skittles (20, 25 or 40) and pupils to make their own circles, grouping the colours, section ing them off and writing the fraction, percentage and decimal for each section. I’ve also given out a template for pupils to colour in given skittles (this was actually to help with interpreting pie charts, but linked in nicely to the fractions, percentages and decimals work the pupils had completed previously. IMG_2292 IMG_2293  IMG_0338 All the files are linked below to use and adapt as wished! 1. Equivalent FDP Mosaic 2014 1. Mosaic Art 1. Mosaic Fractions Sheet 2. FDP Calculation Foldable 2. FDP Starter 2. Interpreting pie charts 2. Interpreting Pie Charts 3. FDP The original idea and basis for these came from TES (complex_number) and an American website, all freely available.  I’ve adapted into my own documents and made them to suit my groups.  Thanks, as always, to the originators of the ideas to sharing so freely, allowing me to use your ideas in teaching my groups.

Unlocking Numeracy

I pinched a great idea from Tes last week for a numeracy activity (sorry to the person who shared I can’t remember who you are to reference you).  Pupils had to find the code to open the padlocks to the box.  Simple and probably used by many people before, but first time I had used the idea, and definitely one I’ll use again.  It was with a bottom set year 9, and most were really motivated to completed these column addition and subtractions, including borrowing and decimals, so they could have a go at unlocking the box.


You might notice the locks didn’t actually lock the box, but the pupils played along!

Locks Column + –