# nRich games to practice key skills

There is a range of “take turns” dice games like this one on nRich.

I see this activity as a way of practicing key skills (in this case column addition) but in a much deeper way than repeated practice as you are working backwards to achieve a result.  I would think of this as adding a significant degree of difficulty over simply doing a page of sums; it would be something you would only chose to do once the basic process of column addition is reasonably secure. However, because it is engaging (i.e. competitive) students are more likely to stick with it.

To avoid the need to provide students with 10-dice an interactive dice could be displayed on the board. nRich have this handy spinners tool here and there are lots of other options online.

All students would then have the same set of numbers and it would be a competition to get closest to 1000.  You might need to note down the numbers as you go to prevent cheating!

Again, of course, the value in the activity comes from the discussion, both in pairs and in whole class.  I like the idea of saying that the target is 1000 but actually rewarding good discussion and reasoning rather than just closest answer (i.e 5 points for a new “noticing”, 5 points for the closest answer)

Another way is to determine all the required random numbers at the outset and the students can fill in the grid with full knowledge of their options.  Less luck involved and so probably less fun!

I would do one game whole-class, where students are playing individually. Then a second game where students are to work together in pairs competing against another pair so they can compare strategies once they have a degree of familiarilty with the problem and get some good discussion going on strategy.

# Reinforcing Place Value at every opportunity

So, I learnt something today from a kid in Year 3.  He gave a perfect explanation of a column addition that made me stop and think.  How would you explain this?

His explanation:

“4 plus 1  is 5, so put a 5 in the ones column. Then twenty plus ninety is one hundred and ten, so we put a 1 in the hundreds column and a 1 in the tens column.  Then one hundred plus three hundred is four hundred so put a 4 in the hundreds column”

This has got me thinking about where else I can reinforce place value when discussing procedures.

# What does “doing” Growth Mindset look like?

The first thing I need to make clear is that I am not the expert able to answer this question comprehensively – well not yet, anyway. (That’s a Growth Mindset, by the way…)

I would love you to read this and help me answer my question. I’ve read a bit myself from esteemed academics such as Carol Dweck and @JoBoaler, seen fabulous teachers like @Helenhindle1 talk about how they do it, but not really done it in my classroom yet. I’d like to think that I use a lot of the language of growth mindset routinely, but one of my targets for next year is to do more to instil a growth mindset in my students.

## What is a Growth Mindset?

My view: at its most basic it is simply students believing in themselves, having greater resilience and recognising that their abilities in Mathematics (or anything else for that matter) are not fixed and that by applying themselves consistently and working at it, they will “get better” at maths.  And it is not just about encouraging lower attaining students.  As Jo Boaler points out in in this article we need to avoid the label “smart” to prevent those kids baulking at challenging problems that they might get wrong first time round.

## Getting the message across

What we are trying to do here is genuinely change students’ self-perception. Just telling students to “change their mindset” is likely to backfire. So we need to convince them why it is true. This is not easy and isn’t going to happen quickly.

Growth Mindset Maths is a great site which contains lots of resources to use.

This lesson plan that has been developed by Khan Academy and PERTS (Stanford Univ.) looks like a great way to introduce Growth Mindset for secondary students.  We all need to develop a good “Personal story” of when we overcame challenges and adopted a growth mindset. PERTS are developing a Mindset Kit which is worth keeping an eye on.

I’m sure there are others out there who have developed resources too. If this is you, please get in touch!

So, here is my list of things I want to do next year.  What have I missed? Please let me know!

• Specific lessons. At the beginning of the year, we can spend some lesson time doing activities such as these.  There is a need to introduce the ideas and talk about the language we will use in the classroom for the rest of the year.  Do we need to spend further lesson time on specific growth mindset tasks later in the year? I guess I will take a wait-and-see approach to that.
• Posters. This really should be a whole school initiative.  Some of them remind me of my time in corporate life when companies went through a phase of putting up “inspirational” posters with words like “Success” and a picture of a man standing on top of a mountain looking very pleased with himself. There may be some cynical reaction to posters but I feel overall they are a useful part of the mix.
• Celebrating success. And particularly highlighting “Success Stories” – individual students who have adopted a growth mindset, worked hard and have the results to show for it.
• Everyday language.  Obviously using it yourself as a teacher, but also picking kids up on it every time.
• Communication with parents.  Ultimately maybe actually trying to run sessions with parents? I don’t know successful that would be, but at the very least using parents’ evenings as an opportunity to use the right language – having a few of those posters prominently displayed will help.
• Written feedback. Whether it is student reports / profiles or written feedback as part of marking, again being diligent to use the right language in that feedback.

Finally, I love the beginning of a new BBC programme called Kick Sum Maths.  The first 2 minutes or so of this ticks all the boxes in my view and would make a good introduction.

## The question of Mixed Attainment teaching

A logical conclusion of the Growth Mindset philosophy may be that you do away with sets and this is certain something Jo Boaler strongly advocates. However, few UK schools have done this. I’ve struggled to find recent data, but an Ofsted survey from 2003-4 found that 17% of schools taught in mixed ability groups at KS3.  Tory and Labour Government policy since this time has tended to promote setting, so I can only imagine that number has gone down since. A more recent blog by Chris Husbands, Director of IoE concludes that the evidence of the effectiveness of setting is “nuanced”.  I can’t help feeling that behind all of this, there is pressure from parents to maintain sets, particularly the more vociferous middle-class parents who are less likely to have kids stuck in the bottom set.

Personally I don’t have a strong view on this. I would be interested to see mixed attainment teaching in practice before forming that view.  But I do feel that most schools and most teachers, would find it a big challenge to switch to teaching in mixed attainment groups.  Does it require a higher level of skill in teaching to differentiate more widely and use mixed-attainment group work effectively? Or is it a question of just getting used to it and adapting to a different way of doing things?

# Place Value – what is 34 tens and 15 ones?

I’ve been doing a Lesson Study this week with 2 colleagues on Place Value with a lower attaining Year 7 group. I might write about that later, but in the meantime, here is one of the resources that we have developed. I think it’s hugely differentiated, fairly low threshold high ceiling task.

In the lesson, I just wrote a few of these on the board.  It was something I hadn’t used before so I went away thinking about the range of difficulty in these types of questions and wrote a series of questions here.

# Uncovering Fraction Misconceptions through True and False cards

Having been inspired by some ideas from Resourceaholic and also from Robert Wilne @NCETMsecondary here, I thought I’d create these True or False cards for use with Year 7.  We have covered fraction of an amount, equivalent fractions, adding fractions, and top heavy / mixed numbers so far, but you could easily adapt these if you want to include, for example, multiplying and dividing fractions. I designed the false ones first which really got me thinking about misconceptions that I think could be occurring.  The true ones were relatively straightforward after that.  Enjoy!

Here they are as a Word doc: Fractions True False cards And if the formatting looks a bit weird, as a pdf doc: Fractions True False cards

# Sometimes you just need to write your own worksheet.

Adding fractions with year 7 today. We’ve spent a bit of time examining equivalent fractions so I felt we were ready. I used an idea that was developed as part of a Lesson Study that I worked on with 2 other teachers a couple of years ago. In the lesson itself we used fraction walls to reinforce the idea of equivalents. After over an hour, we were there, with most being able to find equivalents and successfully add fractions, some no longer using the fraction wall.

So, on to the next lesson. I feel like I have a good sense of how they need to develop this and how I need to scaffold it for them. It’s one of those occasions where I could hunt around online and in text books to find a set of questions that might be OK. Or, if I sit down and think deeply about this, in 10 minutes I have the perfect set. For my class. At this point in their learning.

So here they are. You never know they might be perfect for your class too. But it’s not very likely!

# Learning times tables – Number Happy Families

I’ve always felt that secure knowledge of times tables at Year 7 is so important simply because it gives kids the confidence to engage in so many maths topics covered in that year.  As such any opportunity to practice is good even when it is in a simple game like this.

# A Simple Factors and Multiples Team Game for 3-4 players

I came up with this idea whilst playing the traditional Happy Families card game with my family when on holiday. Kids seem to love this game – could I create a maths game as engaging?

I’ve tried this several times with Year 7 classes, playing in teams of 3 or 4 and they love it.

It takes very little preparation or explanation – in fact the students make the resources themselves!

# The Cards

You need a set of 36 blank cards for each team. Anything will do.  I spent about 10 minutes furious chopping on the guillotine for 7 teams, getting 12 cards out of each A4 sheet, so 3 sheets per team, 21 sheets in all.

The learning starts by getting the teams to create their cards using the following instructions:

1, Arrange your cards into 4 columns by 9 rows

2, You need to write the first 4 multiples of each number 2 to 10 so that every card has a number on it.

I put the 36 blank cards and the above on a slip of paper in an envelope and gave an envelope to each team.  With a bit of discussion within the teams, they worked out what they needed to do, but if you feel the task needs a bit more scaffolding you could use this diagram:

# The Game

Once each team has their cards laid out on the table, they can start playing.

1. Shuffle the cards and deal them all out.
2. The objective is to collect “families” of numbers, e.g. 3,6,9,12 is the 3 family. The player with the most families wins.
3. Play starts with the first player asking one of the other players (they decide who) for a particular card, e.g. “Natasha, do you have a 5?” If Natasha has that card, she must hand it over. The first player can ask again (again, they can chose any player). If the answer is no, play moves on to the next player.
4. When a player has a family they must lay it face up on the table.
5. Play continues until all the cards are gone – it’s that simple!