What my children taught me about multiplication and 3-d shapes.

I had wondered if talks about the boys’ study of the story of maths would be difficult to put together. When Eldest chose to research Times Tables, I wondered how easy it would be to come up with demos.
In the event, he had plenty to say and show. I encouraged Eldest to try and find patterns of his own in the multiplication tables by colouring them in on number squares.
We explored this Japanese method of multiplying numbers by drawing lines and counting the intersections. Eldest decided not to include this in his final presentation, but I thought it was great, and much easier than drawing endless bags of sweets (my usual multiplication illustration).
He did find out about the joys of the eleven times table. He also discovered that
ab + b(10-a) = 10b
He didn’t put it like that, but I found his explanation complicated! If you set out the times tables from one to nine in a grid. Take any sum you want (except the fives), then find the sum in the same column that is equidistant from the edge (which is why you can’t use the fives). Add the answers together and you will have a number in the ten times table.
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By way of example:
3×4 is the third from the top in column three.
7×4 is the third from the bottom in column three.
12+28=40
40 is four tens.
It’s not going to change the face of modern mathematics, but Eldest was having fun with numbers and enjoying making his own discoveries. Good enough.
Middly’s talk was on 3d shapes. He made some, using nets I gave him:
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He used our plastic shapes to make some designs of his own:
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He drew a plan, with a key, showing his designs.
He told us the names of many solids. He even introduced us to the concept of anti prisms (thanks to Wikipedia).
Finally he drew on our white board:
cm³ means cm cubed
Because, as he put it: ‘it’s true, but it doesn’t mean anything if you say it out loud.’
I am pretty happy with our first maths presentations. The boys have chosen to research abacuses and sand timers next!
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Test-Driving Beyond Consequences

Beyond Consequences is not just a book, there are many spin-off books and courses. I have just read the basic book. It’s by Heather Forbes and Bryan Post who have both gone on to write other, similar books.
I’ve been reading this one on my Nook. I’m trying to buy fewer solid books to leave a bit more space in the house.
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The structure makes me a little uncomfortable. Each chapter describes a problem (e.g. aggression, lying, stealing, all the usual suspects), then it describes the ‘Traditional Approach’, before giving the Love-Based Approach.
The description of the ‘Traditional Approach’ strikes me as rather hyperbolic. It suggests that traditional therapists view traumatised children as ‘manipulative’ and that many therapists insist a child should be made to ‘submit his control to those in charge.’ Having read many of the books referred to in the footnotes myself, I think this is a rather unfair characterisation of their advice.
I also feel uncomfortable with the description of the book’s approach as ‘Love-Based’. There’s an unpleasant implication that other approaches are less loving, which I don’t think is accurate.
That said, this book does have a few new ideas. It suggests, for example, that anger is rooted in fear. I found this idea very interesting.
I was struck by the chapter on adult fears, and the suggestion that my own anger, as a struggling parent, could be rooted in my own fears. When the boys’ behaviour is really difficult, I do fear for their future. I worry about what will happen to them as adults, if they continue the same behaviour. I am also aware that – though I had a happy childhood with no trauma to speak of – I am very effected by behaviours in the boys that ‘replay’ situations from my childhood. I had plenty of run-ins with my siblings as a child, and I would agree that seeing the boys interact can stir up my old disappointments and frustrations with my own siblings. Perhaps acknowledging these fears will stop them getting in the way of my relating to the boys in the moment. I am hopeful and I have been making more of an effort to work through my own feelings.
It is helping me to stay a bit calmer in the really tough moments. And ways of keeping my cool are such a vital part of parenting, I value the book for that alone.
Some of the suggestions seem a bit idealistic. The book gives the standard advice of waiting until after things have cooled off and then talking about what happened. We haven’t ever managed a book-style discussion about behaviour. When I say ‘I felt disrespected when you growled at me’, the boys do not ‘hang their heads in shame’ or say ‘I guess I was still mad about my toy breaking’, instead my children shout ‘I didn’t growl at you, idiot!’ The boys do not appreciate having discussions of what went wrong after they have calmed down. They do not want to talk about how they feel, or even how someone else might feel. But, we are working on that separately. So, it may just be a case of ‘too soon to try that’.
The book also suggests giving a child a hug and saying ‘you’re safe’ to head off a violent outburst. I’m not sure how that is supposed to work. I got bitten. Perhaps I need to try and spot potential eruptions earlier. Perhaps the boys find touch too hard, and I should try keeping my distance for now.
On the other hand, the book does say ‘expect to fail’. Which, perversely, I found rather heartening. We always fail when we try to follow parenting advice, so it’s nice to have that provided for in the book!
And we did have a really good day yesterday, more peaceful than we’ve had for a few months. Maybe as I get better at the love-based reactions, I’ll have some more of these good days.

Measuring

Every few months I rearrange our timetable. I decide what we’re going to study and how. When this happens, I always ask the boys what they would like to learn (this is how we came to be learning French). This time around, Middly said that he wanted to learn Measuring. So, here are a few activities we did to explore measuring.
First, we played with our trundle wheel.
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We made maps of the garden together.
I found some conversion charts online and we measured our feet in inches then found out our shoe size and compared it to the measurements taken in a shoe shop. I couldn’t find a good chart for working out width. But I did find this online shoe size calculator from Start right. So we used that.
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When I took my lovely break, Daddy took the boys to the woods to measure trees. They compared two methods found online:
1) Comparing people’s heights with the tree’s height.
2) The bottom method, where you see how far away you have to get before you can see the top of the tree when you bend over and look through your legs.
My mum gave us her proper scales, with two sets of lbs and oz weights and two sets of gram weights.
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We had lots of fun finding out how many ounces in a pound and how many grams in a pound. We checked the weights against one another. Then we weighed various packets of sweets to check whether we got what we paid for!
All in all, measuring has turned out to be a pretty good choice by Middly!
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‘Teaching’ French

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I didn’t plan on the boys learning languages. Their communication skills are bit delayed. We’re not worried anymore, they speak clearly almost all the time and are working very hard on their language skills. But I really thought that one language was more than enough for them to handle.
Home educated children don’t have to follow the National Curriculum and my intention was to take advantage of this freedom by skipping languages. Eldest, however, had other ideas. At school, he had French lessons so when he came out of school he asked to continue learning French.
I hardly want to discourage the boys from learning. So I went ahead and put French on the timetable.
It is, perhaps, one of our stranger lessons! We have some workbooks:
We have a CD and book set, which has a simple game to play on every double spread by Dorling Kindersley.
We also use online games from the BBC and the Duolingo app on my phone.
We have taken the boys to France twice, which they loved. We have done the traditional parenting trick of speaking French when we don’t want the boys to understand us – quite possibly the most efficient method of teaching words like ‘gateaux’ and ‘bonbons’.
My latest purchase is quite exciting. A home educating friend told about a book called The Avion My Uncle Flew. It’s written mainly in English, with a few French words scattered throughout.
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As the book proceeds, more and more French words are introduced, until the end where a letter is composed entirely in French. The idea is that, by the end, the reader will be able to understand an entire letter in French. It’s a great idea! If anyone knows of anymore books like this, please let me know!
But, basically, it’s our busy-work lesson. I want the boys to enjoy themselves, I’m not really expecting much progress. They do try quite hard, they are getting better at recognising words, I am unsure whether their pronunciation will ever be comprehensible. We make a couple of attempts at pronouncing a word, then I smile and praise their effort. Eldest finds it almost impossible to imitate pronunciations of English words that he hears frequently, so he cannot repeat the French that he hears. He makes an attempt, and that’s enough for me.
The most impressive aspect, for me, has been their sheer persistence. One year into home education and they still want to keep trying with French. I am very proud of their sustained efforts. If nothing else, they are developing their determination!
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Siblings

I’ve never been the parent of an only child. I met the big boys at the same time and brought them home together.
Obviously, there was a time when Eldest was on his own, but that was before I ever heard of my boys, back when he was with his birth family.
But, then, I’ve never been an only child either. I’m the second oldest of five children. There was another child in the family before me. Having always been someone’s sister, I was easily won over by the ‘keep siblings together’ argument.
I’m not sure what bond I expected my boys to have. I have a different relationship with each of my siblings. But, I think that I expected it to be basically positive.
Hmm . . .
The boys have a complicated relationship. They find each other very difficult to deal with at times. They remind each other of things that they would rather forget.
Having both boys around has also normalised a lot of rather extreme behaviour. Of course we can hardly test my theory, but I suspect that the boys are more aggressive because they see their brother being aggressive. When I try to discuss their difficult behaviour, the boys often respond with ‘well, Eldest does it too’ or ‘Middly’s worse than me!’
On a purely practical level, I’m not always sure which boy is responsible for broken items or missing things. This can make life a bit tricky. I think they take things when they’re feeling scared, but, if I don’t know which child is taking things, it’s confusing. I’m unsure which child is struggling at times and I find it harder to spot behaviour patterns.
Of course, the boys have to share attention and space and toys. All of that can be difficult for them. It can be difficult for any siblings, of course. But the boys, who don’t entirely trust that there will be enough to go around, probably find sharing extra hard.
We have a few techniques that help sometimes. We have Colour Coding to help decide who owns what, we have The Hat to help make choosing demonstrably fair. We have Special Toys (which are changed frequently, sometimes several times a day) which don’t have to be shared, we have special time when the boys get a bit of undivided attention. But, it’s still hard.
Living with a traumatised child is tough at times. Living with a traumatised child when you are also a traumatised child is even harder.
Of course, there is a lot of debate these days about whether siblings like the boys should be kept together at all. Martin Narey in particular is arguing that each case needs to be considered carefully since some siblings could benefit more from separate placements. But, the boys are together and we’re doing our best.
The sad reality is that sometimes I think the only people who benefit from keeping the boys together are me and my husband. We get to have them both! I would never want to be without either of my boys and I hope and pray that one day they will feel the same about each other.