I wrote a while ago about teaching basic algebra to children and taking away their fear. But what do you do when it becomes a little more complicated?
When working with a pupil recently we came across this problem:
and the child was unsure how to start. I reminded her of when we had looked at ordering fractions and asked how she did that.
“I can’t do 3/5, 8/10 and 12/15,” she said “because they are all different, so I have to make them the same. I know 10÷2 is 5 so I can do 8÷2 and turn 8/10 into 4/5, and I know that 15÷3 is 5, so I can 12÷3 and turn 12/15 into 4/5. Then I put them into order – 3/5, 4/5, 4/5 – and then I turn them back so 3/5 is the smallest and 8/10 and 12/15 are the same.”
I praised her for remembering so well and then told her this problem was just the same. It looked hard because k, m and n were all different, but maybe she could make them the same.
As soon as she started to think of the problem in that way she was able to see that m could be changed into 3n and k could be changed into 2n, so the problem was 2n + 3n + n = 1500 or 6n = 1500. Once she had worked out that this meant that n must be 250 she had no problem at all in converting 2n back to k and 3n back to m, giving the solution k=500, m=750 and n=250.
Algebra – it’s not too hard. It’s just like ordering fractions!
If you live in north Birmingham and would like to book my services as a private maths tutor, please get in touch.
There is a KS2 and a KS3 version of the book, but the blurb on them recommends getting just one or the other as the content is very similar. I’ve been using the KS3 book with upper KS2 with no problems. Unfortunately I haven’t had the opportunity to use many of them yet, but I’m itching to get a chance.
My Year 6 French beginners really enjoyed the survey where they had to find the name and age of everyone in the class. Obviously they already knew the real names and ages of their classmates, so I gave each of them a card with a French name, an age between 1 and 12 (as those were the only numbers we’d learnt) and a symbol to show how they were feeling.
You do need to monitor this activity quite closely, as some of the children will try to take the easy way out and copy answers over other pupil’s shoulders, but on the whole I found that the children had fun with it, and I heard lots of good French spoken in the classroom,
What activities or resources do you use to increase the amount of language spoken in your classroom? I’d love to hear your ideas in the comments below.
It’s the summer holidays. Hopefully everyone is enjoying the time off, but if you or your young ones are getting bored, why not have a look at these books?
For KS1: Gobbolino the Witch’s Cat by Ursula Williams. This is an old book now – I remember reading it when I was a child myself – but it’s still just as appealing now as it was then. You can’t help but feel sorry for poor Gobbolino who really doesn’t want to be a witch’s cat. The story tells of his adventures as he searches for a home where he can be just a normal cat.
KS2: Rick Riordan’s Percy Jackson series. Poor Percy Jackson doesn’t realise that he’s a demi-god until one of his teachers tries to kill him. After that his life gets seriously turned upside-down when he discovers that his best friend is a satyr and that the god of war really has it in for him If, like me, you have an interest in Greek mythology these books are even more special, but even if you’ve never been a fan of classical history the Percy Jackson series is a great read that will appeal to boys and girls alike. Start with Percy Jackson and the Lightning Thief and just keep going! I’ve finished this series, but on my summer reading list I have the second series: The Heroes of Olympus.
KS3: The Everlost Trilogy by Neal Shusterman. What happens when you die if you don’t end up where you are supposed to be? You end up in Everlost, and the only ways to avoid sinking into the centre of the earth are to keep moving or to find a ‘dead spot’ (a place where somebody else has died) to stand on. Everlost is divided into those who want to help the lost souls find their way to where they should be, and those who want to stop them. With a cast including pirates, ogres and people who can take over the bodies of the living, there is quite a battle. For younger readers it’s just a good read – for older readers it has quite an existential feel – Jean-Paul Sartre would have been proud!
KS4:Unwind (also by Neal Shusterman). This one covers some quite gritty issues. Imagine a world where it is illegal to terminate a pregnancy, but when your child reaches the age of 13 you can change your mind. If you decide that having your child was a mistake you can apply to have them ‘unwound’, which involves every single part of their body being used in transplants to save other people’s lives. How would you feel if you had grown up believing your family loved you until the day the authorities come to unwind you? How would you feel if you had grown up in a family that believe in donating 10% of their possessions to charity, and you are their 10th child? This book follows the lives of some children who are on the run to save their lives. To escape the ‘unwind order’, they must stay alive until they are 18.
Young Adults: There probably aren’t many people who haven’t already read Suzanne Collins’ Hunger Games Trilogy, but if you are one of them – what are you waiting for? It’s set in the future after there has been some sort of uprising, and the divide between the rich and the poor is very clearly defined. As a punishment for the uprising, the various districts are forced to enter two of their young people, one boy and one girl, into a contest where they have to fight to the death in the name of entertainment. Katniss Everdeen and Peeta Mellark may be teenagers, but the action is tense and fast-paced enough to keep adults turning the pages as well. I have heard a few critics say that this book is just a rehash of Stephen King’s The Running Man, but to me this seems a bit harsh. It is true that The Running Man was probably more visionary at the time, because reality TV wasn’t the bulk of entertainment in those days, but The Hunger Games is more than just reality TV taken to extremes – especially as the plot unfolds further in the second and final books.
These are my recommendations for summer reading. What are yours? I’d love to hear your suggestions in the comments below.
I’ve lost my Gran.
She’s still there,
I see her every Sunday.
She still sits in her favourite chair by the fire,
which is always on, even in summer,
because she says she’s cold.
Sometimes when she sees me, she smiles,
asks how I am and how my friends are.
We natter about the neighbours,
gossip and giggle.
We play her old wartime music,
sing along together
even though I don’t know the words.
But sometimes when she sees me she’s confused,
doesn’t recognise me,
calls me the wrong name.
That makes me sad.
Sometimes she’s scared of me, and that’s worse.
Thinks I’m a doctor come to put her in a home,
or a thief after her jewellery and nick-nacks.
Sometimes she shouts and swears,
has tantrums and throws things,
kicks and scratches, bites.
Then I don’t recognise her,
and that breaks my heart.
I’ve lost my Gran.
She’s still there, frail body in her favourite chair.
But in her mind she’s gone away.