puzzing intrigue

This kid does impress me at times.

OK, I know i’m somewhat biased and, as his mum, it’s my job to be impressed by him… soooo, at the risk of seeming a little ‘braggy’ i’m going to share a snippet from Mac’s recent school work.

Math(s) is still Mac’s favourite subject, it comes easily to him, he enjoys success with it and it’s easier for output than most literacy/writing based activities… so, what’s not to love?

In class Mac and his and his peers (now in 6th grade) were working on number patterns. Mac was working well and was given the first addition number pattern to complete as a warm up.

8, 16, 32, 64, 128

Mac typed “doubling” as his response to the teacher’s aide, ‘M’, to explain the pattern.

He was then required to provide ‘M’ with a subtracting pattern for her to try and work out, and so he typed:

100, 75, 50, 25

She easily identified it was subtracting by 25 each time.

But it none of this was really challenging Mac so ‘M’ upped the anti and asked him to create a really hard number pattern for her to do.

This is what he typed:

44, 88, 264, 1056, 5280

To quote Ron Burgundy, “well that escalated quickly”.

Seems he followed his brief… it is a tricky pattern.  Mac’s aide, ‘M’, worked on it for quite a while but he had her pretty stumped. None of the other kids in class could get it out – Mac assured them it was a proper pattern, that the numbers were correct.

Mac’s teacher, Mrs M worked it out… eventually… and in the end Mac gave the rest of the class the solution.

But it’s these little snippets and insights that intrigue us about this child.  Mac doesn’t use a calculator, it would be too tedious on this communication device.  When asked about his ‘methods’ for many things he says he “just knows it” and can’t explain his working.  Also, on his device he can only type left to right, unlike many instances in calculations where the rest of use might work right to left. So there’s plenty of times we adults are not quite sure what to do next, while Mac just keeps on doing his things his way, and yes, impressing and intriguing us as he goes.

Oh, and the answer?

Well, really I need to give those who love a good maths puzzle the chance to do it themselves.

But be sure to put your solution in the comments, I’ll pop Mac’s explanation he used for the class in the comments too, but don’t peek. 😉

Oh, and just so we don’t get too carried away as ‘braggy parents’, I do love the comment in his school workbook immediately following this entry which said… “Mac then dozed off in his wheelchair for a brief nap after all his work on number patterns”, seems it’s exhausting this math(s).

Way to go on the snoozing at school Macco!

kenken: no-brainer for differentiated instruction?

You’ve probably seen these puzzles appearing in your newspapers over the last few years.  Looking a bit like a weird Sudoku puzzle they are worth a second glance.

click the image to learn about the inventor

KenKen puzzles have built in differentiation, potential for collaborative learning and are readily available as free resource.   Is that not the ultimate in universal design in learning?

For an auditory or visual scanner they are great because you have a small number of answer options compared to other puzzles.  For a 4×4 puzzle you only have to enter 1, 2, 3 or 4 in each square – much less tedious for a scanner.

Kenken puzzles can contain all maths operations but, just as easily, can be simplified to only include ‘addition’ operations for someone not yet able to cope with division or multiplication (and don’t look any different – which can be important to some learners).

Here’s two examples of different puzzles, one simple – the other more complex.  Using colour is another way you could differentiate for learners – for example someone still learning their colours and number identification may work alongside others to complete all the “purple squares”, or groups can work together each on their own colour based on individual competencies.

The basic instructions are:

The numbers in each heavily outlined set of squares, called cages, must combine (in any order) to produce the target number in the top corner of the cage using the mathematical operation indicated.

Cages with just one box should be filled in with the target number in the top corner.

A number can be repeated within a cage as long as it is not in the same row or column.

A solved 3 x 3 (addition only) puzzle looks like this:

The KenKen website is a great resource.  Educators can sign up for the KenKen® Classroom program, where they will supply KenKen puzzles to you every week.   Parents are most likely able to apply too – they gave me a subscription and my next step is to start setting the puzzles up on Mac’s computer for him.

interested educators simply click the image

puzzling puzzles

Mac likes maths.  He really likes it when we give him ‘super duper hard maths’ questions (if we call them that they sound exciting) and so each afternoon for the trip home from school I give him a maths puzzle to ponder.

He answers it when we get home.

I am still trying to work out just what he does and doesn’t know in his maths concepts so we jump all over the place.  I also try to bombard him with lots of extra information to see if he is able to extract just what is important considering he needs to do all these in an auditory fashion.

Some of the recent puzzles have been.

• When I was walking down the steps today there were three lizards.  A big one, a little one and a middle sized one.  Lizards have four legs, how many lizard legs did I see?

MAC’S ANSWER:  12
METHOD:  Yes/No switches with possible answers starting at zero and going up by one.

• Today, when I was coming to collect you I saw four tractors.  A red one, a blue one, a green one and an orange one.  Tractors have four wheels each…  How many tractor wheels did I see?

MAC’S ANSWER:  16
METHOD:  Auditory Scanning on the Macaw numbers 0-14 then chose the “I need more numbers option” chose 16 from the Macaw numbers 15-30

• When I went to the shop I saw Natalie, Gabby, Sally and Will.  Natalie, Gabby and Sally are girls and Will is a boy.
  What fraction of the group were boys?
  a) half
  b) one quarter
  c) three quarters

MAC’S ANSWER:  1/4
METHOD:  Yes/No multiple choice options

• What fraction of the group are girls?
  a) half
  b) one quarter
  c) three quarters

MAC’S ANSWER:  3/4
METHOD:  Yes/No multiple choice options

• On my way to school today I passed the bike shop.  There was a trike and two bikes out the front.  A trike has three wheels, and bikes have two wheels each.  How many wheels did I see all together.

MAC’S ANSWER:  7
METHOD:  Auditory Scanning on the Macaw numbers 0-14

• If you were to add together the ages of your cousin Alex, your cousin Lucy and you what would the total be.  Alex is 13, Lucy is 10 and you are 6.
  We have just started getting Mac to tell us the digits to write the number ie “What is the ‘tens unit’ and what is the ‘ones unit’ ie positional notation for numbers to see if that is easier for him”.

MAC’S ANSWER:  29
tens unit = 2  ones unit = 9
METHOD:  Auditory Scanning on the Macaw numbers 0-9 using the positional notation of numbers

• On my way to collect you I saw three people picking apples.  I asked them ‘how many apples have you picked?’  They said “15 and we are going to share them equally”.
  How many will they each get?

MAC’S ANSWER:  5
METHOD:  Auditory Scanning on the Macaw numbers 0-9

• What if they picked 18 apples?

MAC’S ANSWER:  6
METHOD:  Auditory Scanning on the Macaw numbers 0-9

• What if they picked 30 apples?

MAC’S ANSWER:  Is it greater than nine? YES
tens unit = 1, ones unit = 0
METHOD:  Auditory Scanning on the Macaw numbers 0-9 using the positional notation of numbers

Out of interest I then asked him what 3 x 6 = and he answered 19. 
Phew, finally he showed some fallibility with his maths.

• I was talking to a farmer today.  He had 56 sheep but sold six of them at the market.  Then he had 10 new baby lambs born.  So he had 56, sold six and ten more were born.  How many does he have all together.

This one took a while for Mac to decide to answer – when I suggested he didn’t know the answer which was OK, considering he is only in first class, he quickly told me what it was.

MAC’S ANSWER:  Is it greater than nine? YES
tens unit = 6, ones unit = 0   60
METHOD:  Auditory Scanning on the Macaw numbers 0-9 using the positional notation of numbers

• Tonight we are having ‘chicken’ for dinner.  How many letters in the word chicken?

MAC’S ANSWER:  7
(although he went through his numbers twice hovering on 8 the first time)
METHOD:  Auditory Scanning on the Macaw numbers 0-9

The good thing is that we can relax a little knowing Mac is currently having a reasonably easy time of understanding basic maths concepts.  He is well and truly coping with the Year One concepts and having a wonderful time being challenged with ‘tricky maths’.  It is nice for him to ‘catch a break’ so he doesn’t have to work quite as hard in every aspect of school.

I have tried to find out how he knows all this stuff, he claims he ‘just knows it’.  I assume there is a strategy there somewhere, but hey, if it works for now, I won’t interfere.

I remember how much I loved doing maths in primary school so I can understand where he is coming from.