Maths Magic

This morning I went to a regional meeting of the East Midlands Association of Maths Teachers to see Andrew Jeffreys perform some maths magic. I picked up loads of tips, not just on maths, but on teaching in general.

Maths and number:

Square roots – what is the square root of 1,234,567,654,321? Pretty tricky to guess at without a calculator

What if you know that:

1×1=1

11×11=121

111×111=12321

now can you work it out? Yes? The square root of 1,234,567,654,321 is 111,111 (would have been great for 11/11/11 last week!!)

Yoikes! is a quick game that will allow you to assess children’s ability to use place value efficiently and in a meaningful way.

Draw ten spaces across a page (like hang man for a 10 letter word). Teacher calls out numbers from 1 to 100 and you have to put them on the dashes in order. If you can’t add a number, it goes in the yoikes bin.

Yoikes

As you can see from my example, I already had 71 and 96 in place when he called out 86, so it had to go in the bin. The first number he called out was 23 – could walk around the room as calling out the numbers so you can see where children are placing the numbers. If 23 was placed anywhere except the first 4 slots, you probably need to talk to that child about place value and it’s relationship in a number line to 100. You could use this game with 1-10 or 1-20 with younger children.

Multiplying by 1001

Everyone in the class pick a 3 digit number, then repeat it to make a bigger number:

234 turns into 234234

What is the probability of someone’s number being divisible by 2 exactly? Or 3 or 5 or 91?

Divide by 91, then by 11 and you will get 234 (works with all three digit repeated numbers)

because: 11 x 13 x 7 = 1001

Because 1000 times a number, add 000 but 1001 would lead to 000 plus the number again, so 234000+234=234234

So multiply a number by 1001 and divide by 1001 and get the same number (but that is boring!) so divided by 91 (13 x 7=91 then divide by 11).

Shape:

Making regular pentagons from an A4 piece of paper.  There is a good explanation of how to do it here with pictures. The final pentagons have two flaps sticking out and two ‘pockets’ at the top, you can use these to slot together to make the dodecahedron.

dodecahedron
dodecahedron

 

There was the camel problem – a great one for a last-minute assembly! (the link is to one involving 17 camels, Andrew showed us 11 camels split 1/2, 1/4 and 1/6 by adding one more camel which is easier to explain and to demonstrate).

A nice little reminder for fractions (could also be used to show equivalent fractions) was to take an A4 sheet of paper and fold it whilst writing the number of thicknesses on the sheet as you went, and the number you started with. You end up writing fractions on each piece until you end up with this:

fractions

…which will make a great display to help children remember which fraction is which and how many quarters in a half etc.

Games:  Nim  to play to think about strategies.

Think of a number – visual demonstration of the proof:

Think of a number, double it, add six, divide by 2, subtract original number. Everyone stand up, sit down if you got 0,1,2,3 (we all sit down at 3).

Do a visual mathematical proof for it. Put mental ‘star’ in one hand with your number in it, photocopy to other hand, then throw it back, (now got 2 stars on left hand), catch six imaginary pennies in right hand, then slice it in half, (now got one star in one hand and 3 in the other), throw star away, left with 3 in right hand.

Neat Fibonacci sequence trick:

Pick any two numbers, then add in Fibonacci sequence until you have 10 numbers, ask children to sum them. When you get to the 7th term, you can just multiple that by 11 (i.e. times by 10 then add 1x the number) and that is the same as the total. So when you get to the 7th term on a flip chart, write the total down on the back of the flip chart and turn it round once the kids have summed the total.

Teaching tips:

On the PGCE we have learnt how to use ‘think/pair/share’ but Andrew added another two steps which work well for maths. First ‘visualise’ your answer (silently) then look at your partner. Only when BOTH of you are looking at each other, do you share your answer. Stops one partner racing ahead of the other.

One hundred squares – be wary of using them, they can be very confusing for counting on and counting back. The small numbers are at the top, the big ones at the bottom, you count left or right or up or down depending on if you are adding 10 or taking it away… much better to use counting on and back with long number line.

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