Learning Maths through Music and Movement

This was originally a blog post in September 2012 – but I’ve added a couple of bits since and will probably continue to add and amend as time goes by.  I hope there’s some helpful ideas here 🙂

Whilst answering an e-mail from a lady who is doing some research for a music in development project in Uganda (she posted up on a group I’m on asking for people who’d be happy to chat to her), it occurred to me that I hadn’t ever posted, in any real detail, about some of the musical/rhythmical approaches to maths that we use here and it would be potentially useful if I did (and then I’ve a record of it that might be useful for ideas for someone).

The following will be rather text heavy, as I don’t have photos for these things as my hands are rather full *doing* them with my children (or full of baby 😉

Percussion Multiples

Each person has an instrument and are given a number.  The group then begins to count: 1, 2, 3, 4 [etc] and each person (or people if more than one person is given the same multiple as part of a larger group) shakes, rattles, hits (whatever) their instrument on the multiples of the number they’ve been given.  This gives a physical experience of multiples and how they fall in sequence and also how they correspond with one another as there will be some numbers when 2 or more people will use their instrument (e.g people given the numbers 3, 6 and 9 would all use their instrument when the number 18 was reached).  The group can make all sorts of compositions based on multiples!
You could also do this with tuned instruments such as bells or chime bars, or use parts of your body – clap, tap, click fingers, etc.
For something a little different, the group could also do this with skip-counting or just saying random numbers.

Multiples and Factors ‘Fruit Salad’ (group game)

Years ago I worked for the Youth Service and we played a game called ‘Fruit Salad’ which can be easily changed to use to practise multiples and factors:
  1. Arrange chairs in a circle with one person standing in the middle. Give each person a number (more than one person can have the same number).
  2. The person in the middle calls out a number and the people who are factors of that number have to get up and swap chairs (whilst the person in the middle also tries to find a chair). Whoever isn’t fast enough to get to a chair is then the next person to stand in the middle and call a number out.
  3. Repeat until you get rather tired!
Example: in our local co-op group there were nine of us and we used 2s, 3s and 4s.  Eight of us sat  in the circle, and the ninth was in the centre.  Put a cap on what numbers people can go up to – try to gauge it to the knowledge/ability of the children involved, as we had littlies we stuck to “12”.  So for “2” only 2s moved; for “3” only 3s moved; for “4” 2s and 4s moved; for “5” no-one moved; for “6” 2s and 3s moved; and so on, until at “12” everyone moves (and a little chaos ensues).

Multiples and Factors Dance or Maths Conga

Each number is given a move to make.  The default can be a side step (where numbers aren’t a multiple of anything else). Then people start to count and move as per the number, e.g: 1 (side step), 2 (clap), 3 (side step), 4 (step forward and clap as 4 is also a multiple of 2), 5 (step backward) and so on and so forth. This can be rather challenging (especially for the clumsier amongst us, i.e. people like me 😉 ) and maybe put an upper limit on the number you count to as some combinations of moves might be rather challenging (or impossible).

You could also conga – multiples of 3 can be a left kick, multiples of 4 a right kick and if you get a multiple of both, jump! Or do whatever combination you fancy.

Using Well-known Rhymes and Songs

This is something that will be familiar to people with a Waldorf-bent to their home education approach. The use of rhymes, songs and action are very important in the exploration and strengthening of various mathematical concepts (as, indeed, it will be familiar to many schools, both Waldorf or not).  “A Journey Through Time in Verse and Rhyme” by Heather Thomas and Eric Fairman’s “Path of Discovery” books are both examples of books that have various suggestions for verses and songs in them and there are plenty available online if you search for them.  Examples of such rhymes include:

There was a family strange indeed;
Each member had a peculiar speed.
They could walk for half a day
Counting footsteps all the way,
Here they come,
Number one.

1. I am proper, neat and prim
My walk is straight, my clothes are trim
So I count my steps and you will see
That every one’s the same for me:
One, two, three, four, five, six, seven [etc]

2. But my two steps are not the sameFor I must lean upon my cane.
Although I’m bent and weak and oldI can still count with numbers bold:
One, two, three, four, five, [etc]

3. I’m a lad, light and gayAnd I’d much rather play.I can run with my ballWhile the numbers I do call:One, two, three, four, five, six [etc]

This poem continues with 4, 5, 6 and the giant, 10.
A fantastic idea that I came across on one of the lists (it would’ve been either homeschoolingwaldorf or waldorfhomeducators on Yahoo and I cannot remember the name of the lady who first suggested it) is the use of “Three Blind Mice” to count in multiples of 3 (also using actions as follows: Three Blind Mice using this rhythm of movement across the song) as follows:
First the original is sung with actions:

Three blind mice
Three blind mice
See how they run
See how they run
They all ran after the farmer’s wife
Who cut off their tails with a carving knife
Have you ever seen such a thing in your life?
As three blind mice.

(then, continuing the actions)

3, 6, 9
3, 6, 9
12, 15, 18
12, 15, 18
21, 24, 27
21, 24, 27
30, 33, 36
30, 33, 36

(we then do it backwards)

This suggestion made me think about other songs/rhymes that would work well with the tables, which led us to use “Miss Mary Mack” for the 4 times table (You Tube has various examples of children/teenagers doing the actions for this clapping game):

Miss Mary Mack, Mack, Mack
All dressed in black, black, black
With silver buttons, buttons, buttons
All down her back, back, back
She asked her mother, mother, mother
For fifty pence, pence, pence
To see the elephant, elephant, elephant
Go jump the fence, fence, fence
It jumped so high, high, high
It reached the sky, sky, sky,
And never came back, back, back
Till the fourth of July, ly, ly.

(then)

One four is four, four, four
Two fours are eight, eight, eight
Three fours are twelve, twelve, twelve
Four fours are sixteen, sixteen, sixteen

(and so on and so forth up to twelve fours and then back down again)

 
We do “Sing a Song of Sixpence” for the 6 times table (great because it references ‘6’ and also ’24’) but it does mean going up to 16 x 6 for it to ‘fit right’ (and we do do this sometimes and I have to admit it is a challenge for me once we get past 12 x 6).  If you want to give it a go the pattern is:

Sing a song of sixpence, a pocket full of rye
Four and twenty blackbirds baked in a pie
When the pie was opened the birds began to sing.
Wasn’t that a dainty dish to set before the king?

The king was in his counting house, counting up his money.
The queen was in the parlour, eating bread and honey.
The maid was in the garden, hanging out the clothes,
When down came a blackbird and pecked off her nose!

(then)

1 times 6 is 6 and 2 times 6 is 12
3 times 6 is 18 and 4 times 6 is 24
5 times 6 is 30 and 6 times 6 is 36
7 times 6 is 42 and 8 times 6 is 48

9 times 6 is 54 and 10 times 6 is 60
11 times 6 is 66 and 12 times 6 is 72
13 times 6 is 78 and 14 times 6 is 84
15 times 6 is 90 and 16 times 6 is 96

(*phew* and then back down again)

Don’t forget to also use activities such as skipping (with a jump rope or elastics) or beanbags which could be used whilst doing the above verses as well.

***

Whilst some of the examples I’ve given are more for younger children (the basic counting family rhyme), others (such as dancing multiples) will work better with slightly older children and teens (because it takes quite a bit of co-ordination – we get in a bit of a muddle here, but will persevere as the children get older).

Hopefully the examples give you some ideas of how to inject a bit of music and rhythm into maths that will hopefully enthuse your children (and you) and show that maths can be a lot of fun!

Nin and Ted playing Pirate Arithmetic

Other Useful Math Resources (That We Actually Use)

  • A pack of playing cards (we have a rather lovely pack illustrated by Lauren Child featuring characters from Charlie and Lola).  We use these to play matching games like “Snap” or “Go Fish” and I’m planning on teaching them “Rummy” and “Whist” this year to challenge them a little more.
  • Board games such as Snakes & Ladders or Ludo.
  • We also have a “Pirate’s Arithmetic Game” (produced by Haba) which the children enjoy (it includes the rules for 3 different games covering addition, but also has additional dice that can be used to make the games more challenging with subtraction and multiplication.
  • Dice games such as Yachtzy.
Nin and Ted play Yachtzy
  • We have a selection of glass pebbles and also pine cones, shells and various gemstones that can be used as maths manipulatives by Ted.  Nin doesn’t really have much need for them now, although I’m planning on using sticks to explain the concept of vertical addition, subtraction, etc.
  • Don’t forget the practical day-to-day applications such as cooking and baking, various craft activies, gardening, etc.
  • NRich has some good ideas for further activities and games that use maths skills.
You may find other ideas under the Maths label.
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