May 5, 2011

Fibonacci, Definite articles and ROYGBIV mashups

What a morning!

Here follows a loose recall of our typical homeschool day...well, a typical very good day when things flow smoothly and inspiration bubbles up from adult and child alike:

While I was busy getting some wheat-free friands in the oven for breakfast, Mike put on the wonderful Nature by Numbers video which introduces the mathematical Fibonacci sequence through images of nature.

I love the F sequence - I read about it in a wonderful maths book when November was still at preschool bugging us (in a nice way) with lots of number questions. It was the first maths book I had opened since I was 15. I was identified as gifted in Primary and given lots of differentiation (70s style which meant my own workbox work) especially in maths, doing Algebra in Year 6 with the wonderful Mr Spring. High school maths was another story - a total disaster which saw me apply to drop maths for the last 2 years of high school - the first student in the history of the school to do so. Shame...but wow am I loving maths now as a homeschool mama!)

The Fibonacci sequence is a mathematical pattern attributed to a mathematician called Leonardo of Pisa, aka Fibonacci. His book in 1202 introduced the sequence to European circles as it appears even earlier in Indian maths.

It is a sequence that is seen extensively in nature - from bee family trees (!), leave whorls, numbers of petals on flowers, fertility in rabbits.
Here is the succinct way Wikipedia expresses it...

In mathematics, the Fibonacci numbers are the numbers in the following integer sequence:
0,\;1,\;1,\;2,\;3,\;5,\;8,\;13,\;21,\;34,\;55,\;89,\;144,\; \ldots\; (sequence A000045 in OEIS).
By definition, the first two Fibonacci numbers are 0 and 1, and each subsequent number is the sum of the previous two.
In mathematical terms, the sequence Fn of Fibonacci numbers is defined by the recurrence relation
F_n = F_{n-1} + F_{n-2},\!\,
with seed values
    After the video Mike read from the Fibonacci chapter in "The Adventures of Penrose the mathematical cat" by Theoni Pappas, finishing up with an activity from the book
    Well - the bug had bitten! Among cries for "more Fibonacci!" the girls sat down and wrote the sequence themselves - July with the aid of a 100s chart. It is a lovely accessible pattern for kids.
    After the friands, we delved into "Grammar Island" from Michael Clay Thompson (MCT) and worked on adjectives as words that adjust and modify the noun...including definite and indefinite articles which was totally new to me! 
    Grammar was a "dirty word" in Australian schools in the 1970s.
    The girls are really getting into MCT. Each time I pick it up I feel a tiny twinge of fear that they won't like doing grammar...the "dirty word" feeling is obviously still ingrained in me. Yet each time they cry "more, more" and once again I have that most wonderful experience as a home educator of saying "no more for today". 
    I am learning that leaving your child wanting more is far preferable to going too far until everyone is almost drunk with tiredness. If only I could learn this lesson in my own projects...hmmm
    After morning tea, running around, and some piano, we came back to representing Fibonacci as a visual sequence. With visual spatial learners I try to include some visual revision almost immediately of the key concept. Here is the Fibonacci sequence drawn on graph paper. Each number is represented by a square of its size. To make things more interesting, we used ROYGBIV for the order of the colouring pencils.
    We love "They Might Be Giants" (TMBG) in the Mansted family! While you may know them as producing music for kids, Mike has followed them for years (since 1982) before their kid friendly transition. Think nerds with guitars...and wonderful lyrics. 
    Anyway, on TMBG's kids Science album is a song called "Roy G Biv" which gives the REAL sequence of colours in the light spectrum (unlike the awful rainbow song "Red and Yellow and Pink and Green, Purple and Orange and Blue...")

    I really love this song as it has ended the frustrating discussion of how to draw a rainbow which has been going on here for... well, feels like forever. At last the girls believe me! Yes, this is a bee in my bonnet because you need to understand the spectrum of light to mix colour accurately in artwork.

    I drew a little series of colour boxes to help remind them the order of colours and so we ended up with a double pattern - Fibonacci with rainbows?

    So here ends the description of our mashup at the Mansted Family Project.

    Fibonacci meets Roy G Biv and Michael Clay Thompson oh, and then collecting tadpoles, November reading a version of Jane Eyre while July reads an Aussie Nibbles. Time for lunch and off to the Suzuki Piano lesson with the wonderful Diti.
    Friand recipe to follow...

    Friand is apparently a French word for a small burnt butter cake...but you don't need to burn the butter, or indeed use butter at all as olive oil is great in these too.

    150 butter (melted) or 110 grams of olive oil
    1 and 1/4 cups almond meal
    1 cup icing sugar
    1 cup of coconut (mix of shredded and dessicated gives best texture)
    1/2 cup gluten free flour
    1/2 teaspoon baking powder
    6 egg whites (150 mls)

    frozen or fresh berries to top (or slivered almonds)

    Turn on your oven to preheat - 180 degrees celsius or 350 degrees fahrenheit. Line 12 1/2 cup muffin tin with patty papers (or grease with melted butter in addition to that above).
    Mix the ingredients lightly together - except the berries - and spoon into the patty papers. Top with the berries. Place in oven for 22 minutes until lightly golden on top - they should be soft in the centre so don't overcook. Makes 12.

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