It's been a while, babies and blue whales

Year 7 has been very busy in term two doing things like school camps and NAPLAN. 
Now we are back with our full weeks of math and looking at patterns in the real world. 

Today we looked at the growth rate of babies in their first 13 weeks. 

The WHO provides the data - we used every two weeks to develop models for predicting - interpolating and extrapolating. This way we could check our maths with the real data! 

We used tables, graphs and developing algebraic rules to make predictions and compared their results.  Alex pointed out how ridiculous it would be to keep using our models into teenage years to illustrate how extrapolation can be unreliable.  Here are some notes from today and Alex's example:

How reliable are our models?

Reasonably reliable for interpolating. 

Not as reliable for extrapolating. Remember Alex calculated the weight of a 13 year old at the same growth rate as babies in their first 13 weeks. 

13 years = 13 x 52 weeks

13 years = 676 weeks

Our formula/equation/rule

Let  t = time weeks   and   k = weight in kg

k = 0.25 x t + 3.3

for 13 years old

k = 0.25 x 676 + 3.3

k = 172.3 kg 

That's not average in any country for a 13 year old boy!

The CDC, in the USA,  says the average weight for a male at 13 years old is 51.68229 kg  That's more than 100 kg lighter than our formula says. 

Can you find the average weight of a 13 year old in another country?

Source: Growth Charts of Children - CDC

BABY BLUE WHALES

We talked about including units on our work to show kilograms otherwise our baby data could be in tonnes or even milligrams. A 3 tonne baby! Crazy!

... or not....? I did some searching....

For interest: Close to 3 tonnes are baby blue whales and their average difference is about 91 kg a day!!

Their formula would be k = 91 x d + 3000 and reliable for 365 days! 

where k = weight in kilograms and d = time in days. 3000 is the initial value (or 2700 - see below). 

After about a year inside its mother's womb, a baby blue whale emerges weighing up to 3 tons (2.7 metric tons) and stretching to 25 feet (8 meters). It gorges on nothing but mother's milk and gains about 200 pounds(91 kilograms) every day for its first year.

Blue Whales, Blue Whale Pictures, Blue Whale Facts - National ...

animals.nationalgeographic.com.au/animals/mammals/blue-whale/

Maths and you guessed it... Christmas

Here is a gift for you from Mathsland - a game. It's the latest thing and Jo Boaler of Stanford likes it so much she is now on the team..

Download Mathbreakers and puzzle it out. It looks like Mathbreakers will just keep growing too.

And this ancient game - I haven't beaten the computer yet. Can you? Cool Math - Mancala

For the next game you will need a 10 by 10 grid - this is called How Close to 100? To make it more challenging try How Close to 1 and use decimals. This is from Jo Boaler.

You will need

• two players

• two dice

• recording sheet

This game is played in partners. Two children share a blank 100 grid. The first partner rolls two number dice.

The numbers that come up are the numbers the child uses to make an array on the 100 grid. They can put the array anywhere on the grid, but the goal is to fill up the grid to get it as full as possible. After the player draws the array on the grid, she writes in the number sentence that describes the grid. The second player then rolls the dice, draws the number grid and records their number sentence. The game ends when both players have rolled the dice and cannot put any more arrays on the grid. How close to 100 can you get?

Variation Each child can have their own number grid. Play moves forward to see who can get closest to 100.