Interpreting Scatter Graphs

Relationships.

Scatter Graphs are an effective quick way of seeing if two variables (measures) have an effect upon each other.

e.g.  I think that the taller you are the heavier you will tend to be.  We can see if this relationship is evident if we take the measures of say 100 people and graph them.

Here are the results for the students in a class.  You can see that each person is represented by a cross (normally we use dots).  The tallest person is also the heaviest.


Line of Best Fit - can you see that there could be a straight line drawn into the graph over the points.  How closely can you see

Scatter Plot Intro

Bivariate Data 1.11 (aka 91036) Internal Three Credits

This counts for numeracy and literacy.  

For this we are going to compare numbers with numbers in a scatterplot (aka scatter graph).  We want for there to be a relationship (this is when the dots form a line).

We start with a question, draw the graph (and stats), write some sentences on what we see and write a conclusion.  This follows the PPDAC idea from the last topic.

Key Words...
Outlier - a dot (representing a person/car/country) that sits outside the line of best fit.
Line of Best Fit - a line best drawn between the dots.  You can hand draw this on.
Tightness - how closely to the line of best fit the dots are.

Intro to Achievement Standard Stats

Change in Course.

This marks the point of the year where we are departing from our numeracy (portfolio) standards of Number, Measurement and Statistics.  I will still be accumulating more evidence from you in these areas but not setting specific work for them.  

The standards that I'm aiming to do over the remainder of the year are...

Box n Whisker (aka Box Plot)

1.  91035 Multivariate Data (internal) worth 4 credits.  This is based on box and whisker graphs (see the picture) and goes through the same PPDAC system (setting a context, collecting data, drawing stem n leaf graphs, drawing dot plots + box n whisker, calculating statistics, making observations and writing a conclusion).   This is a Level One Standard 

Scatter Plot Graph

2.  91036 Bivariate Data (internal) worth 3 credits.  This is based on scatter graphs.  But goes through the same as multivariate... PPDAC system (setting a context, collecting data, drawing stem n leaf graphs, drawing dot plots + scatter graph, calculating statistics, making observations and writing a conclusion).   This too is a Level One Standard 

These level one standards I hope we have some 'merit' grades from our class.  I will teach these topics to that upper level.

example of a mathematical network.  

3.  91260 Networks (internal) worth 2 credits.  This is a unique level two maths paper as it's not based upon any prior knowledge (basically networks is about moving across a map).  For this standard you will learn from scratch.  The credits will count for 2015 and next year level two.  This is the least challenging of the level two standards and is not an indication of the challenge in level two maths.  If you want to do level two maths you will need to do full Achievement Standard level one first.  

Depending on the classes success here will determine if we attempt a level one or level two internal probably standard.  I will indicate this to you well in advance.  Potentially another 2/3 credits.

PPDAC

Statistical Inquiry Cycle
A very common thing for all people to know is how to compare groups.  If I said which fish is bigger, snapper from Waihi or snapper from Whitianga?  I would expect you to approach the problem in a systematic way.  

We call this the "Statistical Inquiry Cycle" and it's summed up in the acronym PPDAC [you absolutely must learn this].  It is a way of approaching the answer correctly.  

In statistics there rarely is the right answer.  Say if we said the that average year 9 at Waihi College weighed 53.4kg.  It would be very unlikely that the a randomly selected student would actually weigh 53.4kg.  

PPDAC stands for...

• P roblem
• P lan
• D ata
• A nalysis
• C onclusion

Here is the summary poster that shows how PPDAC is a cycle that repeats upon itself.  It was invented by Auckland University Statistics Department and is the cornerstone of NCEA Stats - you can get about 50 NCEA credits directly from being good at PPDAC.

Kiwi Fruit Harvest

Waihi College Kiwi Fruit Harvest

The school's orchard is nearly ready for harvesting.  The school has 3 hectares of commercial crop of kiwi fruit.

Kiwifruit is produced for two main markets - export (these are finest grade kiwifruit) and the local supermarkets (these are the over/under sized or unusually shaped or marked kiwifruit).

Today we're going to measure out our sample from the orchard.

I want you to have the length width height (all to nearest cm) and weight (nearest gm) measured.

We'll have a database formed for recording this information.

This we'll use to do some statistics and graphs in our investigation.

We will be looking to see if there is a relationship between the height and the weight of kiwifruit here at Waihi College.

PPDAC

Plan - how can we gather a 'fair' sample of fruit?  What are we measuring and how are we measuring it?  What units are we going to use?  Are we rounding or making any judgement calls (e.g. a fruit with a hole in it?  The measuring is evidence for the portfolio on measurement.  

Data - we will record this on a spread sheet in class.

Analysis - we will use a scatterplot to show our data.  We will make statements about what we see.

Conclusion - there maybe a relationship (maybe not).  If there is - is that relationship positive/negative, strong?  Can we make a logic statement about what happens with length and weight?

The First Graphs

First Up Graphs

The two most common graphs (these are acceptable for the numeracy standard 26626) are back to back stem and leaf graphs.  These show the numbers/data for two categories.

The trick here is to know how to read the numbers,  Can you see where the before number is 82 beats per min?

The benefits of the back to back stem and leaf graph is that you can easily see the spread of the data and make an quick comment.  "the pulse rates are generally lower (smaller numbers) in the before category.

You can also quickly find the highest, lowest, median numbers (and the quartiles).







The second most important graph to do is our dot plot graph.  These look like.

Contexts

Getting the Context Right

You need to have for this numeracy unit standard (26627) is a real context.  E.g. We can't just hand in a page on mobile phone prices - unless this has a real context.

E.g. the school ball in July is coming up for you guys - this is a real context that we can do some statistics on.

When you are doing your work you have to include a decent descriptor of the context.  Why is it real for you to be working on?


We begin our statistical investigations with a common question.  This needs to have the right wording...

"I wonder if boys spend less on mobile phones than girls at Waihi College in year 11"  The bits underlined are complusory - the I wonder if and the specific context of where the data comes from.  

Example of What To Hand In...

Here is the best type of template you can use to hand in. 

It is important that you do this as you have to have a real world reason for doing what you're doing.  



_____________________________________________________________________

Name                              Activity Heading                                              26626


Context.   - (here you write up what it is that you are investigating and why we are doing this).  


Evidence of Data.   - (here you can show what data you have used to generate your statistics and/or graphs).  Most likely this will be a list of about 30+ numbers.  


Statistics.  - (you will have to show mean/median/mode/range... perhaps quartiles and interquartile range).  


Graph(s).  - (you will most likely have a graph or two).   These need to be really well done - no errors).  


Observations.  - (what do your eyes tell you about what you have investigated?).  State the obvious.  Trend and Unusual Features are key.  


Conclusions.  - vital!  (what has all this taught you.  What do the results say?  can you back it up with the graph or statistics).  

26626 Intro To Statistics

Numeracy Statistics

The final of our three 'numeracy' standards this year is on Statistics (the study of lots of numbers).

Here is a copy of the actual standard (click here).

Here is what the evidence collection will look like...

Compund Interest

How To Get Rich

There is a lot written about how to actually get financially independent in your life.  You should want to know more about how finances work.

Typically you can see how people who should be rich aren't... take Mike Tyson... he was undisputed world champion.  He was getting paid millions of dollars per fight ($35 in one against Evander Holyfield).  He had an estimated net worth of $300,000,000 US dollars (about $400 million in NZ).   How ever he lost his fortune.

This post is not about boxing, it is not about careers with big incomes (although that helps).  This post is about 'Interest' - the money that is paid for borrowing money.  It is something that very very few people can avoid.

Interest is charged as a % of the amount borrowed (called the principle).  The calculation of the percentage is shown for a full year (p.a. is latin for per year).

But it's never a simple thing.  The banks/lenders will want to recalculate interest and add that onto the amount you borrowed.  This is called compounding...

The trick to getting rich is to be able to save an amount of your pay and invest it to gain compound interest.  Equally it is important to avoid getting charged compound interest (pay off your loans quicker).

New Worth Example

No Qualification Job

I've created this example for you - it is an attempt to show you how a decade of work will look if you are able to save kiwisaver and one twelfth of your income.  

It is definitely not a template for you to copy - yours will be your own and you'll need to personalise it.  Pretty much you need to be aware that in the short term those instantly into entry level jobs (I've put the pay at around minimum wage - which has just gone up yesterday) probably will feel richer than those who gain extra skills (trade or education).  But remember that those who train further will almost always get high wages or salary.  

The thing that you can see is that there are calculations around adding, multiplying, fractions, percentages (which I've done as decimals), and integers (the car loan is a negative).  

Don't copy this example as yours - but it shows you what you're aiming for.  

Net Worth Calculations

Future Focused Individual Study

The purpose of this lesson today is to get you thinking about the big picture future plans around your lives.  For this activity I want for  you to imagine that you are 25 years old (about a decade away).

I want for you to make a loose plan around what things you want to do/accomplish/try over the next ten years.  I want for you to pick some pathways.

Primarily this is a way of looking at some careers/jobs that you could have in the future.  To research these (pays, how to get the job, what schooling you need) you need to go to the careers website www.careers.govt.nz and look up various interesting jobs.

You can then calculate how many years of income you have from now until then (remember some careers need to have poly or uni training.


Then I'd like you to think about what sort of savings you can make over the next 10 years.  It would be good idea to try and calculate a fraction of your pay (say one twentieth).   You will also be put into a kiwisaver scheme where you'll save another 3% of your pay.

There are chances for you to find some integer money values (from things you will owe money for).  Think about student loans, car loans, mortgages.

Then I would like to you to create a theoretical net worth calculation.


Net Worth is the dollar value at any particular moment.  It is calculated by taking all the value of things you own and taking off the things you owe.

E.g.    Bob has a $12000 car, a $270,000 house, super annuation worth $23,000 a mortgage on the house of $210,000 and a car loan of $7,000.  His net worth calculation is...

NET WORTH = WHAT YOU OWN - WHAT YOU OWE
                        = (12 + 270 + 23) - (210 + 7)
                        = 305 - 217
                        = 88                                         Bob's net worth is $88,000 dollars.

Subway Shout

Subway (Activity From BOPMA)

This is an activity about spending money.  It can be evidence for adding (lots of different items), minus (what change you get), timesing (several of these particular ones), division (splitting the bill).

Potentially you can do some fraction or percentage calculations.

E.g. What % of the money was spent on drinks or What fraction of money was spent on subs?


Hint change the $ value from 55 and change the number of people.

The premise is unique to you as you will choose how much money you have to spend.  How many people are eating and what items you will buy.

Integers

Integers Are A Challenge

For Numeracy you need to show me once that you can do integers.  This is tougher as integers represents all numbers on a number line that have no fraction or decimal.

They can be positive or negative.
e.g. Yes Integers
        153
        3,998
        -45
        -1,000,000

e.g. No Not Integers
         21.5
         - 1/2           (minus a half)

Because this topic integers is in a portfolio there has to be a real life context.  Negative numbers are a challenge in real life.   e.g. I can show you 20 pens, I can show you 8 pens, I can even show you zero pens.  But I can't show you negative five pens.  

The best thing to use is the idea of money.  Negative money is when you owe someone money.  E.g. my bank account can show I have $100, my bank account can show that I have $33.  It can also show that I have minus $25 (i.e. I have over drawn the account - spent too much).  

Here are the basic rules of Integers...

Real life examples can be thinking about how your real life finances (net worth) will look like after you've taken out a student loan, overdraft, car loan or even a mortgage.  Most young people will have a negative net work (all the things you own - all the things you owe) from about the age of 18 to 40.  That's when they'll have finally paid off their debts.  

[I'm aware that the last paragraph has lots of technical financial terms in there so will have to take the time to explain this stuff].  

Other Fraction Situations

Please Hand In...

I'll need to gather off each of you some more evidence towards 26623 today.  Yesterday we did some fraction work - I posted three possible questions about NCEA credits and fractions with those yesterday.  Here are some other situations that you could use...

Donation To Charity.  
Lots of people like to give a fraction of their pay/pocket money to charity.  You could do a page on where your money comes from (that can be evidence of adding).  Then you can calculate a fraction that you could give away (like giving away 1/12th to the SPCA).

Survey of Canteen
You can take out one interval and see how many people are buying food from the canteen.  Then you can work out what fraction of them a buying a certain item (like a pie).








Budget For Shopping.
You can take your family shopping receipt and work out what fraction of the bill goes to things like fruit or meat or treats or toiletries etc.




Again all of these need to be personalised to your own experiences and you'll need to have these each on their own piece of paper.  

Do ask me questions and for help - I'm here to guide you through.  
Great to see the progress of most of you - I've a summary document to show you all where you are at heading towards the credits.  

Subjects at Waihi College

Here is your subjects...

Fractions in Real Life

Fractions For Numeracy

One of the more challenging things that you'll have to do is to show you can do fractions in a real tense (real life).

Remember that your fractions should be found from your own numbers in a real example.

Here is the online exemplar example from www.nzqa.govt.nz website.

[this is a great place for all kiwi students to know where to find the difficulty of each part].

Here is a plan for a hui with lots of people - you can see how many people are coming along and that the first problem is a fraction one (one third).

Can you see that the answer has words, working out and units (cups) so that it shows all required.   


Here are some practice ones for you...

1. John weighs 98 kgs.  The doctor tells him that his weight 2/15ths fat.  How much kgs of fat is that?
2. The doctor tells him that he needs to lose 1/10th of his weight.  How much should he weigh after a diet?

Actual real life problems that you can work on.

NCEA Level One.  You need to get 80 credits to pass Level One.  What fraction of all your credits is 80 credits?

NCEA Level One.  How many credits will you expect to have sat by the end of this term - i.e. what is one quarter of your internal credits?

NCEA Level One.  What fraction of your credits offer literacy?  What fraction of your credits offer numeracy?

Dealing with Fractions

Fractions
This is an area of confusion for a lot of students.  Fractions are old school mathematics and require some pretty powerful head space.  Unless you have a calculator (then it's easy)... you guys are allowed calculators.

Here is the logic behind fractions...

Fractions are things that confuse heaps of students... lots get through without ever really knowing what they're all about.  I always think about fractions with my stomach.  I think of bars of chocolate (cause they're rectangles) or cakes (cause they're round).

The key things you need to know is that they're parts of wholes.  They lie between the numbers on a number line...

They don't always have to be between 0 and one (e.g. you can have 'three and a half'.

Class activity - competition to see where a fraction of a line is on the whiteboard (some rewards up for grabs).  



Equivalent Fractions -

here is the link 

This is when the fraction shows the same amount of a fraction but looks different.  This is an interactive teacher led animation.  You can see how the fractions are the equal (balanced) but have different numbers top/bottom.  Other good learning here is the decimal on the bottom - you can use a calculator to find this (use the divided by button).

Here is the button on the calculator for fractions...

Can use see the grey button under the "Abs" button.  That's for fractions.


Try some of these...

1.  What is one fifth of 730?

2.  What is nine tenths of 860?

3.  What is five twelfths of 288?

4.  Increase 50 by one quarter.

5.  Increase 180 by two thirds.

6.  Decrease 360 by one tenth.

7.  Decrease 440 by three fourths.

BBQ

Context Number

Here is an e-copy of the work we are doing on the school BBQ.

It is a rich document where you can find lots of work on...

Adding/Subtraction/Times/Dividing

Percentages/Fractions/Decimals

(not so easy on integers).

Remember you have a page - name on top with 26623.

Show working/symbols (like "=" signs).  Write some words to go with your working.  

Do ask for help.  

Numeracy Problem

Part Time Work

Please calculate for me how much work you will need to do in order to buy a surfboard (substitute in other gift) worth $345.00 (or what ever)

Remember...
Separate Paper, Sentences, Working (aka maths symbols like "="), Units, Reasonable Answers.

Computations

Adding, Minus, Times and Divide.
These are a core component of what you have to be able to do at year 11.   They are the most common problems and ones that you've been learning for years.

This year I'm not going to teach you the methods of + - x or / ... these have been covered extensively previously.  This year I'm going to teach you about the communication of your calculations.  

For numeracy you will need to be clear in what you are doing.  Some students can look at a problem and find the *right* answer... but that is all they put down.  This is not as important as being able to show/communicate your working.  

For all your work - remember that I've got to keep all your evidence [that's why you need to name your pages]  You will need to clearly show...

1. Words - telling me (the marker) what you are calculating.
2. Symbols - all the add/minus/times/divide symbols (and fractions/decimals/etc)
3. Any Units - like "hours" or "days" etc.  
4. There should be a logical order if possible.  

Remember for 26623 (Number Standard) your answers have to be 'reasonable' - they can't be crazy off.  E.g. saying "For lunch I ate 540 kgs of food".  

Evidence In Numeracy

This is What I Need From You

The way that the portfolio works is that you've got to show me that you can use your maths knowledge in the real world.  I need the date, the paperwork or video or photo, and that it relates to real life.  You will need to help me with accumulating this evidence.

There are three topics that we will do with our portfolios...
Number & Measurement & Statistics.

Here is the paperwork that each standard has -

Personal Goal This Year

Personal Goals

It is  really important that you keep on track this year.  Here are some things that will greatly help you this year...

1. Everything matters - every single assessment is vital - don't think "oh it's only worth two or three credits".  Yo will need to keep constantly ahead of your work.  This is for all your subjects.  
2. Know what you have chances in.  Know exactly how many credits you have available to get your 80 credits.  If you have 100 available from you subjects you will need to pass four out of every five standards.  
3. Remember that the externals are harder too pass - work hard on those internals why you can get ahead.  
4. Turning up makes a big difference.  Waihi College students that passed Level One in 2014 averaged 89.3% attendance.  Those that failed Level One averaged 73.8% attendance.  
5. Most students have two subjects that they do really good at.  Then there are four other subjects... you have to concentrate on these ones.  You can't afford to have bad subjects - ones that you don't pick up standards in.  Attitude is important but so is effort and seeking help.  

Definitely put this maths course to the top of your attention.  Our course is about accumulating up evidence that you've got the maths.

Welcome to Year 11 Maths

Welcome to the start of our year here at Waihi College. 

This course is a vital ingredient for getting through your NCEA Level One.  This is probably the most important class you will have this year - numeracy is the number one reason any NZ student fails NCEA.  

NCEA needs...

1. 80 or more credits - typically you will be offered between 90 and 135 credits (depending on your subjects), 
2. Literacy (10 credits)
3. Numeracy (10 credits).  

To get numeracy you will need to get the ten credits either... in a portfolio (no tests but documented work) or in achievement standard tests.  The challenges is that there are not many standards that have numeracy (physics and one geography standard and maths).