# 8 Extended Math

## Statistics Work – Friday 24th of May

Today will be a busy day. We have quite a bit to do.

Last lesson, we worked on GeoGebra but did not finish the work. I have included a manual HERE that shows step by step what to do with screenshots and the like. Before you ask – not it’s not copied from the internet and yes I did make it.

Our plan work in order of completion is below:

1. Ex 12.04 Q 1-6 on Page 425-426
2. Complete GeoGebra work as shown on manual HERE. Some instructions are also on previous blog posts
3. Complete some work on your Math Report. Remember this is due on Monday.

## Continuation of GeoGebra

For today, we will be working again with GeoGebra. This is a program that you will use a lot in the future – so it helps to know how to use it. Instructions for today is below:

1. Open GeoGebra and go into the document you created last lesson.
2. Remove the names on all points in the graph. This can be achieved by double clicking on one point and then select Object Properties. Once this is done unselect Show Label. Select the same for all points from the area on the left of the screen. Close the box and all point names should be removed.
3. Now – we are going to to learn about quartile ranges. A quartile range is the middle 50% of the outcomes. This is often used instead of range as it removes any outliers which may skew the data. We can find the upper and lower quartile two ways (by GeoGebra and via a simple rule). They are
• Lower Quartile = C.F X 0.25 .
• Median = C.F X 0.5
• Upper Quartile = C.F X 0.75.
• Your Interuartile range will then be written as the following:
• Interquartile Range: Lower Quartile – Upper Quartile (The – is a dash and not a minus sign)
For GeoGebra, the method is a little more complex but is easier for more data.
• First – double click on the graph with 2 fingers and choose the second graphics option. Make sure you choose positive direction only for the x and y axis. Also remember to click show grid on the Grid Tab. Feel free to change the grid color.
• Second – find out the 1st Quartile. This can be done through writing y=C.F X 0.25. A line will be drawn through this intersection of the graph. Then choose intersection between two object and click on both the line and the line for the graph. Now a new dot should be included. (is 2.18). So write x=2.18. Label this as Q1 (First Quartile) on the bottom part of the X axis
• Third – complete the same for the median and second quartile. Label these as well on the bottom part of the X axis. I’ll show you how to do this – but you will need to listen.

If you finish early – then you can work on your math report.

## Starting GeoGebra

Over the next few lessons, we will be starting GeoGebra. For today, we will be making a simple cumulative frequency table and graph on GeoGebra. Instructions on what to do is below….

1. First – install GeoGebra 4.2 from HERE
2. Open GeoGebra. Don’t forget to turn on the Spreadsheet view. (View -> Spreadsheet View)
3. Add some data into the Spreadsheet. I suggest using data from Q6 Ex 12.03, but make the Outcome 0-13. A = Outcome, B = Frequency, C = C.F
4. Make coordinates for the outcome and C.F. Follow my instructions on how to do this – I’ll explain verbally.
5. Remove SHOW LABEL. I can show you how to do this individually – there is also a way of doing this all together
6. Now choose New Point and Polymod. Click on each point and press the first point when finished. A line now exists between all points.
7. Save your work. We will use this next lesson.
8. Complete your Math Report

More Instructions coming soon.

When finished – you can complete your Math Report. Also – save your file as we will use it again on Thursday

## A Large Range of Questions

Today, we are continuing on with statistics. The areas of range, mean, median and mode will be explored. Questions to be completed are Ex 12.02 Q 3-8 pm Page 411/412

## Cumulative Frequency

For today, we will be looking at cumulative frequency tables. It’s just a normal frequency table, but you add the total number of outcomes for that specific number (we will talk about this in class). Today’s work is below:

Ex 12.01 Q 4, 5, 7 & 9 on Page 407-409

## It’s Probably The Last Time We Do This!!

It’s A Friday! It’s Period 8 ! So what exciting activity are we completing? Pop Quiz??? No…. Test??? No…. Textbook Work? Umm yeah – your really going to do that now!! What about playing cards under the guise of working on probability?? Umm – it’s probable we might do that…

So – get into groups of 3 or 4 students. Then go to THIS DOCUMENT and choose one person from your group to speak to me. This person will be called THE CHOSEN ONE!!

This person will be given instructions to follow. Each group will play 21 a total 20 times. Write down in the document who wins how many times. There needs to be a total of 20 wins.

Once finished – answer the following questions:

1. Which person won the most? Was there a pattern to this?
2. What rule did you follow to try and win the most? Did it work most of the time? Yes or no and explain why….
3. Is 21 a game of skill or luck? Explain why you think this way….

## Some Extra Tree Diagram Questions

Below are some revision questions for tree diagrams since there are not many questions in the revision packet.

Q1) There are 5 Blue Sweets, 2 Green Sweets and 1 Orange sweet in a packet. If you remove one sweet, it will not be replaced.

a. Draw a tree diagram for the above if two sweets are removed.

b. Find the probability for the following if 2 sweets are removed:

P (Getting 2 blue sweets)

P (Getting an Orange Sweet)

P (Getting 2 Orange sweets)

P (Getting 2 Sweets of the same color)

What is the change of getting 3 blue sweets if 3 sweets were removed?

2) You have 2 dice with the numbers 1, 2, 3, 4, 5, 6. They are both rolled at the same time.

a. Draw a tree diagram to show the different options when rolling two dice.

b. Show the probability of getting the following: when rolling two dice

P (rolling one 6)

P (rolling two 3′s)

P (total score is 9)

P (rolling a 3 but not a 5 or 6)

## Tree Diagrams

For todays lesson, we will be completing some tree diagrams and collating the probability of certain events occuring. Instructions on what to do is below.

1. Neil likes dice. So, he decides to roll 3 of his 3 sided dice. Construct a tree diagram which shows the different options he might roll.
• What is the probability of rolling at least two 6′s?
• If Neil was to add all of the possible dice combinations together, which number will be the highest probability of rolling?
• What is the probability of rolling one 1?
• What is the probability of rolling one 2 and one 3?
• What is the probability of rolling a 3 and not a 2? Explain.
• 2)Claude loves to use his awesome magical skills to amaze, confuse and humble his fellow classmates. His main trick uses 4 face card from a deck of cards (1, 2, 3, 4). His trick involves you picking three cards and him telling you what the total of your cards will equal
• Construct a tree diagram showing the different outcomes from the 6 cards available if we take a total of 3 cards. Remember that the cards are not replaced?
• Which number will be the most common? What probability do we have of getting this number?
• Which score/s is the least likely to be chosen by any specific student.
• If you were Claude’s enemy and you wanted to find out his trick to this awesome piece of magic (aka probability), what would be your rule?
• Akari was really annoyed with Claude as he did not say hi to her as he walked past her this morning. As such, Akari used her own magic by replacing every card with the exact identical card taken out by Claude. Contruct a new tree diagram that shows the different options for choosing three cards which are now replaced (1,2,3,4).
• What is the most common score? What probability is there of getting this score?
• How does this change the probability of Claude choosing the correct answer? Explain using the data you have collected.

## It’s Probably Fun Activity

For today, we will be looking at some generalized experimental probability through the classic game of 21. We will also complete the students favorite activity – textbook work!! General instructions are below:

21 Activity

• For this activity, you need to get into groups of 3 or 4 students. We will be collecting some results and looking at the data to interpret the probability of winning a game.
• First, complete the following questions in your notebook.
1. Which number do you think will be the most common winner in the game of 21? Explain why.
2. Do you think the game of 21 is fair or not fair? Explain why
3. Is 21 a game of skill or a game which requires skill and knowledge. Explain
• Once every student in your group has finished, then I want you to play the game of 21 a total of 15 TIMES. Please remember record the winning number in THIS DOCUMENT on Page 1. Don’t worry – the statistics part of this game will automatically be completed for you. We will learn this in your next topic after your exam.
• We will have to wait for all groups to finish the game. As such, you can finish the work from last lesson - Ex 4.02 Q 3-5 on Page 102
• When all groups have finished, then complete the following questions…..
1. Did the games of 21 you played seem fair? Explain why.
2. Which number was the most common? Was this different than what you were expecting?
3. Do you think there is an easy way to work out the probability of winning this game? Explain the best you can.
4. Is the game of 21 a combined event or independent event? Explain why

Once you have completed this – you can start the fun work of working from a textbook. Complete Ex 4.03 Q 5-9 on Page 108. Remember to always show the probability using the probability of an event equation:

P(E) = n(E) / n(S)

E = Number of ways the event can occur

S = Number of ways all events can occur

Remember that P(E) will always be 1 or under

## Probability Introduction

For today, we will be completing two small activities. Instructions are below:

1. Go to the following website HERE. Try these games (4 of them) and tell us in your notebook if the game is fair or not and why. 1 or 2 sentences per game should be enough
2. Complete some really fun questions from Ex 4.02 Q 3-5 on Page 102.

Remember the simple general rule for probability…

Experimental Probability = Number of times the event occurred / total number in sample

In time, we will also complete some small activities which DO NOT use the textbook or coins/dice.

Our general skills we will learn for this activity include:

• Calculate the probability of simple combined events using probability diagrams.
• Construct and use tree diagrams with and without replacement.

As you can see, it’s quite a short unit and A LOT easier than what you have completed previously. I expect there to be limited homework for this unit which should give you time to revise for your upcoming exam.