# Probability and Percentage increases and decreases

Following our assessment task yesterday it is clear that some students need to revise certain areas of the work we have done in term 1 and 2:

Probability – Relative frequency with ten questions to complete.

Percentages – How to convert fractions and percentages to a pie chart (360 degrees) with ten questions to complete.

Percentage increases and decreases – Worked examples and five problems to solve.

Stem and Leaf plotsWorked example and thirteen questions to solve.

Problem #1: You have a list of 7 numbers. The average of the numbers is 9. If you take away one of the numbers, the average of the numbers is 8. What number did you take away?

Problem #2: Martin has completed five Maths tests and received an average score of 80%. What is the highest average he could have after the next test?

Problem #3: A Year 7 class was asked “How many goals did you shoot at lunchtime?”. The lowest answer was 5 and the highest answer was 20. The total of all the answers was 60. What is the smallest number of students who could have been asked?

# What are the Chances?

Image Source

You will be familiar with hearing discussions about probability in terms of words, if not quantities – “It isn’t likely to rain on the washing today”, “The chances of winning the lotto are very small” “It is equally likely that the other team will win”. For the remainder of this term we are going to use numerical representations of probability, including tree diagrams, two-way tables and Venn diagrams.

# “Lies, Damn Lies and Statistics!”

Learning Intention: Students will understand that data can be displayed in various ways and they will be able to interpret different types of graphs, including bar graphs, pie charts, stem-and-leaf plots and scatter plots.

Success Criteria: Students will complete the following activites and be able to explain what the graphs tell us about the data collected.

The above quote, popularised by Mark Twain, refers to the ways that politicians can sometimes “manipulate the data” to suppport decision-making. The same data can often be used to support or disprove a theory, depending on the emphasis. Over the next couple of weeks we will use the data from the CensusAtSchool questionnaire to learn more about summary statistics and graphing. Some of the activities we will do are:

You can use the random data sampler to display the data relevant to each question.

# Last week of term 3!

This week is our last week of school before September holidays and we also have Parent-Student-Teacher interviews on Wednesday afternoon and evening. I expect each of you to come along and discuss your progress in Maths with your parents as well as show them some of the great work you have been doing this semester. We will talk about your goals for Term 4 and beyond and how Maths is relevant to your future.
Well done to all of you who completed the Probability test last week – I was very pleased with the results.
Monday (period 3): Mathsmate and discuss the answers for the Proability test.
Tuesday (period 3): Skill builders for areas of improvement from Mathsmate
Wednesday (period 1): Converting fractions to decimals and percentages.
Thursday (period 1): Rates and Ratios.
Friday (period 3): Mathletics

Areas of Difficulty:
Some of you have been having problems with the following Mathsmate Questions:
Number 18 Expressing numbers as a product of it’s prime factors – Try this interactive at the NLVM “Factor Trees”.
Number 13 Operations with negative integers – “Color Chips – Subtraction”

# Progression Points for Probability

At Hawkesdale College the Numeracy Professional Learning Teams have been looking at the progression points for each of the five strands of mathematics and starting with Number, assigning assessment tasks for each level. During the next five weeks, while Tara is taking the year 8 Maths class, we are studying a unit on Probability, so it is a good opportunity to unpack the progression points for this sub-strand.

Progression Point 3.25 – “use of fractions to assign probability values between 0 and 1 based on symmetry”. All our students have demonstrated the ability to place the chances of specific events occurring on a number line, so they have achieved this level of understanding. Some examples were: randomly choosing a day of the week and getting a weekend day, rolling a dice and getting an even number, using a spinner with five equal sections and getting a specific colour.
Progression Point 3.75 – “simulation of random events” and “calculation and analysis of the stability of a sequence of long run frequencies where the number of trials increases”.
We have used dice, coins and computer and iPod (using the app “iChoose”) simulations of other random events.
Virtual Dice: Simulation of throwing one, two or three dive.

Probability Tree: A bag contains 4 red counters and 7 blue counters. A counter will be taken from the bag, its colour noted and then returned to the bag. Students complete the corresponding probability tree, with uneven chances.
Snakes and Spinners is an assessment activity from the Learning Federation.
The “Dice Duels” series of activities (L2634 to L2640) is also from the Learning Federation.
Podcast about “slot machines” – we call them poker machines in Australia. What do you think is the likelihood of winning the maximum pay out at the pokies?

# Using an iPod for probability experiments

Screenshot from iChoose

Year 6/7 students continue to explore probability in our maths classes, today with iPod touches. “iChoose” is a free application, with a number of options for random choice results – coin toss, dice, cards, girl/boy and more.  Students did  timed trials to collect data (both coin tosses and dice throws) and collated class results. Each student used the iPod calculator to work out their percentages of each result and then compared individual data with class data to show that the greater the number of trials, the closer to the theoretical probability the experimental data gets.

We also used real dice and coins (swapping over so all students had a turn at both the real and virtual) and compared the results. At the end of the lesson, students completed an ‘exit slip’, with three important things that they have learnt about probability. Most students were able to complete this successfully, writing how to calculate probability, how all outcomes add to 100% and about experimental and theoretical probability. Even students with greater learning needs were able to state that they had learnt how to work out percentage and how to tally results. It is pleasing when you can engage students with a wide range of learning abilities in one class and hear that each of them has benefited from the lesson.

# More Probability interactives on FUSE

Go to FUSE and type in the Learning Resource ID number into the search box to try each of these activities. Then leave me a comment below to tell me what you have learnt, which of the activities you enjoyed most and why you thought it was the best.

Fish tank probability at SYHVH2 – choose the number of fish to create specific probabilities.

Coin Tossing at LJRJ83 – see the results of 100 coin tosses and decide if it is a counterfeit.

Dice Duels – Airport subtraction at ES8BPH – roll the dice to see if your plane can take off.

Dice Duels – Airport addition at 5RUC3L – roll the dice to see if your plane can take off.

Dice Duels – Go-Kart Race – at CRMNX3 – roll the dice for Kart racing

# What is the Probability you can use your netbook today?

Image Source – Screenshot

Congratulations to all those students who were succesfully able to log on to the Ultranet on Friday! Well done. Today we are going to continue with the topic of probability using some computer activities. Firstly, we will go through some revision of what we have learnt so far using the BBC – KS3 Bitesize Maths site – Revision of Probability. Then you can do the BBC Bitesize Activity on your netbooks.

When you complete that activity, and if you feel confident, you can go on to the BBC Bitesize Probability Test. When you complete the test, take a screen shot of your result and save it in your maths folder as a JPG file (copy into Paint or Irfanview and rename with your name – for example, “Britt’s test”), then send it to me by email, making sure your name is attached.

If you think you need more practise before doing the test, you can try these activities:

FUSE – Foul Food Maker – What are the chances of worm pasta, fly soup, fetid fungi or a bug burger? (Easy)

Exploring Probability in the Snow – What is the numerical probability of a snow-boarder choosing a particular ski-run?

Hands-on – Create a spinnner where one result is double the chances of another (For example, you are twice as likely to spin a red as you are to spin a blue).

If you have an iPod – download iChoose – a simple program with a choice of a coin toss, dice throw or choose a card. Do ten trials and record your results, then ten more and add your results to another class members. What do you notice about the results as you record more trials?

# What’s the Chance of Rain?

We often use the language of probability in conversation – “There’s a good chance of rain today” or “He is almost certain their team will win”. In mathematics, we can give precise values to the probability of a particular event occurring, ranging from 0 for impossible to 1 for certain. Draw a number line across your page, labelled zero at left and 1.0 and 100% at right. Mark 0.25; 0.50 and 0.75 on your line. Now match ‘likely’, ‘even chances’ and ‘unlikely’ on your line. Label where you think the following events will be:

• Essendon winning the coin toss at the beginning of the game
• Snow falls in Darwin
• Drawing a red heart card from a shuffled pack
• Rolling a six on a die
• A baby is born – it’s a girl!
• The sun rises in the east tomorrow
• Water boils in the fridge
• A horse wins the Melbourne Cup
• Mrs Gow winning Australian Idol