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?

Welcome to Year 8R Maths class!

What do you find most difficult about maths?… at AnswerGarden.ch.

At Hawkesdale P12 College we have five maths classes per week. Eack week you are required to complete a Mathsmate homework sheet, which will be corrected each Friday. You can get help for these worksheets at the Mathsmate Skillbuilders site, which has a sample question with all the working and answers shown as well as some more problems to complete. I am pleased with the way each of you answered the questions on the first worksheet – well done!

We also use Mathletics, an online maths program that students can access from school and, if they have interenet access, at home. Each week I will allocate Mathletics tasks to be completed and you will have time in class to practise these activities, as well as play sums races against other students.

It is important that if you have persistent difficulty that you ask for help – if you keep trying and don’t understand a problem, we need to discuss the problem so your maths can improve. To assess where you are now with your maths, you will have a go at the Online Adaptive Number test , with the session key: GXH9ZNQN. Please try to complete the questions to the best of your ability.

Shapes with Symmetry

symmetry

Go to the Shape tool and draw, color, paste, slice, rotate, reflect, expand, and contract various shapes. Create a picture that has vertical or horizontal symmetry (eg. mountain reflected in a lake, a rocket ship, UFO, Christmas tree, an animal – use your imagination). Make sure you take a screen shot, convert it to a jpeg file in Irfanview and email as an attachment to me at my gmail address. This is an assessment task, so use at least five different shapes!

Maths learning on iPods!

screen capture Fraction Factory

Screen Capture of the Fraction Factory application for iPod Touch

As I wrote at Technoscience, I attended the Slide2Learn conference recently, learning about how to engage students in their Maths learning with Touch technology. Many parents may be concerned that their children are using these mobile devices for entertainment, rather than solid educational purposes. Victorian schools have tended to move away from ‘rote learning’ – continuous drills of multiplication tables for example – although many students still find instant recall of number facts difficult. Although I usually suggest to my students that they practise at home, perhaps with a multiplication grid on the back of their toilet door or above their bed, most kids I know are unlikely to spend the time necessary to make much of a difference. However, with an iPod Touch in their hands, they can practise with some of the following applications:

  • Times Tables Free – count the apples in groups, listen to the answers to multiplication facts and generate random questions.
  • Count By  – a 100 number grid with different colours to count by 5’s for example – also useful as an Erastothene’s seive, to find prime numbers.
  • Brain Tuner and Maths Magic Lite – maths problems with basic operations
  • Write Answer – Sums Lite – use your finger to write the answer to basic operations
  • Column Subtration for ‘take away with big numbers’
  • Math Tappers is a great blog with lots of examples of different maths apps
  • Math Magic – Simple, colouful design with multiple choice style qustions
  • Number Rumble – ($2.99) Basic operations to learn and quiz from Leapfrog – looks and sounds great!

Fractions are often a very difficult concept for middle years students and there are some great applications to practise sequencing fractions, finding equivalent fractions, ordering and converting as well as performing basic operations with fractions.

  • MV Fractions from Maths Village – short videos showing how to solve fractions problems
  • Fraction Factory – Move a fraction cog onto  the correct position on a number line(shown above)
  • Number Line – Move fractions and percentages into the correct order on a number line (shown below)
  • Match Up (LITE)- Match fractions and percentages and Match Up ($2.99)

Screen capture Number Line

Screen Capture of the Number Line application for iPod Touch

So, how do teachers (or parents) know what students have been practising without peering over their shoulder? You can take a screen shot of the result (most applications give a score or show you are ready for the next level) by holding the top (on/off) button and pressing ‘home’ at the same time – this image is saved in  ‘Photos’ .  Students can show you this image from their photos or send it to a blog (using Posterous) or to any email address.

How I plan to use this in my 6/7 classroom, is to have three groups of 8 or 9 students, with one group working on iPods, another teacher focus group and the third group on Mathletics or a hands-on problem solving task from Maths 300. Each student in the iPod group will be required to identify a learning need – perhaps ‘practising my 7 times tables’ or ‘learning to add fractions’ and search for at least two applications that purport to meet that need. They will then trial those apps. and complete a PMI or SWOT to identify which activity helped them most or which one they found most useful and why. This would also be submitted to the teacher as evidence of the work completed. I am really looking forward to implementing this kind of differentiated learning in my classes!

Assessment of Area and Perimeter

LC house plan

The assessment task for this unit of work is for you to draw the plans for a house, labelling the dimensions of each room and calculating the area of each room. The plans must be scale drawings, so you may like to have 1cm = 1m or 1:100. Your house should include at least two bedrooms, kitchen, lounge/living area, bathroom and laundry. Make sure you have allowances for door openings, wardrobes and hallways, if required. You can download an assessment rubric for this task at the Year 7 Wiki – Maths – Measurement Page.

JG house plan