Technomaths

Today your task is to identify an area of difficulty – use your Mathsmate sheets or Mathletics activities – and write yourself a goal. For example, “Today I will work out how to simplify ratios” or “I need to practise converting fractions to percentages”. You can print out the Skill Builders from Mathsmate or use the corresponding activities on Mathletics to practise. Ten minutes before the bell, leave a comment below about your goal and what you achieved.

We have spent the last few weeks learning about algebra – what do we know now, that we didn’t know before?

• Pronumerals, co-efficients, variables and constants
• Expressions
• Backtracking
• Solving equations

This site, MathsNet has some algebra games you might like to try. Choose the expression or constant that you need to remove from the equation and apply the opposite sign.

So far we have looked at the basic rules for algebra in expressions – leaving out the multiplication sign and the ’1′ in front of a pronumeral, adding and subtracting ‘like terms’ and multiplying and dividing with pronumerals. Next we will look at multiplying and dividing with indices and then using equations.

Maths is Fun has a quick tutorial on how to use exponents with six questions you can try online.

The Algebra Balance Scales are all about doing the same thing to both sides. So if you remove to blocks from one side do the same to the other side.

Algebra Balance Scales with Negatives is a little more difficult – balloons act as negative numbers to counter-act the weights.

When you have spent about 15 minutes on each activity, leave me a comment to let me know what you found easy, what you found difficult and what you learnt from these two interactive learning objects.

Some people admit they don’t like algebra, usually because of a negative experience at school in maths class. In fact, algebra has a pretty bad name, even amongst students who don’t really know what it is about (perhaps we can blame the popular media for that?). In fact, algebra is just a way to model mathematical expressions and equations using pronumerals instead of numbers. Like another language. Here are three sites to start you off on the right foot with algebra:

Shape times Shape is an activity where you discover which shapes represent which numbers, using a series of multiplication problems.

BBC Bitesize has an introduction to algebra using formulae.

Maths is Fun also has an introduction to algebra which includes a brief explanation with some examples.

Another interesting way to learn about algebra is with “Off Road Algebra” from MathMatters. This resource includes videos of off road motorcycles riding up ramps and off jumps and some other dirty stunts. The maths is a series of problems including converting litres to gallons, working out the length of the third side of a triangular track and time and distance.Check out the MathMatters – HotChalk website here.

Prior to starting this unit students should be able to recognise simple number patterns (addition, subtraction, multiplication, division and indices) and understand that (multiplication and division) and (addition and subtraction) are opposite terms. We will start with an activity to reinforce working with positive and negative numbers at Algebasics.
“Maths is Fun” has a good Introduction to Algebra, that we will go through in class. Students then need to be able to recognise like and unlike terms. There are some more practise questions at MCA Online: Like and Unlike Terms Algebra for Children is another site that may assist you to work with like and unlike terms.

As each of you have netbooks to use at school and at home, you may like to access the National Library of Virtual Manipulatives site, which has a great range of interactive tasks for year 6 to 8 Algebra. I like the “Coin Problem”; “Factor Tree” and “Function Machine”.

I would like to be basing this unit of work on some of Dan Meyer’s Resources at “Algebra: The Supplement”. Dan Meyer has curated 40 weeks of algebra learning activities, while we have just ten weeks until the end if term, so we will try to do some of the most powerful problems that have been posed.

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”

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?

Miss Tara Richardson has produced another video “Sketching Linear Graphs” – her blog is at “My Blog”

Learning Intention:
Students will learn how to sketch linear graphs.
Success Criteria:
There are three different methods you can use to draw a linear graph
1. You can identify the y-intercept and gradient (rise over run) from an equation.
2. You can substitute values into an equation to find at least two co-ordinates.
3. You can use the intercept method to plot two points on the x and y axis. Plot the graph by substituting x=0 (the y-intercept) into the equation as the first point and substitute y=0 into the equation to find the second point.
Tell me which method you prefer to use and why?

Learning Intention:
Students will understand how to calculate the gradient of a straight line using three different methods.
Success Criteria:
You will be able to calculate the gradient of a line when given the linear equation, the graph or two sets of co-ordinates on the line.

Over the next five weeks, Miss Tara Richardson will be taking your Maths and Science classes as part of her teaching rounds in her final year of a Graduate Diploma of Education. She has created these great videos for YouTube to assist your learning about linear equations. Do they help you to understand gradient and y-intercepts and equations? Let her know what you think about them by clicking on the ‘like’ or ‘dislike’ buttons.

This fun game from HotMaths requires you to use linear equations to knock out cockroaches on a cartesian plane. Choose a weapon and determine the equation of the line, which represents the path of a weapon, that is used to destroy cockroaches. Draw on your knowledge of the gradient and y-intercept of a line. There are different levels which get progressively harder as you move through the levels. Hints and a printable report, outlining your progress, are also available. Let me know what you learnt in the comments below.

Slopes and Equations of lines from Geogebra  has a series of five activities which begin with asking you to choose two points on the given line, then following the instructions and using the rule for gradient, calculate the gradient. The next activities ask you to find the gradient from a line you create and the last two activities require you to find the equation of the line. Good luck and have fun! Let me know how you go in the comment section. Which of the two sites helped you to learn more about gradient and linear equations?