Technomaths

Algebra Balance Scales

October 13, 2011

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.

Introduction to Algebra

October 12, 2011

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.

New Unit on Algebra next term

September 18, 2011


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.

Last week of term 3!

September 17, 2011

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?

Sketching Linear Graphs

August 16, 2011

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.

Algebra versus Cockroaches

August 11, 2011

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?

Gradient

August 9, 2011

The gradient of a ramp is very important if you are a builder or in a wheelchair – too steep and it is too difficult to wheel up and too shallow and it is very long and expensive to build. The Australian Standard (AS1428.1) requires that
ramps should be of a gradient of 1:14 (if over 1250mm in length) and 1:8 if less than 1250mm in length. The ramps at school were built 15 years ago; measure them and determine if they meet the current Australian Standards.

Take a photograph and measure the slope of the slide (or another example of gradient) in the playground. What is it’s gradient? (rise divided by run). Label your image (in Paint) and send it to my email address. The following screenshot shows the slopes generated in Graphmatica (Free download here). The pink line is the slope of the ramps inside our old school building. It sits between the recommended Australian standard (white) and the maximum Australian Standard (red). The new building has a wooden ramp with a slope of 1:14, which is the recommended Australian standard. Choose one of the slopes we measured and describe it in the comments below.

 

Learning Intention: Students will learn to draw a line graph to represent a data set, including the appropriate scale, axes, labels and title. They will also use technology to create a graph using the same data to compare the process and the product.

Success Criteria: A successful line graph will include the following:

  • lines drawn neatly with a ruler and greylead pencil or a digital graph with appropriate data
  • an appropriate scale to show the data clearly
  • clearly labelled and equal increments on both the horizontal and vertical axes
  • labels on each of the axes that identifies the appropriate data (time in years, population in 100,000′s for example)
  • a clear and accurate title that explains the purpose of the graph
  • Students may also be able to extrapolate the graph to make a prediction about future data.

“Every five years the Australian Bureau of Statistics (ABS) runs the Census of Population and Housing. This year 29 000 collectors will be part of a 43 000 strong Census workforce that will paint our national portrait in numbers. The Census is a questionnaire filled out by everyone who is in Australia on Census night, except foreign diplomats and their families. It’s so important that it’s mentioned in the Australian Constitution.

The Census counts the number of people in Australia, and information about them like what work they do, what education they have and the households they live in. This information helps decide where services such as hospitals, schools and roads will be built. The Census of Population and Housing is also used as the starting point to estimate the population of Australia, the states and territories and small communities.

This Census involves delivering 14.2 million Census forms to Australia’s 9.8 million households and then transporting and processing more than 46 million pages of data. Census is also changing with the times: 30% of the population are expected to fill out their forms online using eCensus.” Read more about the Census at “Maths by Email”.

The following task uses data taken from the results of the census to produce a line graph that shows the changes in the “Estimates of the Indigenous Australian Population since 1901″. Complete the graph with greylead and a ruler and answer the following questions:

  1. Give reasons for why a line graph is the most appropriate way to present this data.
  2. Explain why a histogram is an incorrect way to present this data.
  3. Look at the shape of the line in your graph. What sort of graph is this?
  4. Use extrapolation to estimate the Indigenous population for 2011.
  5. Do you think your estimate will be correct? Give reasons for your answer.

Now use Create-a-Graph, Excel, ChartGo or the Online Chart Tool to create another line graph using the same data. Compare your paper version with the digital version. In the comments section below let me know which tool you used and how the graphs compared. Which was easier and why? Which was a better product and why? Which tools would you prefer to use? How might you use these tools in the work place?


This is James’ graph, which includes SCALE, AXES, LABELS and a TITLE. Well done!