Technomaths

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!

Learning Intention:
To understand how cartesian coordinates are used on maps and in mathematics to describe locations and linear equations. Also to understand the relationships between co-ordinates that are reflected across the x and y axis.

Success Criteria:
Students will be able to draw up a cartesian plane, correctly locate and plot coordinates on the plane, as well as be able to identify where points exist using cartesian coordinates. They will complete the games and activities above and identify what they have learnt from each of the interactives.

Maths is Fun – Cartesian Co-ordinates

Shodor Interactives – General Co-ordinates

The links above take you to several activities to help you learn about Cartesian coordinates. Go to the first activity (Interactive cartesian co-ordinates) and plot three points to form an equilateral triangle in one quadrat. Write the co-ordinates down in your book, then reflect the triangle into each of the three other quadrats. List the plotted points in your book. What do you notice about the relationship between the plotted points?

Now. draw a shape of your own choice in one of the quadrats – it could be a simple polygon, a star, heart or more complicated original design. Then write down the co-ordinates of it’s vertices (in order). Reflect the shape into each of the quadrats and write down their co-odinates. Give a partner your list of co-ordinates and see if they can determine the shape you have created using the co-ordinates given.

Find out the answers to the following questions using your netbook for research:

  1. What is Descarte’s most famous saying?
  2. What did he see on a placard in the town of Breda, that challenged him?
  3. What branch of mathematics is named after Descartes?
  4. What habit did he give up up in the last year of his life?
  5. Now find a map of the school and create a set of cartesian co-ordinates on it. Work out the co-ordinates of the most important places in the school.

exterior angles of a triangle

Learning Intention: To understand why, in any triangle, the exterior angle is equal to the sum of the two interior angles not adjacent to it.

Success Criteria: To be able to calculate the missing angles in a triangle, given enough information.