Angles Assessment

Building in Perth (author’s photo)

1. Can you find an acute, right, obtuse, straight and reflex angle in the image above?

2. Fold an A4 sheet of paper into six sections. In each section draw one of the following angles, estimate it’s size and then measure it. Make sure you label each drawing.

(a) obtuse

(b) right

(c) acute

(d) reflex

(e) complementary angles

(f) supplementary angles

 

 

Measuring Angles, triangles by side length and angle size.

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Image Source

Learning Intention: You will understand that angles are measured in degrees and be able to name and identify different types of angles and triangles. You will be able to use a protractor effectively and be able to estimate angle sizes.

Success Criteria: You will be able to estimate, draw, measure and identify angles measured in degrees. You will be able to identify, name and draw triangles by side length and by angle size.

This term we will start by measuring angles, using a “rotogram” and then a protractor. You will all need your geometry kit this semester – compass, sharp grey lead pencil, protractor and a good ruler.

What are acute, right, obtuse, straight and reflex angles?
What are equilateral, isosceles and scalene triangles?
What are acute, right and obtuse triangles?
Can you have an equilateral right angled triangle or an obtuse equilateral triangle?
Can you have an obtuse isosceles triangle or a right-angled isosceles triangle?

Task 1: Work in a group of three. Each person should draw and cut out six copies of an equilateral, isosceles or scalene triangle, using different coloured paper. Share your shapes so that each person in the group has two of each type of triangle. Now, tear off the corners of one of each type of triangle and match up the corners to demonstrate the sum of the angles in a triangle.

Task 2: Do the same for acute, obtuse and right angled triangles. Do you think the sum of the angles in a triangle will always be the same? Can you explain why? Do you think the same would be true for quadrilaterals, pentagons and hexagons etc?

The Maths Masters have written a very interesting article in The Age about the triangles in Federation Square.
Read more

Interpreting Graphs

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Graph created in Excel by Jakob Linke, Year 7

Learning Intention: This week you will continue to work with line graphs, bar charts, pie charts and scatter plots. Your learning intention is to understand how to describe various graphs in words. You need to be able to interpret the information given.

Success Criteria: You will be able to look at the scale, axes, labels and title of different graphs and be able to describe what they mean. You will be able to match a graph to it’s description and draw a sketch graph from a sentence. These are the activities planned:

1. Find a graph with data in a magazine or newspaper. Cut it out and paste it into your books. Look carefully at the title, axes, labels and scale. Write a few sentences describing what the graph shows.

2. “Which graph is which” worksheet. You will be given nine small graphs and have to match scenarios to the shape of the graph.

3. Maths300: Temperature Graphs. Match the average maximum and minimum temperatures to Australia’s capital cities.

4. Match the graph to the Olympic record time/distance.

5. Which kind of graph would best represent the following situations?

  • Height of a plant growing over time?
  • The various heights of different plants of the same species in a greenhouse, over time?
  • Thousands of plants in a crop to determine which genotype was the fastest growing?
  • Percentage of different species of plants in an area of forest?

6. “Purchasing pantyhose” and “Blood Bank” graphs

7. Go to the Melbourne Grand Prix map and note the speed and distance from the start as each car makes it’s way around the track. Draw a graph that shows distance from the starting line on the horizontal axis and speed on the vertical axis.

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Stem-and-Leaf Plots and Scatter plots

Learning Intention: Students will understand what data is suitable for graphing on a scatter plot and be able to describe the significance of a “line of best fit”.

Success Criteria: You will draw a correctly labelled scatter plot from our arm span and height data and determine if there is a relationship between these measurements.

Last week you learnt the definitions for mean, median, mode and range and created a stem-and-leaf plot using the height of students in Year 7. You also measured the length of seven leaves and calculated the mean, median, mode and range of this data. This week we will investigate another type of graph, the scatter plot. Use the data we collected from our Year 7 Maths Survey to graph arm span against height (in centimeters).

This week we may also get the chance to do other activities with scatter plots:
1. Barbie Bungee
How many rubber bands are needed for Barbie to safely jump from a height of 400 cm?
What is the minimum height from which Barbie should jump if 25 rubber bands are used?
How do you think the type and width of the rubber band might affect the results?
Do you think age of the rubber bands would affect the results–that is, what would happen if you used older rubber bands?
If some weight were added to Barbie, would you need to use more or fewer rubber bands to achieve the same results?
State a possible relationship between the amount of weight added and the change in the number of rubber bands needed.
(thanks to Mrs Jirkovsky at North Adams Public School for writing about this activity on her blog!)
2. Be an actuary – distance vs earthquake intensity.

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“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.

Summary Statistics – Mean, Median, Mode and Range

Learning Intention: Students will understand the meanings of the terms “mean”, “median”, “mode” and “range” and be able to calculate these summary statistics from data supplied to them.

Success Criteria: Students will be able to calculate the mean, median, mode and range from given data.

We are now doing a unit of work on statistics and you will need to know the following terms:

  • Categorical data (cannot be measured by quantity, for example, colour of eyes, favourite footy team)
  • Numerical data (can be measured by quantity, for example, number of students at school)
  • Continuous data (eg. height, weight, length of foot) can be a decimal number.
  • Discrete data  (eg. number of pages in a book, number of students in a class) cannot be a fraction or decimal.
  • Mean = average (total of all scores divided by number of scores)
  • Median = middle score (arrange data from smallest to largest and find the middle number)
  • Mode = most frequent score
  • Range = difference between largest and smallest score

The Australian Bureau of Statistics collects data to assist businesses and the government to plan for the future – where to build freeways, hospitals and schools, for example. Every four years they distribute a census across Australia to gather data about housing and population. How is a “survey” different to a “census”? Each year they invite schools to particpate in the “CensusAtSchool” program, which I have signed us up to. After you have completed the survey, we can use the data to work out the summary statistics for the “hours of sleep per night“. There are some other great activities we can do at quick maths activities from the census at school survey.

 

 

Student surveys, data and graphs

Learning Intention: Students will understand how to collect data using a tally and create a frequency table and bar graph using the data. They will understand how to convert fractions to decimals and percentages. They will create a pie chart using this data by converting 100% to 360 degrees.

Success Criteria: Each student will produce a poster that includes a frequency table (including fractions, decimals and percentages), bar graph and pie chart of their chosen data, collectecd from the Year 7 Maths Survey.

  1. First collect your data in tally form
  2. Add each category and find the total
  3. Represent each category as a fraction
  4. Convert to a decimal (2/25 = 16/100)
  5. Convert to a percentage 16/100 = 16%
  6. Create a bar graph using this data
  7. Remember to add SALT to your graph – Scale, Axes, Labels, Title
  8. Turn your bar chart into a pie chart (multiply percentage by 3.6 because 100% = 360 degrees)
  9. Make sure you have a key to interpret your data.
  10. Add a beautiful title and colour to present your poster.

Go to Create-A-Graph and use your data to check that your graphs are correct. Print out the computer generated graphs to add to your poster.

 

 

Survey and Feedback

Thank you for completing the survey about your maths learning last period – it is helpful for me to know how you learn best and if you have any difficulties with your maths. This period I would like you to consider the feedback you get back from teachers – notes on your work, a mark, verbal feedback or anything else that lets you know how you are going and how you can improve. Could you please click on this link to a Wallwisher page and leave a comment about the kinds of feedback you get from teachers and which types are the most effective ways to improve your learning.

For the Year 7 Maths Survey results please click on this link.