# Angles

Image source

Learning Intention: “Demonstrate that the angle sum of a triangle is 180° and use this to find the angle sum of a quadrilateral.”

Success Criteria: Students will draw 2 copies of each of the triangles (acute, right-angled, obtuse, equilateral, isoceles and scalene) and show how, when the corners are removed, they can be placed on a straight line to form 180 degrees. This demonstrates that the sum of angles in a triangle is always 180 degrees.

This term we have started a new unit of work, learning how to estimate and measure angles. We have also identified and named triangles according to their side length and angles. Make sure you can identify and draw each of the following:

• equilateral triangle (three equal angles)
• isoceles triangle (two equal side and two equal angles)
• scalene triangle (three different angles and three different side lengths)
• acute angled triangle (all angles less than 90 degrees)
• right angled triangle (one angle of 90 degrees exactly)
• obtuse angled triangle (one angle greater than 90 degrees)

Remember that all the angles in a triangle always add to 180 degrees. The following links are to some interactive activities to investigate angles:

What’s my angle? from Ambleside Primary School.

Angle Activities from Ambleside Primary School.

Guess the angle from Crickweb.

# What are the chances?

Learning Intention: Students will understand that the scale of probability ranges from zero (impossible) to 1 or 100% (certain). They will be able to calculate simple probabilities by working out the number of desired outcomes divided by the total number of outcomes. Students will use tables and tree diagrams to work out the number of possible outcomes.

Success Criteria: You will be able to draw a probability scale, labeling it with different examples that are impossible, very unlikely, unlikely, 50:50, likely, very likely and certain. You will use coins, dice, spinners, cards and other tools to calculate the probability of various outcomes. You will use tables and tree diagrams to assist you to calculate the number of possible outcomes. For example; Annie throws a fair coin and a six sided dice. How many possibilities are there? How many of these are Heads and Even?

BBC Bitesize: Probability

Maths is Fun: Probability

Probability Games

National Library of Virtual Manipulatives: try Coin Toss and Spinners.

# Fibonacci Series

One of my favourite Maths lessons is about the Fibonacci series, using the YouTube video “Nature by Numbers“. Firstly, I ask students to add 0 and 1 and then the two previous numbers to make a sequence. 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89 etc. All students are capable of this, even if some use a calculator.
I then show students the video and we discuss all the examples from nature that show the Fibonacci sequence. We search for examples on Flickr – sunflowers, pine cones, succulents and nautilus shells. Although some people claim this is spooky, the pragmatist in me believes that nature exhibits this sequence as it is the most efficient way to pack objects (leaves, petals, seeds, she’ll compartments) into a small space.
If we divide each number in the sequence by the number before, the answer approaches what is called “phi” or the golden ratio, approximately equal to 1.618. Now we can discuss how this ratio was used by ancient Greeks, Euclid and perhaps even Leonardo da Vinci in the “Vitruvian Man”. Many architects, artists, photographers and others believe that this ratio represents the perfect proportion to render the subject most beautiful.

Phi and the Golden Ratio in Art

Golden Ratio in Art and Architecture

Fibonacci Numbers in Nature

# Year 7 Favourites

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

# Barbie figures and ratio

Learning Intention: Students will understand how to calculate and simplify ratios using body measurements as an example.

Success Criteria: Students will be able to correctly estimate the ratio of various body proportions, using average class data.

Do you think that “Barbie” dolls portray a realistic image of a human figure? What about “Bratz” dolls and Manga figures? What is it about these figures that make them so appealing to children? We are going to investigate the proportions of “Barbie” dolls and other figures to compare their ratios with the average year 7 student from Hawkesdale college. We now have the data that gives us some average measurements of height, head circumference, arm and leg length and chest, waist and hip measurements of the average student in our class.

• As you can see from the figure above, “Barbie” has a head to height ratio of 4 to 28cm or 1:7.
• Her leg to height ratio is 14cm to 28cm or 1:2.
• Her neck to height ratio is 2cm to 28cm or 1:14.
• Her head circumference is larger than her waist circumference.
• Her foot length to leg length is 2cm to 14cm, so, 1:7.

Calculate the same ratios for the average Year 7 student, using our data. What can you conclude?

Bill Genereux has written a terrific post about the proportions of superheroes, from a book that teaches people how to draw comic book heroes. Malyn Mawby has also written a great post about using Da Vinci’s “Vitruvian Man” to learn about ratio and proportion.

Image Source

# Our survey results

Image source

Learning Intention: Students will understand the meaning of mean, median, mode and range. They will understand how to calculate an average from given data and be able to work out the range of that data. They will then use the data to explore and compare ratios.

Success Criteria: Students will correctly calculate the average and range of the given data and use the data to make some comparisons of ratio.

Statistical values, such as mean, median, mode and range, help us to determine trends in the data. They are used in a variety of ways in business, education and government organisations. For example,  a company might want to find out about which customers spend the most money in their shops, so they can target their advertising better. Governments might need to find out about the age groups in their community, so they can distribute funding to health care, aged care, kindergartens, schools, universities, hospitals and other services.

• The mean (or average) of a set of numbers is calculated by adding all the numbers together and dividing by the number of values. It will always be somewhere between the smallest and largest value. What is the average height of students in Year 7 at Hawkesdale P12 College? Is there a height difference between males and females?
• The mode is the most frequently represented score. A shoe shop will need to order more pairs of popular sizes – 8, 9 and 10 – than smaller or larger sizes, for example.
• The median is the middle value – halfway between the smallest and largest value.
• The range is calculated by subtracting the smallest number from the largest number. What is the range of arm lengths in Year 7?

# Fractions interactives from NLVM

Fractions as we know them today weren’t used in Europe until the 17th century. However, Egyptians have been using fractions since at least 1800BC, although they never wrote fractions with a numerator greater than one. These are called unit fractions. Fractions with a numerator greater than one were expressed as the sum of unit fractions. Find out more at the History of fractions and Egyptian fractions.

The National Library of Virtual Manipulatives has a range of interactive applets that you can access to learn about fractions:

Try at least three of these interactives and write a comment below about what you have learned.

Image is a screenshot from the Cool Math 4 Kids site.

When adding or subtracting fractions the first thing you need to do is make sure that the denominators (bottom numbers) are the same. If all the denominators are the same you can simply add or subtract the numerators (top numbers) and then simplify the answer if required. If the denominators are different, you need to find a common multiple and convert both fractions, so that the denominators are the same. Activities 4 and 5 below show how this is done:

1. Adding Fractions from Cool Maths 4 Kids.

2. Three simple steps to adding fractions from “Maths is Fun”.

3. BBC Bitesize – fractions activities – Choose the fractions activities from BBC Bitesize (Equivalent fractions and ordering and comparing fractions).

4. Adding fractions with different denominators from “Maths Playground”.