# Week 1: Positive and Negative Integers

A number line represents a series of integers extending to infinity in both directions – it is important that the numbers are evenly spaced and there are arrows on both ends. In real life we use negative numbers to represent debt (“in the red”), distance below sea (or ground) level and temperatures below zero degrees. But we haven’t always had a way to represent these concepts and at one time mathematicians didn’t believe negative numbers existed. (Read the about the history of negative numbers below).

Negative Numbers Game from BBC Bitesize

# My favourite Middle Years Maths sites and resources

This year I will be teaching both Year 7 and Year 8 students Maths in our small, rural school in SW Victoria. With relatively small class sizes and 1:1 BYOD we have great opportunities to engage students with high quality digital resources that help to foster a love of Maths learning.

Or, in the case of some teenagers, make them hate it a little less? Let’s face it, I work with adolescents every school day, and many of them haven’t yet found their passion. They have strong opinions about what they like (“Call of Duty” and One Direction, for example) and what they hate (mostly homework, uniforms and algebra). CoD and ID are much more relevant and useful than…..whatever.

So, to get on with this post, my intention is to share the middle years Maths resources that I find most useful, hopefully because students find them authentic, relevant or just plain fun, while addressing curriculum statements.

My Most Useful Sites and Resources:

• ABC Splash – high quality resources, aligned to the national curriculum.
• ConCensus – This game uses data from the Australian Bureau of Statistics to allow users to make graphs and diagrams using selected postcodes and categories.
• Choose Your Own Statistics – This interactive activity has ten different categories (including demographics, weekly wages and homelessness) with infographics and a tool that allows users to visualise the data.
• Area of a Triangle – a cartoon interactive that assists students to learn and practice the formula for calculating the area of a triangle.
• Algebra – it’s a piece of cake – a series of eight videos that explain some simple algebraic concepts using a “number crunching machine”, recipes and simple patterns.
• National Library of Virtual Manipulatives – Huge range of applets across all areas and age groups. (If you have difficulty accessing these interactive animations, try a different browser, update or enable your Java).
• NRICH – enriching mathematics – Great problem solving activities for a variety of ages.

# Year 6 to 7 Orientation Day!

Congratulations on completing Year 6 and welcome to Hawkesdale P12 College for Year 7. This blog is where I will post some of your Maths classes for next year. If you scroll back through the posts you can see some of the work we have been doing this year in Year 7 Maths.

1. Open Powerpoint and insert a 5 x 5 table.
2. Add Christmas themed clip-art to each cell of the table.
3. Cover each image with a shape, using “Insert” > “Shape”.
4. Number the shapes in each cell from 1 to 25.
5. Add animations, so that when you click on the shape, it disappears and the “treasure” is revealed.

TASK 3: Hour of Code (see post above).

If you have finished, you may like to create a Christmas card for your friends or family. When you have finished you may like to try some of these games:

# Apps for Year 7 Maths – Number

Image source – screenshot from the “Motion Maths” app, in which the user must tilt the device to “bounce” the ball at a specific point along a number line.

This term we are starting with the characteristics of whole numbers and then fractions and decimals, including the following concepts:
– positive and negative integers
– square numbers and square roots
– factors and multiples
– prime and composite numbers
– prime factor trees

There are several apps that may assist you or your child to understand these concepts. The following apps are all available on IOS devices (iPhones, iPods and iPads) and some may be available on android devices.

– Zoom (place value – ordering whole numbers)
– Wings (greater than and less than, multiplication)
– Motion Maths (fractions)
– Wishball (place value, addition and subtraction)
– Fraction Factory (fractions, decimals and percentages)
– Number Line (fractions, decimals and percentages)

# 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

# Substitution in Algebra

Learning Intention: Students will understand that substitution into formulae is a valuable mathematical process that is useful in many real-life situations.

Success Criteria: Students will work through a series of substitution exercises and identify useful formula for converting units of measurement (eg. Celcius to Fahrenheit; ounces to grams; miles to kilometers; calories to kilojoules). Students will use the formulae to calculate the height of a person knowing the length of their femur bone.

Forensic scientists are responsible for piecing together information about crimes, such as identifying victims and perpetrators from DNA evidence, fingerprints and bones. One formula that scientists use is to calculate the height of a person(h) from the length of their thigh bone – called a femur(f) in centimeters. The formula is as follows:

height = 69.09 + 2.24 x femur OR h = 69.09 + 2.24f

Walking along the beach, your dog retrieves a human thigh bone! It is 45cm long. How tall was the person this bone belonged to?

A fellow blogger, Malyn Mawby, has written a great post about how she used the Vitruvian Man to teach a lesson incorporating ratio, percentages and algebra. Do your body parts match the ratio of the Vitruvian Man?

Use the Internet to research at least five of the following and give an example of each.

1. Calories to kilojoules
2. Miles to kilometers
3. Celcius to Fahrenheit
4. Ounces (oz) to grams
5. Pounds (lbs) to kilograms
6. Acres to hectares
7. Inches to centimeters
8. Australian dollars to British sterling
9. Feet to metres
10. Time in Hawkesdale to time in Greenwich, UK.

Learning Intention: Students will understand the difference between area and perimeter and that if you double the area of a paddock, you do not necessarily double the perimeter.

Success Criteria: Using a fixed quantity of fencing, students will model different areas of paddock. With a fixed area of paddock, students will find different perimeters.

A farmer has 3.6 kilometres of fencing. Convert to metres and design five different paddocks using all the fencing. Calculate the area of each paddock. Which has the greatest area?

A farmer needs a paddock of 2400 metres square. Design four different paddocks with this area. What is the perimeter of each of these paddocks?

# Length, Area and Volume

Learning Intention: Students will understand the similarities and differences between types of measurement – length, area and volume.

Success Criteria: You will be able to measure and calculate length, area and volume of squares, rectangles, triangles and their prisms. You will create a Venn diagram to compare length, area and volume.

For the first 60 seconds of class list all the units of measurement you can think of.

Last term we learnt about measuring the perimeter and area of two dimensional shapes. With the pre-service teacher, Mrs Bos, we measured the perimeter and area of the playgrounds in the school.
This term we will start by looking at three dimensional shapes – cubes, rectangular and triangular prisms. If you look at the shape of your text book, you will see it has six surfaces – three pairs of rectangles with the same area. There are three measurements you need – length, width and depth. Calculate the surface area of this rectangular prism using these three measurements. Now calculate the volume of your textbook using these three measurements – length x width x depth.

# Transformations – Reflection, Rotation, Translation & Dilation

I just popped this is so I don’t forget about this great idea for learning transformations when we do it later in the year!