Pythagoras and Square roots

Slide1

Pythagoras was a famous mathematician who lived about 2500 years ago. He is credited with being the first person to prove that in any right-angled triangle there is a special relationship between the squares of the three sides. The theorem has an important role to play in everyday life because right-angled triangles occur in construction, navigation, planning, design and packaging. Pythagoras’ theorem is one of the great geometrical theorems.

Man, Myth and Mathematician – Pythagoras of Samos – Genius (YouTube video – 45 minutes)

Pythagorean Theorem Lesson from BrainingCamp

Video Interactive from Maths Interactives (Skate Park)

Video interactive from Maths Interactives (Construction)

Pythagorean interactive from BrainingCamp

1. A carpenter wants to build a handicap ramp over a set of steps that is 12.0m long and 5.0m high. How long will the ramp be?

2. A massive new digital TV has a width of 160cm and a height of 120cm – what is it’s diagonal measurement?

3. A window sill is 12 metres above the road in building. A ladder is placed 5 metres from the wall and reaches the window sill. How long is the ladder?

Year 8 – Exponentials with Aliens!

cretaphus_v2_by_deadpoolrus-d3l8anx

Image Source

The Exponential Monster!

So far you have learned about the rules that apply when using indices. But how might they be used in the real world? A good example is when bacteria divide and multiply – the population increases exponentially. The human population took 300,000 years to reach the first billion people, 130 years to add the second billion and only 12 years to add the fifth and sixth billion. We passed the seven billion mark last year. Find a table that shows the world’s human population and draw a graph using Excel, showing this data.

Year 8 – Index Laws

indexlaws

The Laws of Indices are simple rules to use when you have the same base number. This is covered in Chapter 3 of your JacPlus online text. Please work through Exercises 3.2 to 3.7.

BBC Bitesize has some worked examples and simple problems about Index Notation, Index Laws and Substitution.

More activities from MathsClass.net – a Hot Potatoes Quiz and OnlineMathLearning.org.

Complete the Bitesize “Test Bite” and two other assessment tasks from the Hot Potatoes series and leave a comment below with your scores.

Week 4: Re-visiting Negative Numbers

These three videos may help you to understand negative numbers:

  1. How they compare to positive numbers
  2. How to add and subtract integers
  3. How to multiply and divide integers

Watch each video and then complete the “Negative Numbers” test again.

Maths Antics – Negative Numbers video #1

Maths Antics – Adding and Subtracting Integers (video #2)

Maths Antics – Multiplying and Dividing Integers (video #3)

Week 3: Basic Operations

Calculator_walther_hg

Image Source

This is a picture of a mechanical calculator, common in Europe in the 1960’s. Imagine using one of these in school! We are lucky now to have very cheap and efficient electronic calculators that can do quite sophisticated operations. However, it is still important to have automatic recall of number facts – like when collecting change at a shop, calculating wages and saving for something special.

This week we will be practicing basic operations – multiplication tables up to 12, indices, order of operations (BODMAS) and short division. In Year 8 we will be doing operations with negative numbers. There are several FREE apps that you can access on mobile devices to practise basic operations:

  • ***Wishball (place value, adding and subtracting)
  • ***Motion Maths Hungry Fish (addition)
  • ***Motion Maths Wings (multiplication)
  • King of Maths
  • Times Tables Quiz!
  • IXL Maths Practice

***I have tried and recommend these ones, but there are lots more available. Choose one, tell me about it and let me know what you think in the comments below.  Please continue to work on your Mathletics activities and Mathsmate worksheets (due Friday).

My favourite Middle Years Maths sites and resources

Screen Shot 2015-01-28 at 2.45.01 PM

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.

Welcome to Year 7 and 8 Maths for 2015!

Math-Tagxedo

There are three areas in the national curriculum that we will study in Maths this year:

  1. Number and Algebra (Terms 1 and 4)
  2. Measurement and Geometry (Term 2)
  3. Probability and Statistics (Term 3)

Year 8 Maths (Term 1)

Year 7 Maths (Term 1)