# Operations with Fractions

You already know that when you multiply a whole number by another whole number, the answer is a larger number. But when you multiply a fraction by another fraction the answer is smaller! Look at the top picture – if you have 2/5 of a pizza left and you need to share it equally with your brother, how much of the original pizza do you get? How can you add 1/3 and 1/6 of a pizza?

Adding and Subtracting fractions – BBC Bitesize

Multiplying and dividing fractions – BBC Bitesize

How to Add and Multiply fractions – WikiHow

# Year 8 – Index Laws

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.

# Year 7 – Fractions

Maths Antics – Converting Base-10 Fractions

Maths Antics – Converting Any Fraction to a Decimal Number

Maths Antics – Comparing Fractions

# Week 4: Re-visiting Negative Numbers

These three videos may help you to understand negative numbers:

- How they compare to positive numbers
- How to add and subtract integers
- 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

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).

# Week 2: Factors, Multiples, Squares and Primes

This week we will review the definitions of the following terms:

**Integers:**Positive and negative whole numbers (not decimals or fractions)**Factors:**Numbers that can be divided into a larger number with no remainder.**Multiples:**The resulting number of multiplying two smaller numbers.**Square numbers:**When result when you multiply a number by itself (eg. 3 x 3 = 9)**Prime numbers:**Numerals with only two factors – one and themselves.

**Resources:**

- Erastothene’s Sieve – for finding prime and composite numbers
- How many factors can you find? (ABC Splash Game) – Easy
- Arrays – meet the factor families (ABC Splash Game)
- Adam Spencer loves prime numbers (ABC Splash)
- Patterns, primes and pascal’s triangle (ABC Splash)

Please write ten examples of each of the terms listed above. Use the following numbers to create a ‘factor tree”: 24; 120; 128; 130; 240; 360; 480.

We will practise our multiplication tables and learn more about prime numbers using the game “Multo”.

# 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).

- This video is not in Reverse (YouTube)
- This video is in Reverse (YouTube)
- History of Negative Numbers and a Brief History of Negative Numbers (nRich Maths)
- How to Add and Subtract Positive and Negative numbers (Maths is Fun)

# 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).
- Algebra Balance Scales and Transformations are two of my favourites for middle years maths.

- NRICH – enriching mathematics – Great problem solving activities for a variety of ages.

# Welcome to Year 7 and 8 Maths for 2015!

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

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

**Year 8 Maths (Term 1)**

- Basic operations with positive and negative integers (and from Khan Academy)
- Indices and square and cube roots
- Terminating and recurring decimals
- Rational and irrational numbers

**Year 7 Maths (Term 1)**

- Prime and composite numbers (and from Khan Academy)
- a game for learning about primes and composite numbers
- Factors and multiples, including prime factor trees
- Basic operations with integers
- Square numbers and square roots