Prime numbers and prime factor trees

Erastothene’s sieve interactive

Prime numbers are special numbers with exactly two factors. Erastothene’s sieve is a way of finding those prime numbers by removing the multiples of numbers. You can see them above. Prime factor trees are useful to show the numbers that a whole number can be reduced to.

Week 1: 2016

Basic operations – Using the four digits 2, 0, 1 and 6 and the four operations (addition, subtraction, multiplication and division) can you make equations that equal all the numbers from zero to 20?

Multiplication –

• Which multiplication tables do you know best?
• What do all the multiples of 2 and 4 and 8 have in common?
• How do you know if a number is divisible by 5 or 10?
• Write down all the multiples of 3 in order and see if you can determine something that they all have in common (clue – add the digits together).

How much are your pancakes?

This recipe serves 4 people, 2 pancakes each

• 2 cups self raising floursifted (250g at 0.32c per gram)
• 2 large eggs, separated (40 cents each)
• 2 cups milk (500ml at 0.25c per ml)
• 2 tsp sugar (8 grams at 0.024c per gram)
• 50g butter, melted plus extra butter or oil for cooking (at 0.88c per gram)

How much do you think it costs to make pancakes at home? How much do you pay at a cafe or McDonalds? When restaurant owners and chefs calculate the cost of their menu they need to take into account the cost of ingredients as well as staff costs, overheads (rent, power, telephone, gas etc) and also make a profit.

Percentages from first principles (Year 8)

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“We have surveyed one hundred people and asked them the question….” I’m guessing all of you have watched Family Feud at least once and heard Grant Denyer read out all sorts of questions and received some surprising answers from the players. This game is based on percentages, which is our topic of study for the next week. There are a series of concepts you need to understand, with increasing levels of difficulty, listed below:

•  I understand that percentage means “out of one hundred”. 30% means 30 out of every 100 or 3 out of every 10 or 0.3 out of 1.0
• I can (always, usually, sometimes, never) convert between percentages, fractions and decimals. For example, 25% = 25/100 = 1/4 = 0.25
• I can (always, usually, sometimes, never) calculate the percentage of an amount (with/without) using a calculator. For example, 15% 0f 300 = 15 x 3 = 45
• I can (always, usually, sometimes, never) calculate a percentage discount, profit or loss. For example, a pair of \$80 jeans were on sale with a 10% discount, what is the sale price? \$80 – (10% of 80) = \$80 – \$8 = \$72.00
• I can (always, usually, sometimes, never) work out the percentage increase or decrease of two amounts. For example, the median house price rose from \$150,000 to \$175,000, so the percentage increase was (175,000 – 150,000)/150,000 = (about) 17%

Some resources:

Percentages, Profit and Loss (Year 8)

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Learning Intentions: Solve problems involving profit and loss, and the use of percentages, including percentage increases and decreases, with and without digital technologies.

Whenever you buy something, the shop owner has to put a price on that item, usually so that he can make a profit. Food such as fruit and vegetables will usually have a smaller margin (percentage profit) than more expensive items such as clothing and appliances. In Australia, the “Goods and Services Tax” (GST) of 10% is applied to almost all consumer items, except fresh produce. So, if you pay \$55.00 for an item, \$50.00 is for the shopkeeper and \$5.00 is the GST, which goes to the federal government tax office.

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.

Week 3: Basic Operations

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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

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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:

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”.