Pythagoras and Square roots

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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?

Counting your cup cakes!

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This is an assessment task for Year 7 Maths.

Cup cake recipe (makes 12 small or 6 large cup cakes)

  • 1/4 cup butter (60 grams)
  • 1/4 cup caster sugar (60 grams)
  • 1 egg
  • 3 drops vanilla essence
  • 3 tablespoons milk (1 tbsp = 20 ml)
  • 3/4 cup S.R. flour (115g)

Method: Set the oven at 200 degrees Celcius. Cream the butter and sugar until light and fluffy. Add essence and egg, mixing well. Add flour and milk alternately, one-third at a time. Stir gently and thoroughly. Place mixture in paper patty pans, two-thirds filling each one. Bake at 200 degrees for 1/5 to 1/4 of an hour. Cool in pans, then decorate each cake with icing.

Questions:

1. Draw up a table and write out the ingredients required for 12 large and 24 large cupcakes.

2. If you want to have equal numbers decorated the same, what different numbers can you use? (What are the factor pairs of 24?)

3. How many minutes is 1/5 of an hour? How many minutes is 1/4 of an hour?

4. If (20ml x 3) of milk is required for 6 large cupcakes, how much of a cup is required for 12 and 24 cupcakes?

5. Calculate the cost of the ingredients for 24 large cupcakes using the Coles or Woolworths online shopping website.

Fractions Eight Different Ways

Learning Intention: Students will understand that there are many different ways to express the concept of ‘part of a whole’.

Success criteria: Each student will produce a poster that demonstrates eight different ways to express a certain fraction, chosen by the distribution of individual fraction cards. We will use these cards and our ‘Fraction Walls’ to demonstrate adding, subtracting, multiplying and dividing fractions.

Each student will recieve a card with a fraction and create a poster that shows this fraction eight different ways (as above for one half). When you have finished, place your poster on the number line in the room.

Year 8 – Exponentials with Aliens!

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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.

Operations with Fractions

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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

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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

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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).