How much are your pancakes?

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.

Year 7 and 8 Statistics

Candies

Image source

YEAR 7 Standards:

  • Investigate, interpret and analyse graphs from authentic data
  • Identify and investigate issues involving numerical data collected from primary and secondary sources
  • Construct and compare a range of  data displays including stem-and-leaf plots and dot plots
  • Calculate mean, median, mode and range for sets of data. Interpret these statistics in the context of data.
  • Describe and interpret data displays using median, mean and range.

Resources for Year 7:

 YEAR 8 Standards:

  • Data representation and interpretation – Investigate techniques for collecting data, including census, sampling and observation
  • Explore the practicalities and implications of obtaining data through sampling using a variety of investigative processes
  • Explore the variation of means and proportions of random samples drawn from the same population
  • Investigate the effect of individual data values, including outliers, on the mean and median

Resources for Year 8:

Supporting Australian Mathematics Project –

Year 7 – Area of Triangles

triangles (1)

To calculate the area of a triangle use the formula:

Area = One half multiplied by the base multiplied by the height  (A=1/2 x bh)

area_triangle

 

Maths with Scratch!

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Although Victorian Education Week is six weeks away (May 17th to 23rd), I am using some of the school holiday break to play with Scratch, so my Year 7 and 8 Maths classes can participate in the “Crack the Code with Maths” challenge. 

Scratch is simple-to-use software, that allows users to create animations using drag-and-drop commands. I hope to use this free program, pre-installed on our government school laptops, as part of our geometry learning this term.

Scratch uses the Cartesian Co-ordinate system to locate ‘sprites’ on a ‘stage’.The screen is a 480 x 360 rectangle, such that: the X position can range from 240 to -240, where 240 is the rightmost a sprite can be and -240 is the leftmost, and the Y position can range from 180 to -180, where 180 is the highest it can be and -180 is the lowest it can be. The centre of the screen, or ‘origin’, is known as (x=0, y=0) or (0,0).

The following links are some examples of what can be achieved with Scratch.

Student tasks:

  • Join the Scratch community, using your school username (eg. gow0049).
  • Explore the links above and other geometry-related Scratch projects.
  • Create your own Scratch project, drawing a different polygon (closed shape with straight sides) in each of four quadrats.
  • Can you create four different triangles? (equilateral acute, isosceles obtuse, scalene right-angled and one other combination of side-length and angle size).
  • Can you create four different quadrilaterals?
  • Can you create a regular pentagon, hexagon, octagon and nonagon?
  • Draw your initials, like these students in 5/6 Clark/Smith Can you translate and reflect your initials so they appear in all four quadrats?

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?

Counting your cup cakes!

cupcakes

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.

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).