# 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.

# Year 7 and 8 Algebra

Image source

There are many skills to learn to master Algebra, but we have already made a great start – You :

1. Can recognise and continue a pattern

2. Understand that a pro-numeral (a letter) represents a variable (changing number)

3. Understand that it is mathematical convention to leave out the multiplication sign in expressions and equations involving pro-numerals.

4. Can substitute positive and negative numbers into an equation

5. Can plot points on a cartesian plane

6. Can determine the equation from a table of values

7. Can solve an equation using backtracking

The next step is to be able to solve an equation by doing the same operation to both sides. Try these online activities:

Algebra Balance Scales (a virtual manipulative from Utah State University)

Algebra Balance Scales with negatives (same as above, but with negative numbers)

Equation Buster – from MathsNet

# Probability and Percentage increases and decreases

Following our assessment task yesterday it is clear that some students need to revise certain areas of the work we have done in term 1 and 2:

Probability – Relative frequency with ten questions to complete.

Percentages – How to convert fractions and percentages to a pie chart (360 degrees) with ten questions to complete.

Percentage increases and decreases – Worked examples and five problems to solve.

Stem and Leaf plotsWorked example and thirteen questions to solve.

Problem #1: You have a list of 7 numbers. The average of the numbers is 9. If you take away one of the numbers, the average of the numbers is 8. What number did you take away?

Problem #2: Martin has completed five Maths tests and received an average score of 80%. What is the highest average he could have after the next test?

Problem #3: A Year 7 class was asked “How many goals did you shoot at lunchtime?”. The lowest answer was 5 and the highest answer was 20. The total of all the answers was 60. What is the smallest number of students who could have been asked?

# Percentages from first principles (Year 8)

Image source

“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)

Image Source

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.

# Year 8 Rates – Distance, time and speed

Learning Intention: “Solve a range of problems involving rates and ratios, with and without digital technologies.”

It is very useful when travelling to be able to solve problems that involve time, distance and speed. For example, how long will it take for me to drive from Hawkesdale to Melbourne or if it takes me 2 hours to ride to Port Fairy, how fast was I riding? The equation we use is: velocity (speed) = distance divided by time. You need two of these variables to calculate the third.

BBC Bitesize has a good explanation and some problems to try.

In the example above, Google Maps shows that it takes 23 hours and 31 minutes to drive to Uluru, 2,157km away. So we have the time and the distance – what is the assumed speed we are travelling?

(1)  Choose two locations and use Google maps to find out the distance between them. Then choose a speed to travel to calculate how long it will take to get there.

(2) Choose two different locations and calculate how fast you would need to travel to get there in one hour.

(3) Send me a copy of your questions and working out.

(4) Do the Bitesize Quiz and send me a copy of your score.

# Year 8 – Increasing volume with three little pigs

Let me tell you a story about three little pigs. The first pig built a house that was 2 metres high by 3 metres wide by 4 metres long. The second little pig wanted a bigger house, so he doubled the dimensions – his house was 4 metres high, by 6 metres wide by 8 metres long. The third little pig wanted to have the biggest house, so he doubled the dimensions again and built a house that was 8 metres high, 12 metres wide and 16 metres long.

Your task is to calculate the surface area and volume of each of the three houses and work out the ratio of SA:V for each house. Assuming that all the houses were made of the same materials and labour was not included, which house would be the cheapest to build per unit volume?

# Year 8 – Measurement and Geometry

National Curriculum Standards: Students convert between units of measurement for area and for volume. They find the perimeter and area of parallelograms, rhombuses and kites. Students name the features of circles, calculate circumference and area, and solve problems relating to the volume of prisms.

To calculate the volume of any prism, multiply the area of the base by the height (or in the case above, the trapezium by the length of the trailer). Make sure all the units are the same before starting your calculations.

# Great Victorian Coding Challenge

Over the next few weeks we are working with Scratch to create projects that demonstrate maths concepts using simple drag-and-drop programming. Please make sure you have completed the following steps:

2. Join the Hawkesdale P12 College Studio and the Victorian Coding Challenge (1, 2 and 3) Studios on Scratch, so you can share your work and see what other students have created.

3. Challenge #1: Create a character that draws a shape and upload to the Hawkesdale P12 College page.

4. 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?

5. Challenge #2: Create a project that explains a maths concept. For example:

• Draw  your initials in block letters and calculate their perimeter and the area they cover. Use the Cartesian Co-ordinate grid as a background.
• Explain how to calculate the perimeter of a polygon or circle.
• Name the parts of a circle (radius, diameter, circumference, sector, arc)
• Describe different triangles (equilateral, isoceles, scalene, right-angled, acute-angled or obtuse-angled)
• Explain how the sum of angles in a triangle always equals 180 degrees.
• Explain how the sum of angles in a quadrilateral always equals 360 degrees
• Explain how to calculate the area of a polygon (triangle, rectangle, parallelogram, trapezium, kite) or circle
• Describe right angles, straight angles and complementary (adds to 90 degrees), supplementary (adds to 180 degrees) and equal angles.
• Describe ‘pi’ and how it can be used to calculate the circumference and area of circles.
• Describe Euler’s Rule about the faces, vertices and edges of a polyhedron (Faces + Vertices – Edges = 2)

Make sure you add your project to the Hawkesdale P12 College Studio page.

6. Challenge #3: Create a simple game that uses maths concepts. It could be something like this Hungry Fish game. Someone even created a Scratch project for Co-ordinate Grid Battleships.

# Welcome Back for Term 2!

Image Source

This term we will be studying Measurement and Geometry.

Year 7 Maths (JacPlus Chapter 9 – Measurement and Chapter 5 – Geometry)

By the end of this term I hope you will be able to:

• Use appropriate units of measurement
• Calculate the perimeter of 2D shapes
• Calculate the area of triangles, quadrilaterals and composite shapes.
• Identify types of polygons (different triangles and quadrilaterals)
• Estimate, measure and draw angles between 0 and 360 degrees.
• Identify the properties of parallel and perpendicular lines and the angles that form between them.
• Calculate the missing angles in polygons, knowing that the internal angles of a triangle add to 180 degrees.
• Recognise various transformations (translations, reflections, rotations and dilations)

Year 8 Maths (JacPlus Chapter 7 – Congruence and Chapter 10 – Measurement)

By the end of this term I hope you will be able to:

• Use and convert units of measurement for perimeter, area and volume
• Calculate the area of various quadrilaterals.
• Calculate the area and perimeter of circles.
• Calculate the volume of various prisms using formulae.
• Identify congruent shapes
• Transform various shapes (translate, dilate, rotate and reflect).
• Solve geometric problems using congruence.
• Work out problems around different time zones using the 24 hour clock.