Transformations and Tessellations (Year 7)

moth_tessellation

 

Image Source

This last week of Term 2 we will be doing some transformations and tessellations. Our learning intention is to understand and describe translations, reflections in an axis, and rotations of multiples of 90° on the Cartesian plane using coordinates and to identify line and rotational symmetries.

Your first task is to use the letters of your name, on a poster, to demonstrate your understanding of translation (slide), rotation (turn), reflection (flip) and dilation (increase in size).

Your second task is to use a shape that tessellates (fits together with no gaps or spaces) to create an artwork, similar to the ones in these YouTube videos:

These links will help you to plan, design and construct your own:

 

Percentages from first principles (Year 8)

family_feud

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:

  1. Introduction to Percentages (Maths is Fun)
  2. ABC Splash video – converting fractions to percentages
  3. BBC Bitesize – Percentages and BBC Bitesize – Finding Percentages
  4. A BBC activity about Percentages
  5. Solving problems with percentages from Math Planet (with two videos)
  6. ABC Splash video – How Banks make Money
  7. Five quick questions to test your percentages from Maths is Fun
  8. ABC Splash – Design a Farm

Percentages, Profit and Loss (Year 8)

pile_coins

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

Screen Shot 2015-06-11 at 8.34.50 AM

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?

uluru_map copy

Your tasks are:

(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.

Euler’s Formula with jubes and toothpicks

Euler_shapes

Learning Intention: To distinguish between prisms and other three-dimensional shapes and to work out the relationship between vertices, edges and faces (Euler’s Formula).

These two Year 7 students are making three-dimensional models with jubes and toothpicks (or satay sticks) to record vertices, edges and faces. Start with simple shapes, such as triangular pyramids, cubes and square pyramids, distinguishing between shapes that are prisms and those that are not. When students have made at least six or more shapes ask them to see if they can find a relationship between V (vertices); E (edges) and F (faces). I usually give a clue that they only need to use addition and subtraction (not multiplication or division).

Slide1

Year 8 – Increasing volume with three little pigs

3pigs

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 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

 

Year 8 – Measurement and Geometry

Screen Shot 2015-05-16 at 8.36.18 PM

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.

Screen Shot 2015-05-16 at 9.01.45 PMScreen Shot 2015-05-16 at 9.38.04 PM

Year 7 – Measurement and Geometry

Screen Shot 2015-05-16 at 7.01.29 PM

National Curriculum Standard: “Students use formulas for the area and perimeter of rectangles.”

The perimeter of a rectangle is calculated by adding the four sides. The area of a rectangle is calculated by multiplying the length by the width.

Perimeter =2 x (L+W) = 2L + 2W

Area = Length x Width = LW  

Find at least three rectangles around the classroom and measure the length and width. Draw a sketch showing the object and the measurements, including the units (millimetres, centimetres or metres). Calculate the perimeter and the area of the object using the formulae above.

For example; your laptop, the table top, your maths book, a window pane, the door, the whiteboard, the front of the heater, the noticeboard etc.

The perimeter of the locker door will be:

(2 x 35) + (2 x 59) = 70 + 118 = 188 cm

The area of the locker door will be:

35 x 59 = 2065 cm^2 (square centimetres)

Great Victorian Coding Challenge

crackthecodeImage Source

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:

1. Join Scratch with your school Username (eg gow0054) and Password. Being a registered member allows you to save and share your work. Make sure Mrs Gow has recorded your Scratch username.

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.