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.
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?
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.
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).
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?
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)
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.
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)
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.
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.
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.
- 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?