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.
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)
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.
Learning Intention: Students will understand how to calculate the area of a triangle, using the rule Area = 1/2 x base x height.
Success Criteria: Students will draw and label at least four different triangles of the same area.
How many different triangles can you draw with an area of 120 cm sq? Use graph paper, where 1 cm ~ 10 cm and label the base and the height, showing any right angles.
Games based learning has been a hot topic in the last year or so and one of the most popular games in educational use has been Minecraft. Although there has been some debate about the value of learning outcomes, many students would agree that Minecraft is a fun way to learn about surface area and volume. This YouTube video, “Minecraft Math – Surface Area and Volume” describes how to calculate the surface area of rectangular prisms and challenges the viewer to calculate the surface area and volume of a huge tower of TNT blocks! Another YouTube video, from the same user, demonstrates the “Volume of Prisms and Pyramids” in Minecraft and offers a challenge to calculate the area of a prism with a pyramid on top.
We spent last lesson looking at the volume and surface areas of various patterns of ‘minecraft’ blocks. Our assumption is that each Minecraft block is 1m x 1m x 1m – a cubic metre. Next lesson I would like you to create your name in Minecraft blocks and measure the volume and the surface area of your construction. Start by using the first letter of your first name. It should be a minimum of five blocks high and three blocks wide. Make sure you take a screenshot of your construction and send it to me by email.
- Students will be able to identify and describe 2D shapes and understand the terms translation, reflection, dilation and rotation.
- They will be able to identify and describe, draw, plan and construct 3D objects.
- Students will complete a poster that shows various shapes undergoing transformations and construct a tessellation from appropriate 2D shapes.
- They will identify and describe 2D and 3D shapes from photographs.
- They will draw isometric drawings with dot paper and nets and construct 3D shapes.
So far we have learnt about the properties of polygons, especially triangles and quadrilaterals, in terms of their sides, angles, perimeter and area. Next we will be looking at TRANSFORMATIONS – how 2D shapes are translated (moved), reflected, rotated and dilated. Your task is to create a poster that shows the letters of your name undergoing each of the following transformations – translation, reflection, rotation and dilation. Draw two copies of each of four block letters of your name and then complete a transformation with one of the letters of each pair.
We will then learn more about 3D shapes and how they are drawn and constructed.
Polygon matching game – identifying 2D shapes.
Sort the shapes – identify and describe polygons
Polygon sorting – regular and irregular polygons.
More interactives from the Maths Zone (2D shapes)
Classifying 2D and 3D shapes – Geometric Figures Game
Drag and drop 3D shapes – Naming 3D shapes
Matching 3D shapes – identifying 3D shapes
More interactives from the Maths Zone (3D objects)
Learning Intention: “Establish the formulas for areas of rectangles, triangles and parallelograms and use these in problem solving. Recognise and solve problems involving simple ratios.”
Success Criteria: Students will be able to calculate the area of various 2D shapes, including triangles, squares, rectangles and composites of these shapes. They will draw a house plan to scale and calculate the floor area of the house.
Homework: Measure the length and width of your bedroom and one other room in your house in meters. Notice that your doorways are about 1.0 meter wide.
Today’s task is to draw a scale plan of a holiday house. A rough estimate of the cost to construct a home is at least $1,000 per square meter. Your budget is $250,000, so the house must be less than 250 square meters in area. Use a scale – 1.0m to 1.0cm is a good way to start. So, 1.0cm on the plan, represents 100cm (1.0m) on the ground. Your scale is 1:100. Your holiday house should include the following rooms:
- Lounge/Living area
- 2 Bedrooms
Learning Intention: To understand how to calculate the area of a triangle and why the formula (A = 1/2 x base x height) works for all triangles.
Success Criteria: Students will complete the interactive “Area of Triangles” activity with at least 80% of answers correct.