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)
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: “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
Your homework this week is to take a photo of a rectangular prism in your home and label it with the measurements that will enable students to calculate the surface area and the volume of the prism. Some examples include a refrigerator, a freezer, a blanket box or a chest of drawers. What is the surface area of the freezer above? Remember you need to use all three measurements of height, width and depth and double for back and front, both sides and top and bottom. Please send your homework to brittgow(at)gmail(dot)com and don’t forget your Mathsmate for Friday!
Learning Intention: Students will understand what data is suitable for graphing on a scatter plot and be able to describe the significance of a “line of best fit”.
Success Criteria: You will draw a correctly labelled scatter plot from our arm span and height data and determine if there is a relationship between these measurements.
Last week you learnt the definitions for mean, median, mode and range and created a stem-and-leaf plot using the height of students in Year 7. You also measured the length of seven leaves and calculated the mean, median, mode and range of this data. This week we will investigate another type of graph, the scatter plot. Use the data we collected from our Year 7 Maths Survey to graph arm span against height (in centimeters).
This week we may also get the chance to do other activities with scatter plots:
1. Barbie Bungee
How many rubber bands are needed for Barbie to safely jump from a height of 400 cm?
What is the minimum height from which Barbie should jump if 25 rubber bands are used?
How do you think the type and width of the rubber band might affect the results?
Do you think age of the rubber bands would affect the results–that is, what would happen if you used older rubber bands?
If some weight were added to Barbie, would you need to use more or fewer rubber bands to achieve the same results?
State a possible relationship between the amount of weight added and the change in the number of rubber bands needed.
(thanks to Mrs Jirkovsky at North Adams Public School for writing about this activity on her blog!)
2. Be an actuary – distance vs earthquake intensity.
Learning Intention: The purpose of this unit of work is for students to understand how to calculate the volume of prisms.
Success Criteria: You will make appropriate measurements of a prism and be able to calculate the volume of that three dimensional shape. For example, measure the circumference of a water tank and calculate how many litres it holds or the radius of a silo and calculate the volume of grain it contains.
Your homework this week is to take a photograph of an object (tank, container, silo, fridge, filing cabinet) and measure the height, width, depth, length, radius or circumference (whichever is appropriate for that object) and record those measurements on the photograph, as I have done above. If you don’t have a camera or webcam, you can use a creative commons image available on the internet. You can use ‘Paint” to add the text to your image and save it as a ‘jpeg’ file. Then email your image so I can compile the pictures in a “Voicethread” or “Powerpoint” file.