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?
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.
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.
Learning Intention: You will consolidate your understanding of how to calculate the volume of three dimensional prisms.
Success Criteria: By completing the set exercises you will demonstrate your understanding of how to calculate the volume of prisms.
James, Emily, Liam and Jeremy – please work on page 344 “Discover – Volume and capacity”.
All other students are to work on page 346 “Explore – Volume and capacity”.
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: 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.
Image Source – Hexagonal prisms at the Giant’s Causeway in Ireland.
Firstly, what is a prism? A prism is a 3D shape that has cross-sections parallel to the base faces the same. Prisms are named for their base, so a prism with a triangular base is called a triangular prism (like a Toblerone package) and one with a pentagonal base is called a pentagonal prism. To work out the surface area of a prism, you need to calculate the area of each face and add them together. To calculate the volume of a prism, you need to work out the area of the base and multiply by the height of the prism ( the distance between congruent faces).