Do they all have the same volume? Identical squares of side one unit contain some circles shaded blue. Some students without prompting soon realised that the width needed to be 2. All 5 to 11 7 to 14 11 to 16 14 to 18 Challenge level: Have a good look at these images.
Growing Rectangles Age 11 to 14 Challenge Level: Quite a few of my students when conducting investigations often stick to integers and have a hard time with using other types of numbers such as fraction, decimals or as they get to KS4 surds etc. Measure problems for inquiring primary learners. Isometric Areas explored areas of parallelograms in triangular units. Some students without prompting soon realised that the width needed to be 2.
I guess we could say the perimeter is measured in ‘units’ and the area in ‘square units’, although some of you, like Matthew above, assumed the squares were 1cm long. An activity for high-attaining learners which involves making a new cylinder from a cardboard tube.
So I continued to press on, is that the only defining feature of a rectangle? To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.
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What’s the largest volume of box you can make from a square of paper? Making Boxes Age 7 to 11 Challenge Level: Wallpaper Age 5 to 7 Challenge Level: But can you work out how many of each?
Lots of comments on this post. What could its perimeter be? In this game for two players, you throw two dice and find the product. How can you change the surface area of a cuboid but keep its volume the same? Paper Halving Age 5 to 11 Challenge Level: An activity for high-attaining learners which involves making a new cylinder from a cardboard tube. Cut differently-sized square corners from a square piece of paper to make boxes without lids. Can you draw a square in which the perimeter is numerically equal to the area?
My local DIY shop calculates the price of its windows according to the area of glass and the length of frame used. Sending a Parcel Age 11 to 14 Challenge Level: Transformations on a Pegboard Age 7 to 11 Challenge Level: Triangle Relations Age 7 to 11 Challenge Level: Overall, Nricu think this is an excellent activity to undertake in lesson.
What happens if perimrter take a ‘middle square’ out of a shape?
Nrich – Can they be equal? – Mrs Mahoney
Cut differently-sized square corners from a square piece of paper to make boxes without lids. How many tiles do we need to tile these patios? Can you deduce the perimeters of the shapes from the information given? I think students need to realise that there is a whole range of numbers out there not just integers and start to realise that fractions, decimals, surds etc are periimeter just numbers.
You could start with the whole group looking at the two shapes given at the beginning of the problem and invite learners to talk about anything they notice.
Fence It Age 11 to 14 Challenge Level: After going through one basic example of how to find the area and perimeter of a rectangle and how I wanted them to set the work out, I introduced them to this problem.
Can They Be Equal? These practical challenges are all about making a ‘tray’ and covering it with paper.
Do they all have the same volume? Brush Andd Age 7 to 11 Challenge Level: Exit tickets — Plenary idea. Age 11 to 14 Challenge Level: