Pouring and Filling

Some excellent watery demonstrations this week:
Depth Time graphs

Depth time graphs of filling different containers. (GeoGebra). Simply select the container you want and the speed of animation, select animate and watch the graph.

From the GeoGrebra resource team, a resource to interpret meanings of different rates of change across a graph that represents the water level in a hot tub.

Volume

From Michigan State University’s  Connected Maths Project Student Activities, one of the Grade 7 Activities is Pouring and Filling which provides a great demonstration of relationships between the volumes of pyramids and prisms. We could tip the contents of a cone into the cylinder for example…

Each activity describes the purpose of the activity and has suggested uses, many activities as this does have helpful how to videos.

These activities are well worth exploring, for example in Grade 6 we have factor and product games and also the very satisfying locker problem. Note the TEDEd lesson video here.

Painted CubeOne of the grade 8 activities is the classic Painted Cube. This activity is so clear; it allows students to build a cube or cuboid out of unit cubes, colour the faces using a palette of colours, then rotate the object to paint the initially hidden sides. The expand option allows students to blow up the prism and inspect will count the number of cubes with 0, 1, 2 or 3 painted faces.

Desmos Graphing Calculator

I wrote about the (free) Desmos Graphing Calculator in June when I first came across it. Since then I have used it a great deal in the classroom as it is a powerful resource, very simple to use and available for students to use at home. Several new features have been added since I wrote that first post. For my school-age students, I particularly like the sliders feature, the trace and the option to use degrees as well as radians for angle measure. You can read the latest blog post from Desmos here.

The ability to share pages is extremely useful for students, particularly now with the addition of sliders; students can be asked to explore families of graphs from simple straight lines for the younger students to polar curves for the Further Mathematicians, perhaps some cubics for GCSE / A Level students. (Note that the value you assign to the variables determines the initial set of values possible with the sliders, click on the values on the slider to edit.) Perhaps explore transformations.

It is very easy to demonstrate a variety of functions, for example, I was recently studying the modulus function with my sixth form students, looking at modulus equations and inequalities a picture speaks a thousand words! (Just type y=abs…)

absolute value

Thank you Eli Luberoff and team for this amazing resource!

See also Pretty Graphs, Desmos DelightsGraphing Inequalities and these posts on my blog for students: Explore Straight Lines and Explore Graphs.

Graphing Inequalities

Thinking about resources to show students how to graph linear inequalities, I can use Autograph in the classroom as I often do but I am always keen to show them resources they can use at home.

The Desmos graphing calculator handles inequalities very well, unlike many free graph plotters it is easy to plot lines of the form x=k. Click on this image to see these inequalities on the Desmos calculator. See also this post on Mathematics for Students.

Desmos Inequalities
Experiment with these inequalities on the Desmos graphing calculator.