# Exploration and Investigation with Technology

This census-taker problem is described in my post Polya – Problem Solving. Given that the product of the three daughters’ ages is 36 we need to look at possible triples with a product of 36. These possibilities are illustrated here on the brilliant Mathigon. These Prime Factor Circles can be found in the Numbers section of Polypad.

Mathigon features on a page in my Use of Technology series.

Happy Numbers is one of my favourite (I have a lot of favourites!) investigations. It is accessible for a range of abilities and offers a great lesson in the value of recording results carefully so you can use previous results and save yourself work! The post includes several useful resources including a happy number checker on Scratch, also an Excel spreadsheet. In this and many of the other activities here once students have done some calculations so we are sure they can correctly perform the calculations required, the use of technology allows them to check their answers and to generate more results quickly so they can spend time thinking about any patterns or connections.

For properties of Numbers see Tanya Khovanova’s Number Gossip.

Diffy is an activity that encourages students to play around with numbers, look for patterns and make predictions. This page, Diffy, includes further information including Don Steward’s wonderful post on the subject, a Diffy checker spreadsheet from Craig Barton and some further reading.

Tim Brzezinski’s GeoGebra resource is great for some hard thinking on expanding brackets. Not only do students get to practise this skill we have the added thinking needed to make sure each digit is used once only. The activity encourages what if type questions, what can we put outside the brackets? Are there some numbers we can’t put outside the brackets? Doing this on GeoGebra is great, it’s easy to drag the numbers around and the resource will check any proposed solution.

The use of a square GeoBoard can support understanding of concepts such as area and properties of shapes.
See the following resources:

PhET Interactive Simulations

GraspableMath

GeoGebra Resources

Autograph Resources

A favourite Underground Maths resource – To log or not to log? This has worked really well every time I have used it. The activity requires students to think about the methods which could be used to solve the various equations. I have always found that in addition to working on indices and logarithms this task has exposed some misconceptions, with students trying to invent some new and invalid laws of logarithms!

This problem is classified as a Problem Requiring Decisions.

Students are often used to problems being posed in such a way that they have all the information that they require in order to start, and no more. Problems (especially from the real world) are very often not like this, and so resources of this type will give students the opportunity to develop the skills needed to deal with this. Some problems might not contain enough information, so students may need to decide on classifications, make assumptions or approximations, or do some research in order to move forward. Some problems might contain too much data, so that part of the challenge is to identify the useful information.

Here’s what my students said:

You can explore all the circle theorems with Tim Devereux’s GeoGebra appletsYou can access each theorem from the menu on the left which includes a useful summary of all the theorems.

Numerical Methods | Mathematics, Learning and Technology (colleenyoung.org)

The shape of the quadratic function – TeachitMaths

Nrich Interactives – Upper Primary Lower Primary
Secondary Collection Secondary Interactive Resources

MEI – Use of Technology tasks using Autograph, Casio Calculators, Desmos, GeoGebra

Mathisfun Interactives