Happy Lines

I am always on the lookout for good maths problems. Problems which make students think. Non-routine problems.

Some students are reluctant to engage with problem solving because it puts them out of their comfort zone. Therefore give encouragement. Give problem solving strategies (Maths Toolbox). If absolutely necessary give hints (scaffolding?).

I recommend that you checkout “Introducing the Maths Toolbox” by Kevin Cummins.

Here is a problem that I used with my Year 10 General Maths class today. It is taken from:

USA Mathematical Talent Search
Round 1 Problems
Year 22 | Academic Year 2010{2011

I introduced the problem by explaining what a happy line was. I drew the 9 dot square grid on the board and my students quickly told me that it had 8 happy lines. So far so good.

When I gave them the 3 x 9 grid many students eagerly set about finding all the happy lines. The first problem was that most students did not understand the difference between a line and a line segment. They counted the 45 degree lines but missed the other angled lines! Some very good discussions and new discoveries evolved.

My biggest challenge in this situation is to not give in to “Teacher Lust”.

Read about how “Problem solving empowers children“.


About webmaths

I have been teaching Mathematics in Victorian secondary schools for 30 years. I use the www to make my maths lessons better. I hope this blog will give other teachers some ideas to try in their own classes.
This entry was posted in Pedagogy, Problem Solving, Visualisation and tagged , , , . Bookmark the permalink.

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