Douglas Buchanan ~ dcbeagleb@gmail.com~ www.dcbeagle.com ~@dcbeagle1
HAPPY NEW YEAR!
New maths!??!
We have to smile when we hear people say, “…. they are teaching new maths these days …” and it is not the same as it was when the grandparents were at school. Rubbish! What has changed, and for the better, is the approach to maths teaching.
Hopefully we are moving away from the rote learning to topics which are relevant to pupils. In the website Prodigy they give 9 Maths Strategies for Successful Learning. The blog looks at the following: explicit instruction; conceptual understanding; co-operative learning strategies; meaningful homework; verbalise maths problems; reflection time; making maths facts fun.
Puzzle of the month
Exploring the Desert (Henry E Dudeney)
Nine travelers, each possessing a car, meet on the eastern edge of a desert. They wish to explore the interior, always going due west. Each car can travel forty miles on the contents of the engine tank, which holds a gallon of fuel, and each can carry nine extra gallon cans of fuel and no more. Unopened cans can alone be transferred from car to car. What is the greatest distance at which they can enter the desert without making any depots of fuel for the return journey?
Website of the month: Maths Is Fun
This website has been around for years, but the material is always being updated covering nearly all spheres of maths teaching. It can be used for reinforcement, puzzling and it is the ideal homework source. Conundrums can be solved as the homework package.
The Maths Box
Most children learn maths through multiple representations and with hands-on activities. By doing mathematics with a variety of tools, students will be able to develop the confidence to solve a broader range of mathematical problems.
Provide Maths Boxes to assist the pupils in understanding mathematical concepts and they should be readily available. There seems to be a trend to throw “the toys out of the basket” when pupils reach 11 years. A big mistake, because the topics become more conceptual and seeing the problem in 3D can only help.
The website TeachStarter gives advice on what should be in the boxes. Counters, dice, cards, timers, counters, calculators, etc. Added to that are links to problem solving conundrums for the pupils to work on, using the “toys” in the box.
Exploring the Desert solution
Dump 5 rations at 90-mile point and return to base (5 days). Dump 1 at 85 and return to 90 (1 day). Dump 1 at 80 and return to 90 (1 day). Dump 1 at 80, return to 85, pick up 1 and dump at 80 (1 day). Dump 1 at 70 and return to 80 (1 day). Return to base (1 day). We have thus left 1 ration at 70 and 1 at 90. Dump 1 at 5 and return to base (1 day). If he must walk 20 miles he can do so by going to 10 and returning to base. Dump 4 at 10 and return to base (4 days).
Dump 1 at 10 and return to 5; pick up 1 and dump at 10 (1 day). Dump 2 at 20 and return to 10 (2 days). Dump 1 at 25 and return to 20 (1 day). Dump 1 at 30, return to 25, pick up 1 and dump at 30 (1 day). March to 70 (2 days). March to base (1 ½ days). Total, 23 ½ days.
Fun at the end of lesson
The video describes 10puzzles which will excite the pupils at the end of a lesson. Always keep their interest in the subject and they will learn!
