Category Rich Tasks

Feb 16 2014

MATHCOUNTS

MATHCOUNTS dog

At a pet store, there are 23 animals. Among the animals in the store, 15 are white, 5 are white dogs and 7 animals are neither dogs nor white. How many dogs are at the pet store?

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Mathematics competitions can often be an excellent source of resources for problem solving and the competition series from MATHCOUNTS is a wonderful example. For US students MATHCOUNTS are currently running their third annual “Math Video Challenge”, a competition for 6th to 8th graders that encourages student innovation as they create and star in their own math videos. Entry to the competition is for US middle school students only (see full rules here) but we can all enjoy the resources. Entrants must create a video based on one of the problems in the 2013-14_MATHCOUNTS_School_Handbook; students entering the competition make a video teaching the problem and showing a real-world application of the math concept on which the selected problems is based. Teams will be able to submit videos until 5:00 PM ET on March 14, 2014.

The 2013-14_MATHCOUNTS_School_Handbook is a great collection of problems; I have seen many in this collection that would make ideal starters. All the answers are provided (page 56 of the pdf) and the index (page 62 of pdf) makes the document really useful because the problems have been assigned to a category such as Algebraic Expressions & Equations (though as the authors note many problems fit into more than one category) and given a difficulty rating from 1 to 7, with 7 the most difficult. The difficulty ratings are explained just before the answers (page 56 of pdf). Note that the references are to the US Common Core State Standards. The question categories are: Algebraic Expressions & Equations, General Math, Number Theory, Problem Solving (Misc), Statistics, Probability, Counting & Combinatorics, Proportional Reasoning, Solid Geometry, Percentages & Fractions, Coordinate Geometry, Plane Geometry, Logic, Sequences, Series & Patterns and Measurement.

MATHCOUNTS ice cream problem

MATHCOUNTS – Problem 102 – Warm-Up 8

I like the look of the combinatorics problems – I could use these with Year 7 or more formally with Year 12! One of last year’s semifinalists License Plates, Questions, and Arguments could be good to show Year 12!

MATHCOUNTS offer the materials from their resources in an interactive format which students can use through NextThought; this platform allows access to all the problems from the Warm-Ups, Workouts, Stretches and competitions. It is free to create an account. Solutions to all the problems can be checked online and full explanations for all solutions are available. To return to the pet store problem which is from Warm-Up 3 the solution available on NextThought is as follows:

NextThought - MATHCOUNTS

NextThought – MATHCOUNTS

As well as the latest handbook two previous editions are also available as well as numerous competition questions. The NextThought platform looks excellent and something I wish to explore further – it allows students to discuss problems and I see it has a whiteboard tool available.

All material is copyrighted by the MATHCOUNTS Foundation.

Apr 7 2013

Why should I memorize something when I know where to find it?

According to this story, told by Nathan Shaw Einstein said this. Now I am very pleased that I share my own ‘capture everything in such a way that you can find it again’ ideas with Albert Einstein! I have found some resources I really like recently – so the usual question – where to put them so I can find them again?

Enrichment
I mentioned in a recent post that I came across an outstanding resource on Combinatorics questions by Dr Jamie Frost thanks to the TES Mathematics forum; well Dr Frost has now made his excellent enrichment materials available on The Reimann Zeta Club. This clearly belongs on a list! So I added it to the Enrichment list (for lots of lists see the ‘I’m Looking For …‘ page. As well as adding this resource I checked the various links and also added the Brilliant website I have talked about recently.

Thinking about Enrichment, my own view is that this should be a natural part of the curriculum for all students and made me wonder where my Rich Tasks list ends and enrichment list starts (I solved the problem by adding the Rich tasks list to the Enrichment list!) A recent excellent addition to the  Rich tasks list is Jonny Griffiths’ Carom-Maths -activities to bridge the gap between A Level and University.

Staying with the subject of Rich tasks, one of the entries on that list is the list of problems from the National Strategies site to develop mathematical processes and applications; those archives make me a little nervous – will they stay? I decided to create an Evernote shared notebook which lists those resources including links to to the problems on Nrich. Another recent addition to the Rich Tasks list is this excellent interactive from NGfL CYMRU to explore the Painted Cube problem (explained clearly here on Nrich)

Starters
I recently read this post by Don Steward and it struck me what a great starter ‘Sum and Product’ would make. I have so many links for starters they have a WordPress blog all to themselves and I have added the Sum and product problem Don describes to the Algebra page there; also new on Mathematics Starters and Plenaries is this link to MathsStarters.net which has a growing collection of starter activities (added to the Collections page); I particularly like the Bingo resources. 

Resources
Working on an excellent project for TES recently (more on that later) I came across an excellent resource on fractions by Kaszal, the resource is an A5 worksheet consisting of 10 fraction calculations, some of which have mistakes and/or inefficient solutions. Students enjoy marking examples like this and it can lead to some excellent class discussions. I have added this to the Spot the Mistake page under Resources.

Douglas Butler’s comment on my post last week made me realise that I should include Autograph here, so a new Autograph page is now available under resources. (All resources on this site are free to use, I have included Autograph (for graphing, geometry, statistics and probability) here as although it is paid-for software, Autograph viewer and all the excellent resources available on line are completely free to use and do not require the Autograph software to be installed.

See also: Looking for things!