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?


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.

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