Math Problem Solving Examples

Math Problem Solving Examples-2
If you don't get a problem right on either our tests or a real SAT test, first try to solve the problem yourself.

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The relevance of these situations to the students is varying.

The situation in the first example is well-known to most people and may be useful in helping primary school students to understand the concept of subtraction.

Check −14: −14(−14 2) = (−14)×(−12) = 168 YES Check 12: 12(12 2) = 12×14 = 168 YES So there are two solutions: -14 and -12 is one, 12 and 14 is the other.

Note: we could have also tried "guess and check": And so L = 8 or −14 There are two solutions to the quadratic equation, but only one of them is possible since the length of the room cannot be negative!

Apart from a few procedure texts for finding things like square roots, most Old Babylonian problems are couched in a language of measurement of everyday objects and activities. The mainmast is broken, the cabin boy is on deck, there are 12 passengers aboard, the wind is blowing East-North-East, the clock points to a quarter past three in the afternoon. At the same time, a local train traveling 30 miles an hour carrying 40 passengers leaves Phoenix bound for Santa Fe...") trails off with a schoolboy character instead imagining that he is on the train.

Students had to find lengths of canals dug, weights of stones, lengths of broken reeds, areas of fields, numbers of bricks used in a construction, and so on. So his normal pay of 40 × = 0, plus his overtime pay of 12 × = 0 gives us a total of 0 There are 12 girls!And 3b = 4g, so b = 4g/3 = 4 × 12 / 3 = 16, so there are 16 boys So there are now 12 girls and 16 boys in the class, making 28 students altogether.The material has been carefully selected to provide an accessible and supportive introduction to advanced problem-solving, and to help you build your confidence, fluency and speed.Start by reading about the materials, or scroll down to get started on the modules.You can ask for help and hints if you’re stuck, share what you have tried so far, offer advice to others and get expert guidance from Cambridge University students and staff.You may also be interested in Stephen Siklos's book, Advanced Problems in Mathematics: Preparing for University, which can be downloaded for free.Prior to this, all mathematical problems and solutions were written out in words; the more complicated the problem, the more laborious and convoluted the verbal explanation.Examples of word problems can be found dating back to Babylonian times. Word problems have also been satirised in The Simpsons, when a lengthy word problem ("An express train traveling 60 miles per hour leaves Santa Fe bound for Phoenix, 520 miles away.Check There are now 16 boys and 12 girls, so the ratio of boys to girls is 16 : 12 = 4 : 3 At the start of the year there were 20 boys and 10 girls, so the ratio was 20 : 10 = 2 : 1 Consecutive means one after the other.And they are even, so they could be 2 and 4, or 4 and 6, etc.


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