Maths as a Game 1

Branka Dejić Mirko Dejić

S H Т А М 1 E M A G A S A imulate t S h ic h w s Problem l Talent a ic t a m e h t a M

Dear Grown-ups, Children aged six to seven develop logical thinking at a constantly growing pace, which is very important for various mathematical activities that stimulate mental development. This book is intended for children of that age group, although its problems may also be solved by younger children that are particularly talented.

The problems are interesting, atypical and have the character of puzzles. Coming up with an idea of how to solve the problem and glimpsing the solution develop the creative potential and the intuition that is required to solve mathematical problems. The brief perplexity at the start of the problem-solving process motivates the child to ponder on it, and the moment the solution comes produces an ‘I Got You!!’ effect.

This brings joy and a desire to carry on, all serving to stimulate creative thinking.

The problems are linked with the various areas covered in the Preparatory Pre-School Programme, and solving them will help children to prepare successfully for beginning their primary education. Pre-school teachers may use the problems to identify children who are particularly talented for maths, as well as to develop an interest in maths in other children.

Always be patient when solving the problems with children. If a child does not succeed in one problem, choose an easier one - success in solving that one will encourage the child. The child needs your support: • accept every attempt by the child to solve a problem, even if he or she does not succeed, because searching for the solution represents children’s creativity; • keep encouraging and convincing the child that he or she can solve the problem; • always fully share the child’s joy and praise him or her for having solved a problem; • provide only basic help – sometimes it is enough to say “You’re on the right track;” • Instead of saying “Let’s do maths,” say “Let us play and see how Michael managed to count the apples.”

It is important that you read the text and that the child understands it, comprehends the task at hand, identifies the requirements, linkages, etc. It is best if the child works just 15 to 20 minutes, several times a week.

The book also contains stickers shown below which the child should use to rate his or her performance in every problem. This the child should do itself, observing the rules explained by you. In this way children are taught to assess their work and judge its value, which has a substantial educative effect. If the child chooses the wrong label, ask him or her to think once again about the rating chosen.

• When a problem has been solved without outside help and without fault, the following rating . is selected • If the child had asked for help or made a minor error, the following is chosen

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• If the child was unable to solve a problem or did so only with a lot of help from an adult, . use this rating We have also included a DIPLOMA which you award to the child for solving problems successfully, provided that more than one-half of all the signs are either or Do your best to ensure that the diploma is really earned. Nothing succeeds better than success itself!

We would also like to extend our thanks to Minja, aged six, who is preparing for her first day in school, for working hard on a selection of problems, and helping us to pick the best ones.

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Dear Children, Some of the following problems may appear difficult, but solving them is easy. All you need is a bit of thinking. And that is exactly what the boy in this story did.

Once upon a time, the Emperor of China received a huge elephant as a gift. The courtiers wanted to surprise the Emperor by telling him exactly how much the elephant weighed, but their biggest scale was not big enough.

Finally, a little boy came to their assistance.

The boy suggested that they take the elephant to the nearby river and put him in a boat. Few people thought that it was a good idea, but as no one could offer a better one, they decided to try it, anyway. The boarded the elephant in the boat, and the boy marked a line on the boat showing how far it had sunk into the water. Then they led the elephant out.

They boy said they should now begin loading the boat with rocks until it sank to the line he had drawn. Many of the grown-ups were now starting to understand the boy’s solution to the problem. After weighing the stones and adding up their weights, they ďŹ nally knew how much the huge elephant weighed.

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Help the Piglet ď ľ Help the piglet to find his house without losing his way.

Which road should he take - 1, 2 or 3?

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Testing Concentration ď ľ Divide the squares in half, divide in circles into quarters, draw

Ex

a spot in each triangle, and leave the rectangles empty. p l e: am

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ď ľ Draw in the circles as has already been done in the above picture.

ď ľ Make three more appropriate links, as has already been done in the topmost link.

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Identical Pairs ď ľ Draw in the things that are missing to make the pairs identical.

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Use Two Figures to MakeOne ď ľ Fill in the empty squares on the right using the example Ex

shown at the top. p l e: am

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Ex

Draw the Common Elements p l e: am ď ľ In every row, the last figure on the right shows the one element common to all three preceding figures.

ď ľ Now apply the rule to the following sequences.

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Mend the Hole ď ľ One piece in the mosaic is missing. Find it from those offered on the right, and colour it appropriately.

ď ľ Draw a line between the hole in the blanket and the piece that was cut out of it.

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