МАТHS

AS A GAME 2Problems which Stimulate

Mathematical Talent

Branka Dejić Mirko Dejić

2

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

• When a problem has been solved without outside help and without fault, the following rating .

• If the child had asked for help or made a minor error, the following is chosen .

• If the child was unable to solve a problem or did so only with a lot of help from an adult, use this rating

• If the child was unable to solve a problem or did so only with a lot of help from an adult, .

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

We have also included a DIPLOMA which you award to the child for solving problems successfully, or

We have also included a DIPLOMA which you award to the child for solving problems successfully, 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.

3

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.

Some of the following problems may appear

diffi cult, but solving them is easy. All you need is a bit of thinking. And that is exactly what the girl in this story did.

Anna, Mark and their father were standing on the bank of a river and wanted to cross it. They had a small boat which could carry either one

adult, or one child, or both children, but not all three. Try and fi gure out how Anna, Mark and Dad managed to get across. Anna was the fi rst to fi nd the solution:

First the children rowed across. Then Mark came back. Then father rowed across on his own. Then Anna returned alone to pick up her

brother, and the two then rowed to the other bank, where Dad was waiting for them.

river and wanted to cross it. They had a small boat which could carry either one adult, or one child, or both children, but not all three. Try and fi gure out how Anna,

Mark and Dad managed to get across. Anna was the fi rst to fi nd the solution: First the children rowed across. Then Mark came back. Then father

4

Where are the Numbers Hidden?

There are numbers hidden in the drawing. Find them, and colour the same numbers with the same colours. Write down how many there are.

1 2 3 4 5 6 7 8 9 10

Write down how many there are.

1 2 3 4 5 6 7 8

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Left Paw, Right Paw

Colour the Apples

Colour every third apple yellow, and every fourth apple green.

How many apples remain unpainted?

Draw a carrot in the first bunny’s left paw.Draw carrots in both of the second bunny’s paws.Draw one in the third bunny’s right paw.Leave the fourth bunny without any carrots.Leave the fourth bunny without any carrots.

6

Less than (<), More than (>), Equal to (=)

Counting and Calculating

Write in the squares corresponding numbers and their relationships – less then, more than, or equal to – as we began in the first example.

Fill in the missing numbers.

4 >

10 9 7 4 1

1 3

4

2

5

1

3 5

1

I know!

7

Greater and Smaller Numbers

Colour the squares with numbers smaller than six blue, and the squares with numbers greater than seven with green.

Compare the Numbers

Fill into the missing fields a number of your choice so that the inequality is correct.

6 9 2 5

2 8 1

4 0

98

2

1

7

3

10

5

6

8

Different Orders

Arrange the figures below in different orders, as we began in the second row.

9

Only Three Colours

Continue drawing the little balls, and then colour them with the three colours shown. The order of colours in each row should be different.

Hmmm…

10

Arrange the Plums

Distribute the plums in the two plates in different ways.

7 77 7

7

7

7

7

7

7