Mirko Dejić and Branka Dejić

ADVENTURES

IN MATH

1

Mirko Dejić and Branka Dejić

ADVENTURES

IN MATH

MA1

1

Activities for developing creativity and giftedness

First grade

Contents

Observations................................................................................................... 8 Quips............................................................................................................. 25 Numbers and calculation............................................................................ 30 Geometry...................................................................................................... 42 Combinatorics.............................................................................................. 50 Brain-twisters.............................................................................................. 54 Measurement............................................................................................... 61 Answer Key................................................................................................... 64

NOTE TO CHILDREN Why do we learn maths? Many students ask themselves this question without realizing the many benefits of problem solving. Whatever we choose to do in life, we won’t be able to do it without maths. Without maths, there would be no airplanes, bridges, toys, trade and many other things. Maths is applied even where we don’t expect it – in painting, music and literature. Maths teaches us how to think logically, and we become smarter when we learn it. This book contains a variety of interesting tasks, most of which you won’t see during your maths classes in school. Not only will solving these problems become a pleasure, but you will also be nurturing your mathematical giftedness. It is very important to be patient when solving problems. Those that might seem difficult at first can usually be solved in a simple way. If you’re having trouble with one problem, move onto the next one. Success will encourage you. Your reward will be feeling joy and accomplishment because of a job well done. Try not to ask adults for help; keep going until you solve the problem on your own. At the end of the book, you will find a key that contains either full answers, step-by-step explanations or solutions for most of the problems. Only look at the answer key after you’ve finished solving the problem. Compare it to your answer and, if needed, try to establish where the error occurred. Try to understand the reasoning behind the answer.

5

NOTE TO TEACHERS AND PARENTS The book presented before you is intended for first-graders, but if children of younger age are able to solve these problems, this might mean they could become great mathematicians in the future. The tasks contained in this book are engaging, unorthodox and dedicated to problem solving. Children are presented with various problematic situation for which they need to find solutions. By independently seeking ideas for solutions and anticipating results, the children are developing both creativity and intuition needed for solving mathematical problems. Brief confusion that occurs at the beginning of the activity will motivate them to find where the problem lies. Then, a solution will pop up, causing the children to have an a-ha! moment. This will bring them joy and desire to keep going. The children will then begin to resemble real mathematicians and researchers. Ensure your child has favourable conditions for problem solving: yy Accept every attempt at problem solving, even when incorrect. These efforts of seeking answers are also expressions of children’s creativity; yy Convince your child they can solve the problem all the way to the end; yy Express genuine joy when your child is successful and praise them; yy Help only by offering them advice when necessary; in most cases, a short “you’re on the right path” will do. Avoid: yy Causing fear in children: ”You are too stupid for this, you will never figure it out”; yy Frustration: when the child is making an effort and we don’t pay attention to their work; yy Forcing children to solve problems – this will cause an adverse effect; yy Words: replace “let’s do some maths” with “let’s play, so we can see how the wolf, the goat and the cabbage managed to cross the river…” 6

The problems are useful for discovering and developing mathematical giftedness. It is especially important to pay attention to the following indicators of mathematical giftedness in children: yy Did the child solve the problem in multiple ways? yy Do they fill in the cognitive blanks independently while solving maths problems? yy Do they ask for help while solving problems? yy Are they persistent when solving problems? yy Are they offering unorthodox answers? yy Are the answers concise? yy Are they quick in problem solving? yy Are they using a wide range of ideas acquired through earlier problem solving? yy Do they express exceptional inventiveness in problem solving? yy Do they find pleasure in solving more demanding problems? yy Are they able to utilise drawings and models? yy Do they stick to their original plan of solving the problem all the way to the end? yy Are they quick to notice new relations? yy Are they able to differentiate between important and unimportant elements in a problem? yy Are they quick to understand the problem at hand and lay out a plan for solving it? The problems in this book have varied aims: some are useful for developing logical and abstract thinking, some are related to spatial orientation, others deal with ways of behaving in certain situations, while many are, simply, fun and interesting tasks â€“ ones that will make us fall in love with maths and motivate us to work constantly. All of them can greatly develop mathematical abilities and intelligence. The most intense period of intellectual development in children is until the age of 13. This is when tasks aimed at advancing cognitive skills are at their most effective. The activities in this book are notably varied, so as to avoid problem solving through repeated patterns. Every problem will present the child with a new situation, so seeking answers will be equal to finding your way in unique circumstances. This requires intelligence, which will simultaneously be utilised and developed.

7

Observations 1. Each rabbit is holding a sign marking their house. Find their houses and write the

corresponding letters in the squares. You will reveal a secret word. Read it out loud.

8

2. Find a matching object on the right for each object on the left. For example: railway tracks and train, which should be marked with (A, 4). Mark the remaining sets. (А, .....) (Б, .....) (В, .....) (Г, .....) (Д, .....) (....., .....) (....., .....) (....., .....) (....., .....)

Б

А В Г

3

2

1

5

Д

4

Ђ

6

Ж Е

7 9

З

8

3. W hich clown is the same as the one shown in the cut up picture? Circle the letter with correct answer. а)

б)

в)

г)

9

4. A boy is looking at himself in the mirror. Which ear is he holding? Circle the correct answer. Left ear.

Right ear.

5. W ork out in which order the circles appear, then fill in the blank ones. Đ°)

Đą)

10

Quips 1. Five birds were perched on the branch. Two moved to a lower branch.

How many birds remained in the tree?

2. There were eight birds on the branch. All the birds flew away, except three. How many birds flew away?

3. What kind of branch does the crow stand on after rain?

4. Seven candles were lit on a birthday cake. They all burned out, except two. How many candles were left on the cake?

5. There are four ships at sea. Two have arrived at the port. How many ships are at sea?

25

6. The apple tree grew 60 apples, and the willow grew by five fewer. How many apples grew on the willow?

7. The fence in the yard has 15 pickets. How many pickets did the fence have when the owner of the house painted three of them?

8. Two friends walked two kilometres together by going to school on foot. How many kilometres did each of them walk?

9. R ob rode a bicycle to school. Each wheel turned

for 15 minutes. How many minutes did the entire bike travel?

10. Ten boys and tens girl climbed a hill in 30 minutes. How many minutes will it take for boys to climb the hill?

11. R ob left school to go home at the same time his brother Michael left

home to go to school. They ran into each other after 10 minutes. How many minutes did each of them walk?

26

12. R ob and Peter were walking to school. On the way, they ran into two friends who were walking home from school. How many children went to school?

13. If Peter didnâ€™t reach the finish line before Mark, does that mean that Peter reached the finish line after Mark?

14. There are three eggs in the bowl. If one egg is cooked in four minutes, how much time will it take to cook all three eggs?

15. H alf of the students have left the classroom. Eleven students remained in the classroom. How many students are in this class?

16. Six boys and three girls were in the classroom during the break. Two girls and one boy stood against the wall. How many children were in the classroom?

17. If a stick is cut in three places, how many pieces will you get? 18. This 12-meter-long beam should be cut into 1-meter-long pieces. In how many places should the beam be cut?

27

Numbers and calculation 1. Cross every fourth pearl starting from the left, then fill in every other pearl with yellow.

2. O nly one number hasnâ€™t been written twice in this table. Try to find that number as fast as you can. Circle it.

5

9

14

22

16

12

21

2

8

6

8

72

14

5

72

18

6

83

22

12

83

16

2

21

9

3. H ow many groups of three do you see? How many circles are there in total?

30

4. H ow much does the notebook cost and how much does the eraser? = 70 pence

=

90 pence

5. W rite the following numbers in the circles: 15, 23, 42, 18, 13, 27, 16.

The arrows show the path from the highest number to the lowest one.

6. W rite the number 10 by using three number ones. 10 = 7. The princess is trapped in the castle. You will set her free if you find the gates marked

with numbers whose sum is equal to the number the princess is holding in her hands. Colour in those gates.

31

8. The prince will free the princess only if he goes through the three doors marked with numbers whose sum is equal to the number the princess is holding in her hands. Fill in the blank squares and colour them in with the matching colour.

a)

+

+

= 10

+

+

= 10

+

+

= 10

+

+

= 20

+

+

= 20

+

+

= 20

+

+

= 20

Đą)

9. The sum of three consecutive numbers is 15. Which numbers are they? Write them in the blank squares.

+ 32

+

= 15

Geometry 1. What’s the difference between these picture pairs? Circle them.

2. Continue writing the “+” sign in the blank space if the shape exists in the picture and the “-” sign if it doesn’t. Слика

Квадрат

1

+

Правоугаоник

Троугао

Круг

2 3 4

1 42

2

3

4

3. Fill in the table with numbers based on the picture below.

5

4. Are there more triangles or circles in the picture?

5. Connect the dots as shown in the picture.

43

6. M ia drew two lines. She marked four dots on the first one and three dots on the second one.

When she counted the dots, there were six of them. How is this possible? Draw the same thing.

7. There is one square side in each grid. Complete the drawings of squares.

8. Complete the pictures in order to get cuboids. а)

б)

в)

9. A line segment is bounded by two dots. How many line segments can you draw using the five dots in the picture?

44

Combinatorics 1. Fill in the circle and the triangle with either blue or green, so they are in different colours. Draw them and fill them in as shown.

In how many different ways can you fill in the circle and the triangle?

2. Fill in the pair of boxes with blue or green, as shown.

3. Continue colouring in the circles by using three colours, as shown. The order of colours should be different in each line.

50

4. Continue filling in the spaces with yellow, green or blue, so that every vertical and horizontal line is made from squares in different colours.

5. Find the order in which the circles in the grid have been coloured. Fill in the blank circles.

6. M um had three sweets in different colours â€“ green, red and blue. Her son Mark took two sweets and left one for his mum. Colour in the sweets that Mark could have taken.

7. Write the numbers 1, 2 and 3 in the blank squares using different orders, as shown. 1

2

3

8. D an, Peter and Mark won three prizes at the marathon. What are all the order in which they could have won? Write the first letter of their names above the podiums.

M

Đ”

Đ&#x;

2

1

3

2

1

3

2

1

3

2

1

3

2

1

3

2

1

3 51

Brain-twisters 1. The mother is 20 years old, the daughter is two. How old will the mother be when the daughter is the same age as her mother is now?

2. The sum of Ben and Ellieâ€™s ages is 16. What will be the sum of their ages in two years?

3. Two years ago, Maggie was five. How old will she be in three years? 4. M aggie is six and Maggieâ€™s sister Emma is two years older. How old will Emma be when Maggie turns 12?

5. In two years, Tommy will the same age his brother Matt is now. Which brother is older and by how many years?

6. P eter is two years older than Michael. Michael is a year older than Jon. Who is older, Peter or Jon, and by how many years?

7. The brother is eight years old, the sister is six. How older than his sister will the brother be in five years?

8. Ed is older than Chris, but younger than Mary. Daisy is younger than Chris. Which child is the oldest and which is the youngest?

54

9. D aisy is three years older than Ella and two years older than Molly. Who is older, Ella or Molly? What is their age difference?

10. A nna and Nick had the same number of pennies.

If Anna gives 20 pennies to Nick, how many pennies will Nick have more than Anna?

11. D an has 100 pounds. Peter has the same amount, plus a half. How much money does Peter have?

12. The rooster weighs less than the goose by three kilograms, and more than the pigeon by two kilograms. By how many kilograms does the pigeon weigh less than the goose? Write the difference in kilograms in the blanks.

2 kg

13. M ister Jones had eight apple seedlings and 15 pear seedlings. He wanted to plant them in two rows, one of apples and one of pears, so that each row is 14 meters long. What should be the distance between two apple seedlings and two pear seedling? Write the answers in the blank fields.

Apples

Pears 55

Measurement 1. A tiger in the zoo drinks a litre of water per day. How will the zookeeper fill a litre of water from the tap if he has two buckets, one 4-litre bucket and one 3-litre bucker?

2. The cat weighs the same as the rabbit. The rabbit weighs the same as three mice. How many mice should sit on the third seesaw so they weight the same as the cat? Draw them.

3. W ho weighs the least? Circle the correct answer.

4. O ne pan is holding a whole watermelon and the other one is holding half of the watermelon and a 3-kilogram weight. The scales are in balance. How much does the watermelon weigh?

5. A pples and pears are in balance, as shown in the picture. Compare the weight of apples and pears and write the correct sign (<, > or =) in the blank space.

61

6. The rooster and the chicken weigh more than the rooster and the rabbit. Who weighs more, the rabbit or the chicken? Circle the correct answer.

7. H ow much does the sugar weigh? Write the correct answer on the weight in the second picture.

8. Compare the masses weights marked with A and C and write the correct sign (<, > or =) in the blank space. a)

Đą)

Đ˛)

62

The book presented before you is intended for first-graders, but if children of younger age are able to solve these problems, this might mean they could become great mathematicians in the future. The tasks contained in this book are engaging, unorthodox and dedicated to problem solving. Children are presented with various problematic situation for which they need to find solutions. By independently seeking ideas for solutions and anticipating results, the children are developing both creativity and intuition needed for solving mathematical problems. Brief confusion that occurs at the beginning of the activity will motivate them to find where the problem lies. Then, a solution will pop up, causing the children to have an a-ha! moment. This will bring them joy and desire to keep going. The children will then begin to resemble real mathematicians and researchers.

ISBN 978-86-529-0438-9

9 78 86 52 9 04 389