1

Gozo College – Rabat Primary School

(Mr. George Curmi)

PROBLEMS AND INVESTIGATIONS PART 1

Math is fun! Worksheets

Year 4

NAME: _______________________________

CLASS: _______________________________

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Bubble gum Janet bought a bubble gum. It cost 6c. She paid for it exactly. Which coins did she use? There are 5 different ways to do it. Find as many as you can.

= 6c

= 6c

= 6c

= 6c

= 6c What if the bubble gum cost 7c? There are 6 different ways to do it. Find as many as you can.

= 7c

= 7c

= 7c

3

= 7c

= 7c

= 7c What if the bubble gum cost 8c? There are 7 different ways to do it. Find as many as you can.

= 8c

= 8c

= 8c

= 8c

= 8c

= 8c

= 8c

= 8c

4

Pick a pair Choose from these numbers.

7 3 1 9 Pick a pair of numbers. Add them together. Write the numbers and the answer.

Pick a different pair of numbers. Write the numbers and the answer.

Keep doing it. There are 6 different ways to do it. Find as many as you can.

+ =

+ =

+ =

+ =

+ =

+ =

5

Now take away one number from the other. There are also 6 different ways to do it. Find as many as you can.

– =

– =

– =

– =

– =

– =

6

Bean-bag buckets Daniel threw 3 bean-bags. Each bag went in a bucket. More than one bean-bag can go in the same bucket.

1. What is the highest score Daniel can get?

+ + =

2. What is the lowest score Daniel can get?

+ + =

3. Find three ways to score 6.

+ + = 6

+ + = 6

+ + = 6

7

4. Find three ways to score 9.

+ + = 9

+ + = 9

+ + = 9

5. How can Daniel get these scores?

+ + = 10

+ + = 5

+ + = 8

+ + = 4

+ + = 11

+ + = 7

8

Sum up Choose from these four cards.

2 4 8 3 Can you make these totals? You can use two, three or four cards. You can’t use the same card in the same sum more than once.

= 9

= 10

= 11

= 12

= 13

= 14

= 15

= 17

9

Bird’s eggs You may need 19 counters to work out this sum. Three birds laid some eggs. Each bird laid an odd number of eggs. Altogether they laid 19 eggs. How many eggs did each bird lay? Find 10 different ways to do it.

+ + = 19

+ + = 19

+ + = 19

+ + = 19

+ + = 19

+ + = 19

+ + = 19

+ + = 19

+ + = 19

+ + = 19

10

Card sharp Take ten cards numbered 0 to 9.

0 1 2 3 4 5 6 7 8 9

1. Pick three cards with a total of 12. You can do it in 10 different ways. See if you can record them all.

+ + = 12

+ + = 12

+ + = 12

+ + = 12

+ + = 12

+ + = 12

+ + = 12

+ + = 12

+ + = 12

+ + = 12

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2. Now pick four cards with a total of 12. You can do it in 9 different ways. See if you can record them all.

+ + + = 12

+ + + = 12

+ + + = 12

+ + + = 12

+ + + = 12

+ + + = 12

+ + + = 12

+ + + = 12

+ + + = 12 3. Can you pick five cards with a total of 12?

12

Pencils Alexia bought some pencils costing 45c. She paid for them using only coins. She had 5c coins, 10c coins and 20c coins in her purse. There are nine different ways how to pay 45c exactly using only 5c, 10c and 20c coins. Find as many as you can.

= 45c

= 45c

= 45c

= 45c

= 45c

= 45c

= 45c

= 45c

= 45c

13

Flour Chef Luca bought some bags of flour to bake some cakes. Some bags weighed 3kg and some weighed 4kg. Altogether Chef Luca had 19kg of flour. How many bags weighed 3kg and how many weighed 4kg? Find two different answers.

What if Chef Luca had 25kg of flour? Find two different answers.

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Birthdays Mum and Paul are talking about birthdays. They take Paul’s age and double it. Then they add 5. The answer is 35. Mum says this is her age. How old is Paul?

Dad and Anna are talking about birthdays too. They take Dad’s age and halve it. Then they subtract 7. The answer is 18. Anna says this is her age. How old is dad?

15

Red squares, yellow squares Anton coloured the four squares in each grid either red or yellow. There are 16 different ways how Anton can colour the grids. Can you find them all?

16

Bicycles and tricycles Amy went to a cycling event. At the event there were some bicycles and some tricycles. Bicycles have two wheels and tricycles have three wheels. Amy counted 25 wheels altogether. How many bicycles and how many tricycles were there? There are 4 different possible answers. Can you find them all?

17

Ben’s numbers Ben has written a list of different whole numbers. The digits of each number add up to 5. None of the digits is zero. Below there is one of Ben’s numbers. Ben has written all the numbers he can think of. There are 16 different numbers. Can you find them all?

23

Write all the numbers in ascending order (from smallest to largest).

18

Rows of coins Take five coins: 1c, 2c, 5c, 10c, 20c. Put them in a row using these clues.

The total of the first three coins is 27c.

The total of the last three coins is 31c.

The last coin is double the value of the first coin.

Take six coins: two 1c, two 2c and two 5c. Put them in a row using these clues. There are two different correct answers.

Between the two 1c coins there is one coin.

Between the two 2c coins there are two coins.

Between the two 5c coins there are three coins.

or

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Roly poly The dots on opposite faces of a dice always add up to 7. Imagine rolling one dice. The score is the total number of dots you can see. You score 17. Which number is face down? How did you work out your answer?

Imagine rolling two dice. The dice do not touch each other. The score is the total number of dots you can see. Which numbers are face down to score 30?

20

Dan the detective Dan the detective looked for a number. He found a two-digit number less than 50. The sum of its digits was 12. Their difference was 4. What number did Dan find?

Dan found a two-digit odd number. One of its digits was half the other. The number was greater than 50. What number did Dan find?

21

Spaceship Some Tripods and Bipods flew from planet Zeno. There were at least two of each of them. Tripods have 3 legs. Bipods have 2 legs. There were 23 legs altogether. How many Tripods were there? How many Bipods?

22

Susie the snake Susie the snake has up to 20 eggs. She counted her eggs in fours. She had 3 left over. She counted them in fives. She had 4 left over. How many eggs has Susie got?

23

Three monkeys Three monkeys ate a total of 25 nuts. Each of them ate a different odd number of nuts. How many nuts did each of the monkeys eat? There are 10 different possibilities. Can you find them all?

+ + = 25

+ + = 25

+ + = 25

+ + = 25

+ + = 25

+ + = 25

+ + = 25

+ + = 25

+ + = 25

+ + = 25

24

Card tricks Chico’s cards are all different. There is a number from 1 to 8 on each card.

1 2 3 4 5 6 7 8

Chico has chosen four cards that add up to 20. What are they? There are seven different possibilities. Try to find them all.

+ + + = 20

+ + + = 20

+ + + = 20

+ + + = 20

+ + + = 20

+ + + = 20

+ + + = 20

25

Queen Esmeralda’s coins Queen Esmerelda had 20 gold coins. She put them in four piles.

The first pile had four more coins than the second.

The second pile had one less coin than the third.

The fourth pile had twice as many coins as the second.

How many gold coins did Esmerelda put in each pile?

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Duck ponds Use 14 ducks each time.

1. Make each pond hold two ducks or five ducks.

2. Make each pond hold twice as many ducks as the one before.

3. Make each pond hold one less duck than the one before.

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Stamps Tilly’s parcel cost 55c to post. She stuck on eight stamps. Each stamp was either 10c or 5c. How many of each stamp did Tilly stick on her parcel?

Number of 5c Stamps Number of 10c Stamps Total Value

28

Maisie the mouse Maisie had between 30 and 50 breadcrumbs. She counted the breadcrumbs in fours. There were 2 left over. She counted them in fives. There was 1 left over. How many breadcrumbs did Maisie have?

29

Stickers The twins collected some animal stickers. They each had the same total number.

Winston had 3 full sheets and 4 loose stickers.

Wendy had 2 full sheets and 12 loose stickers.

Every full sheet has the same number of stickers. How many stickers are there in a full sheet?

30

Sandcastles Lisa went on holiday. In 5 days she made 80 sandcastles. Each day she made 4 fewer castles than the day before. How many castles did she make each day?

31

Fireworks Emma had some fireworks. Some made 3 stars. Some made 4 stars. Altogether Emma’s fireworks made 19 stars. How many of them made 3 stars? How many of them made 4 stars? Find two different answers.

What if Emma’s fireworks made 25 stars? Find two different answers.

32

Treasure chest Captain Hook found a treasure chest with 25 gold coins in it. He decided to divide the coins into four piles.

In the first pile he put some coins.

In the second pile he put two less coins than in the first pile.

In the third pile he put one less coin than in the fourth pile.

In the fourth pile he put twice as many coins than in the second pile. How many coins were in each pile?

33

Broken calculator Carla’s calculator is broken. Unfortunately, none of the buttons work except the 3, 5, +, – and = buttons. Can you help Carla make all the numbers from 1 to 20 using her broken calculator?

= 1 = 11

= 2 = 12

= 3 = 13

= 4 = 14

= 5 = 15

= 6 = 16

= 7 = 17

= 8 = 18

= 9 = 19

= 10 = 20

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Cup cakes Katrina baked 24 cupcakes.

She gave ¼ of the cupcakes to her sister Anna.

She gave ⅓ of the cupcakes to her friend Sally.

She shared 9 of the cupcakes among her three children. How many cupcakes are left?

35

Sudoku Here are two Sudoku puzzles for you to solve. Remember, when you’ve finished these puzzles, each one should have the numbers 1, 2, 3 and 4 in every row, every column and every block of four squares.

4 2

1 2 3 The second puzzle is a bit harder than the first one.

1 4

2

3

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How old? Try to work out how old these children are. William: “If you double my age and take the answer away from twenty, you get six.” Bob: “Double my age is the same as four times four.” Lucy: “In ten years’ time I will be twice as old as I am now.” Freddie: “Three times my age minus 8 is the same as double my age.” James: “I’m three years older than my sister; our ages add up to 21.”

37

Poor Max Mary has a set of shape cards and she tells her brother Max that the shapes stand for different numbers and that he has to work out what they are. She tells him:

+ = 9

+

= 3

+ = 6

+ + = 13

Can you work out which numbers the shapes stand for?

= =

= =

38

What were they thinking of? Simon thought of a number. He doubled it and added 7, getting the answer 25. What was his number? Jill thought of a number. She added 5 and then halved the result. Her answer was 11. What was the number she first thought of? Sophie thought of a number. She multiplied it by itself and took away 5, getting the answer 59. What was her original number? Brandon thought of a number. He multiplied it by itself, added 1 and then halved the result, getting 13. What number did he start with?

39

Football friendly Last year Liverpool played Manchester United in a pre-season friendly match. Of course, the game was anything but friendly, with three players being sent off and one player finishing the day in hospital. The fans thought it was a pretty good game. FINAL SCORE:

LIVERPOOL 3 MANCHESTER UNITED 1

If this was the final score, what could the score have been at half-time? There are 8 possible scores. Can you find them all?

LIVERPOOL MANCHESTER UNITED

LIVERPOOL MANCHESTER UNITED

LIVERPOOL MANCHESTER UNITED

LIVERPOOL MANCHESTER UNITED

LIVERPOOL MANCHESTER UNITED

LIVERPOOL MANCHESTER UNITED

LIVERPOOL MANCHESTER UNITED

LIVERPOOL MANCHESTER UNITED

40

Weight for it Samantha’s mum has just bought some new bathroom scales. When her friend Judy comes round, with her little brother Bill, they all try out the new scales. Here are some results for you:

With Judy and Bill standing on the scales together, the reading is 40kg.

Bill and Samantha together weigh 60kg.

Samantha and Judy together send the scales to 80kg.

What would the readings be if Samantha, Bill and Judy weighed themselves separately?