How many times would you use the digit 7 to number the pages of a 100 page book?

Problem Solving 1

You are standing in line at the movies.

You count 18 people behind you. There are 23 people standing in front of you. How many people

are standing in line?

Don’t forget to include yourself!

Problem Solving 2

If you collect one Oiler card the first day, 2 Oiler cards the second day, 3 Oiler cards the third day and so on, how many Oiler cards will you have altogether after 9 days? What about

after 14 days?

Problem Solving 3

It is said that a giant turtle came from a river with a “magic” square written on its back. The sum of the numbers in each row, column and diagonal will be 15. Find the missing numbers in this magic square. Use

each of the numbers 1 to 9 only once.

6

5

8

Problem Solving 4

Jack opened his math book at these pages. The sum of the two page numbers is 193. When the book is open the pages are side-by-side. Where would Jack

open his math book so that the sum of the two pages is 265?

Problem Solving 5

How many different ways can you arrange the digits in one thousand eighty four? Make a list.

Problem Solving 6

In how many different ways can Karrie divide her 17 quarters between her two piggy banks? She

must have one or more in each piggy bank.

Problem Solving 7

Karen has sixteen dollars worth of pennies. If she laid them side by side, how long would her line

of pennies be?

Include your answer in mm, cm and m.

Problem Solving 8

Jack, Hal and Mona live on the same country road. Jack lives 13km from Hal. Mona lives 5km from Hal. How far does Jack live from

Mona?

Problem Solving 9

David and his mom had a discussion about David’s remembering to bring home his math homework.

David’s mom agrees to pay David for remembering. David’s pay would be as follows: $0.01 the first day, $0.02 the second day, $0.04 the third day, $0.08 the fourth day, $0.16 the fifth day and so on. How

much will David be making on the eleventh day? What about on the 23rd day?

Problem Solving 10

Amanda is thinking of two 2-digit numbers.

These two numbers have the same digits. The sum of the digits of each number is 9. The difference between the two numbers is 9.

What are Amanda’s two numbers?

Problem Solving 11

Jane pays $72 a month for her weight training lessons. She goes to her lessons on Wednesday nights and Saturday mornings each week. How

much does each lesson cost?

Problem Solving 12

The family dog, Maggie, eats 1.6kg of dog food in one week. There are 52 weeks in a year. How much food will Zach eat in three weeks. How

much in 2 months? How much in a year?

Problem Solving 13

Greg’s number is between 55 and 80. His number is divisible by 3 and by 9. Greg’s number is not

divisible by 7. What is the number?

Problem Solving 14

The number on Barb’s football shirt is less than 100. The number on Barb’s shirt has factors of

6, 8 and 9. What is the number?

Problem Solving 15

You decide to buy a gift for $1.25. You have only quarters and dimes. List all the combinations of coins that you could use to pay the cashier.

The cashier will NOT give you change.

Problem Solving 16

Can you make a stairway with 28 blocks?

How many steps will there be?

(Hint: 3 blocks makes a stairway with 2 steps.)

Problem Solving 17

Be a detective! Arrange the digits 4, 5, 6, 7, 8, and 9 in the boxes to get the largest possible difference. Use each digit

only once. ▢ ▢ ▢ - ▢ ▢ ▢

Problem Solving 18

The Trans-Canada Highway is 7775km from Victoria to St. John’s. The Smith family, who lives in Victoria, travelled by

car to Montreal. On the third day, the family arrived in Winnipeg. How many more kilometres must the Smith family

travel to reach Montreal? Victoria to Winnipeg – 2337km

Montreal to St. John’s – 2602km Victoria to St. John’s – 7775km

Problem Solving 19

Bev decided to build up her arm muscles. She did 2 push-ups each day of the first week. During the second week she did 4 push-ups each day.

She continued to increase the number of push-ups she did by 2 weeks. How many push-ups will Bev

be doing at the end of 40 weeks?

Problem Solving 20

A grade 4 teacher buys seven sheets of stickers. Each sheet has eighteen Alberta emblems on it. How many mountain peaks are

there on the 7 sheets of stickers?

Problem Solving 21

George is a lumberjack. His job is to cut logs into smaller pieces. How long will it take

George to cut a 20m log into 10 pieces if George can make one cut in three minutes.

Problem Solving 22

At 12:00 noon, the hands on the clock face are together. If you watch the clock face until

12:00 midnight, at what times will you see the clock hands together?

Problem Solving 23

If you use 40 dots to make a pentagon,

how many dots will be on each side?

Problem Solving 24

This triangle was named after the French mathematician, Pascal. What numbers will go in

the next 2 rows in this triangle?

Problem Solving 25

When Jewel looked at this figure, she saw more than 16 squares. She decided to find as many

different squares as she could. How many squares will Jewel be able to find?

Problem Solving 26

1, 4, 9, 16, … are called square numbers. Square numbers can be found by adding odd numbers together or by

multiplying a number by itself. What odd numbers will you add together for the square number of 64?

Problem Solving 27

Harold’s calculator is not working properly. The 5 and 7 keys are jammed. He needs to find the sum of 971 + 1543. How might he do this and still use his calculator? What is the sum?

Problem Solving 28

A small school bus has seats for 24 passengers. On a field trip to Grande Prairie there was one

empty seat for every 3 occupied seats. All passengers had their own seats. No one was

standing. How many passengers went on this field trip?

Problem Solving 29

Sixty-four is a special number. It is both a square number and a cubed number. It is squared because 8x8=64. It is a cubed number because 4x4x4=64. Find the next number that is both a

square number and a cubed number.

Hint: It is less than 1000.

Problem Solving 30

There are 3 boxes of gift cards in the classroom. The sum of the cards in boxes A and C is 135. The difference between the number of cards in

boxes B and C is 65. The sum of the cards in A and B is 200. How many cards in each box?

Problem Solving 31

The grade four class set up their paper mache model of a Brachiosaurus on tables placed end to end. The length of one table is 1.32m. The dinosaur model is 6m long. How many tables

should this class place together?

Problem Solving 32

Priscilla the ladybug is at the top of a square – based pyramid. She wants to go down to vertex A travelling along only the edges. Once Priscilla is down, she can’t go back up. How many different paths can she take? Which is the longest path?

Which is the shortest path?

Problem Solving 33

Webster’s super bouncing ball bounces exactly half the height from which it is dropped.

Webster drops the ball from the top of a 96m high building. If someone catches the ball when it will only bounce to 3m, how many metres will the

ball have travelled.

Problem Solving 34

Douglas is cutting his round birthday cake. He can make only 3 straight cuts from one edge of

his cake to another edge. There are 7 guests at Doug’s birthday party. How will he have to cut the cake so he has enough pieces to give each

guest a piece of cake? (The pieces do NOT have to be equal in size.)

Problem Solving 35

Prime numbers have only two factors – one and the number itself. There are 10 prime numbers

less than 30. What are they?

(Do not include the number one.)

Problem Solving 36

Three-fourths of the Math Club members are girls. During one Math Club meeting one-fifth of

the boys were present because only 3 boys attended. How many children belong to the math

club?

Problem Solving 37

If 2 dice are rolled, what are the possible sums on the faces that show up? Do you think that each sum will show up an equal number of times?

Why? Roll a pair of dice 40 times.

Graph the number of times each sum is rolled.

Problem Solving 38

If you toss two coins at the same time what are your chances of throwing two heads? Or two tails? Or a head and a tail? Toss two coins

together 100 times to help answer these questions.

Problem Solving 39

Put 4 coins in a cup, shake the cup and toss the coins on the table. Your toss could end up as all heads, 3 heads and one tail, 2 heads and 2 tails,

one head and 3 tails or all tails. Toss the 4 coins 50 times. Graph your results. Which combination

of coins occurs most often.

Problem Solving 40

The children of room 7 were asked to arrange 5 square tables for a science display. After trying out various

arrangements, these children decided to arrange the tables like this:

What are the other eleven ways these children could have arranged the tables? One side of each table must match

one side of another table exactly. These arrangements are considered to be the same.

Problem Solving 41

Kevin is in a math contest. He must find the sum of the first 50 numbers as quickly as possible.

He is not allowed to use a calculator. Help Kevin find the sum.

1+2+3+4+5+6+7+…45+46+47+48+49+50= ?

Problem Solving 42

The top, bottom, and sides of a 3 x 3 x 3 cube are painted blue. How many cubes of the 27

small cubes have one blue face? 2 blue faces? 3? 4? 5? 6? 0?

Problem Solving 43

Dorothy wants to take her mouse, her dog and her cat across the river on her raft, but Dorothy has several

problems. -the raft will hold only Dorothy and one pet at a time

-if left together, the dog and cat will fight -if left together, the cat will probably eat the mouse

How can Dorothy take her pets across the river safely?

Problem Solving 44

William’s license plate number has 5 different digits. William discovered that the license plate

could be read meaningfully even when it was upside down. The digits in the upside down number are in

order with the smallest digit being in the ten thousands’ place. What is William's license plate

number?

Problem Solving 45

Five children are jogging around the school-yard (after-school) today. However, all 5 children do not jog every day.

-The first child jogs every day. -The second child jogs every second day.

- The third child jogs every third day. - The fourth child jogs every fourth day. - The fifth child jogs every fifth day.

The children plan to race the next time they all jog together. How many days from today will their race be held?

Problem Solving 46

Valerie’s family travelled from Edmonton to Banff. Leaving Edmonton, the odometer registered this: 33611. Banff is 271km farther than Red

Deer. Entering Banff, Valerie read the odometer. It registered this: 34039. What was

the odometer reading in Red Deer?

Problem Solving 47

The kitchen tap is dripping. Michael collected 1000 drops of water in a mL cup. About how

many mL of water did Michael collect?

Problem Solving 48

While you are working in a greenhouse, your employer asks you to bring him exactly 4 litres of water. You can find only a 5-litre jar, and a 3-litre jar. They have no markings. How can you use these to measure exactly 4 litres of water.

Problem Solving 49

I am a 5-digit decimal number. The digit in the hundreds place is the same as the digit in the

tenths place. This digit is also the largest odd number. The digit in the tens place is the same as the digit in the hundredth’s place. This digit is the smallest even number.

The remaining digit is the largest even number. What number am I?

__ __ __ . __ __

Problem Solving 50

Farmer Jones owns sheep and turkeys. He counts 23 heads and 80 feet. How many sheep does Farmer Jones own? How many turkeys?

Problem Solving 51

You know how old you are in years.

How old are you in DAYS?

Hours? Minutes?

Problem Solving 52

This is your next assignment:

Arrange the digits 6, 7, 8 and 9 in the boxes to get the largest possible product.

Use each digit only once.

▢ ▢

x ▢ ▢

Problem Solving 53

Mark drove downtown to shop. He entered the parkade at 11:20 and left at 2:40pm. How much did Mark pay for

parking? Parking Rates

$0.50 for each ½ hour or less $4.50 maximum

$1.00 from 6:00pm to 6:00am

Problem Solving 54

Molly decided that it was time to put her money into the bank. She emptied her piggy bank and

put her coins in rolls. She had 2 rolls in quarters, 3 rolls in dimes, 1 roll in nickels and 1 roll in pennies. How much money will Molly be

able to put in the bank.

Problem Solving 55

Carmen counted her hockey cards. When she counted them by 4’s, she had one left over.

When she counted them by 5’s, she had 3 left over. Carmen has more than 60 cards, but fewer than 80. How many hockey cards does Carmen

have?

Problem Solving 56

Mary, Karie, and Barry are triplets. Their dad bought them a pizza to eat for lunch. Barry ate 2/10 of the pizza. Mary at 2/5 of the pizza.

Dad at ½ of the pizza which was left. Karie ate the rest of the pizza. Which triplet ate the most

pizza?

Problem Solving 57

Two consecutive odd numbers when multiplied together have a product of 1155. What are

these two numbers?

__ x __ = 1155

Problem Solving 58

You decide to order a sundae at the Ice Cream Parlour with one flavour of ice cream and one topping. There are

8 flavours of ice cream and 4 different toppings from which you can choose. How many different sundaes could you

choose.

Flavours: butterscotch, chocolate, mint, orange, peach, peppermint, strawberry, vanilla

Toppings: chocolate chips, coconut, marshmallow, nuts

Problem Solving 59

Sophie couldn’t remember whether she put 677, 767 or 776 marbles in the jar. She does remember that each time she put in a green

marble, she put in 7 red marbles. Are there 677, 767, 776 marbles in the jar.

Problem Solving 60

Is it true that the human heart beats

about 5000 times an hour.

Problem Solving 61

Janice delivers parcels in a 15 floor office building. During the morning she dropped off 6 parcels, each parcel to a different floor. She went up to the 6th floor. Then down 3 floors. Up 10 floors. Down 4 floors. Down 7 floors. Up 9 floors. On what floor did Janice drop off

her 6th parcel?

Problem Solving 62

Kenny emptied his piggy bank. He counted 30 coins. Three-tenths of the coins are dimes. The rest of the coins are pennies. What is the value

of Kenny’s coins.

Problem Solving 63

Buddy’s bank balance is $239.64. Buddy wrote a cheque to pay for a pair of skis and a pair of

roller skates. What will Bud’s new bank account balance be?

Skis: $92.69 Roller skates: $63.99

Problem Solving 64

Which letters of the alphabet are symmetric? Which letters have more than one line of

symmetry?

Problem Solving 65

Gail, Wendy, and Sally are cousins. One of the girls is in grade 3, one is in grade 4, and one is in grade 5. The grade 5 girl goes to a different school from the other two girls. Gail and Sally are together in their school choir. The grade 3 girl lives next to the grade 5 girl. Gail lives 3 blocks from Wendy. Which girl

is in which grade?

Problem Solving 66

A fly walks along each edge of a square shaped box before he flies away. How far did the fly

walk on the box?

(One side of the box is 0.25m)

Problem Solving 67

The buzzer rings because of elevator overload. The capacity of this elevator is 800kg.

Estimate the number of adults in the elevator.

Problem Solving 68

In a math class, Marshall weighed some objects. - The thumb tack had a mass of 0.46g

- The nail had a mass of 4.16g - The paper clip had a mass of 2.92g - The marble had a mass of 5.63g

- The pin had a mass of 0.08g Which 3 objects would have a total mass of 7.16g?

Problem Solving 69

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