Problem solving games (100)

Planes a)

Application: Problems involving multiplicative relationships

A company produces airplanes and plans to triple the number of planes they produce by the end of next year. This year, they produced %a% planes. How many planes are they planning to produce next year?

The numbers just in case: %2%, %3%, %4%, %9%, %12%

Baby carrots a)

Application: Problems involving additive relationships

Alice takes %a% baby carrots and %b% pieces of celery for her lunch. Mario takes %c% baby carrots. How many more baby carrots does Mario take than Alice?

Dana b)

Application: Problems involving multiplicative relationships

Currently, Dana is %a% years old and she is half of Barney’s age. Barney is also twice as old as George. How much younger is George than Barney?

Just in case numbers : %1%, %2%, %3%, %4%, %5%.

Dana a)

Application: Problems involving multiplicative relationships

Currently, Dana is %a% years old and she is half of Barney’s age. Barney is also twice as old as George. How old is George?

The numbers just in case: %1%, %2%, %3%, %4%, %5%.

 

Caleb b)

Application: Problems involving multiplicative relationships

Caleb saved $%s% in the last month. This is half of the price of a soccer ball. A baseball cap costs $%c%. What is the price of the soccer ball?

The numbers just in case: %1%, %2%, %3%, %4%, %5%.

Caleb a)

Application: Problems involving multiplicative relationships

Caleb saved $%a% in the last month. This is half of the price of a soccer ball. A baseball cap costs %b%$. How many baseball caps can he buy with his savings?

The numbers just in case: %1%, %2%, %3%, %4%, %5%.

Dessert d)

Application: Problems involving additive relationships

Sarah has some apples. In %m% minutes, she eats %p% apples. After, she has %l% apples left. How many apples did she have in the beginning?

Tower b)

Application: Problems involving fraction expressions

Jackson visited a tower famous for its stairs. When he arrived at the third floor, he read the following sign: “You have climbed %m% stairs, but this is only one fifth of what you still have to climb.” In total, how many stairs does the tower have? 

Numbers just in case: %1%, %2%, %3%, %4%, %5%

Tower a)

Application: Problems involving fraction expressions

Jackson visited a tower famous for its stairs. When he arrived at the third floor, he read the following sign: “You have climbed %m% stairs, but this is only one fifth of what you still have to climb.” How many stairs does he still have to climb? 

Numbers just in case: %1%, %2%, %3%, %4%, %5%

Thomas

Application: Problems involving fraction expressions

Thomas has a third of the money Nicolas has. If Thomas spends half of his money, he will only have $%r% left. How much money does Nicolas have?

Numbers just in case: %1%, %2%, %3%, %4%, %5%

Bag of marbles b)

Application: Problems involving fraction expressions

A bag contains %r% red marbles and %g% green marbles. How many white marbles do I need to add to the bag to have a %2% in %3% chance of picking a white marble? 

Bag of marbles a)

Application: Problems involving fraction expressions

To play a game, we need a bag containing white and black marbles. For the moment, the bag contains %s% marbles of which %n% are black. We want the probability of picking a white marble to be 25 percent. How many white marbles do we need to add to the bag to adhere to this probability? 

Numbers just in case: %1%, %2%, %3%, %4%, %5%

Marco and Basil b)

Application: Problems involving fraction expressions

Marco and Basil played a problem-solving game and won points. Marco compared his points to Basil’s and said, “Basil won more points. I won only %f%-ninth of his total points.” Basil said, “I won %p% points. How many more points did I win than Marco?”

Find a solution that uses the least amount of information.

Numbers just in case: %1%, %3%, %8%, %9%, %12%

Marco and Basil a)

Application: Problems involving fraction expressions

Marco and Basil played a problem-solving game and won points. Marco compared his points to Basil’s and said, “I won only %f%-ninths of the points that Basil won.” Basil said, “I won %p% points. What fraction of Marco’s points did I win?”

Find a solution that uses the least amount of information.

Numbers just in case: %1%, %3%, %8%, %9%, %10%

Nicolas c)

Application: Mixed problems

Nicolas read a few pages of his book on the first day, and %n% times more pages on the second day. During both days, he read a total of %a% pages. How many fewer pages did Nicolas read on the first day than on the second day? 

Numbers just in case: %1%, %2%, %3%, %4%, %5%

Nicolas b)

Application: Mixed problems

Nicolas read a few pages of his book on the first day, and %n% times more pages on the second day. He read %a% fewer pages on the first day than the second. In total, how many pages did Nicolas read on both days? 

Numbers just in case: %1%, %2%, %3%, %4%, %5%

Nicolas a)

Application: Mixed problems

Nicolas read a few pages of his book on the first day, and %n% times more pages on the second day. He read %a% fewer pages on the first day than the second. How many pages did Nicolas read on the second day? 

Numbers just in case: %1%, %2%, %3%, %4%, %5%

Magic sheep

Application: Mixed problems

%n% magic sheep have %p% legs in total. How many of these sheep will have %4% legs, if the remaining sheep have %5% legs each? 

Bicycle paths c)

Application: Mixed problems

In the park, there are %3% bicycle paths. The green path is %a% km shorter than the red path. The red path is %b% km longer than the blue path. How many kilometers shorter is the green path than the blue path? 

Bicycle paths b)

Application: Mixed problems

In the park, there are %3% bicycle paths. The green path is %a% km shorter than the blue path. The red path is %b% km longer than the blue path. How many kilometers longer is the red path than the green path? 

Bicycle paths a)

Application: Mixed problems

In the park, there are %3% bicycle paths. The green path is %a% km shorter than the blue path. The red path is %b% km longer than the green path. How many kilometers longer is the red path than the blue path? 

Pine trees d)

Application: Mixed problems

In the park, there are %p% trees, some pine trees and some limewood trees. After a hurricane hit, %l% lime trees fell. This meant that there were now %x% times fewer limewood trees than pine trees. How many pine trees were there before the hurricane?

Numbers just in case: %1%, %2%, %3%, %4%, %5%

Pine trees c)

Application: Mixed problems

In the park, there are some pine trees and %t% limewood trees. After a hurricane hit, %l% lime trees fell. This meant that there were now %x% times fewer limewood trees than pine trees. How many pine trees were there before the hurricane?

Pine trees b)

Application: Mixed problems

In the park, there are %p% pine trees and some limewood trees. When a hurricane hit, %l% limewood trees fell. This meant that there are now %x% times fewer limewood trees than pine trees. In total, how many trees (pine and lime wood) were there before the hurricane?

Pine trees a)

Application: Mixed problems

In the park, there are %p% pine trees and some limewood trees. When a hurricane hit, %l% limewood trees fell. This meant that there were now %x% times fewer limewood trees than pine trees in the park. How many limewood trees did the park originally have?

Perimeter

Application: Mixed problems

The perimeter of a rectangle is %p% cm. One of the rectangle’s sides is %4% times smaller than the other. What is the area of the rectangle? 

The numbers just in case: %1%, %2%, %3%, %5%

Walking paths b)

Application: Mixed problems

In the forest, the green walking path is %c% times shorter than the orange walking path. The orange walking path is %d% times longer than the blue walking path. How many times longer is the blue walking path than the green walking path?

Walking paths a)

Application: Mixed problems

In the forest, the green walking path is %c% times shorter than the blue walking path. The orange walking path is %d% times longer than the blue walking path. How many times smaller is the green walking path than the orange walking path? 

Honey pot c)

Application: Mixed problems

Winnie the Pooh had a pot of honey. He ate %a% grams of honey, which was half of the honey in the pot. How much did the full pot of honey weigh, if the pot weighed %b% g?

The numbers just in case: %1%, %2%, %3%, %4%, %5%

Honey pot b)

Application: Mixed problems

Winnie the Pooh had a pot of honey. He ate %a% grams of honey, which was half of the honey in the pot. Now, the pot weighs %b% grams. How much did the full pot of honey weigh?

The numbers just in case: %1%, %2%, %3%, %4%, %5%

Honey pot a)

Application: Mixed problems

A pot of honey weighed %a% grams. When half of the honey was eaten, the pot weighed %b% grams. How heavy is the pot when all the honey has been eaten? 

The numbers just in case: %1%, %2%, %3%, %4%, %5%

Honey c)

Application: Mixed problems

A pot of honey weighs %a% grams. When a third of the honey is eaten, the pot weighs %b% grams. How heavy is the empty pot?

The numbers just in case: %1%, %2%, %3%, %4%, %5%

Honey b)

Application: Mixed problems

A pot of honey weighs %a% grams. When half of the honey is eaten, the pot weighs %b% grams. How many grams of honey did the pot originally have?

The numbers just in case: %1%, %2%, %3%, %4%, %5% 

Honey a)

Application: Mixed problems

A pot of honey weighs %a% grams. When half of the honey is eaten, the pot weighs %b% grams. How heavy is the empty pot? 

The numbers just in case: %1%, %2%, %3%, %4%, %5%

Reservoir b)

Application: Mixed problems

A large reservoir contained %r% L of water. A smaller reservoir contained %s% fewer liters of water than the larger reservoir. How many liters of water did the smaller reservoir contain? 

Reservoir a)

Application: Mixed problems

A large reservoir contained %r% L of water. A smaller reservoir contained %s% times less water than the larger reservoir. How many liters of water did the smaller reservoir contain? 

Road trip b)

Application: Mixed problems

A tour bus traveled %t% km to go to Trois-Rivières. This distance is %o% km less than the bus traveled to Ottawa. How many kilometers did the bus travel to go to Ottawa?

Road trip a)

Application: Mixed problems

A tour bus traveled %t% km to go to Trois-Rivières. It traveled %o% times further to go to Ottawa. How many kilometers did it travel to go to Ottawa? 

Anouk’s butterflies c)

Application: Mixed problems

Anouk has a butterfly collection that she puts in %r% red boxes and %y% yellow boxes. She has %s% species of butterflies and in total, she has %b% butterflies. In total, how many boxes did she use to hold her collection? 

Anouk’s butterflies b)

Application: Mixed problems

Anouk has a butterfly collection that she puts in %r% red boxes and %y% yellow boxes. She has %s% species of butterflies and in total, she has %b% butterflies. How many butterflies does she have of each species?

Anouk’s butterflies a)

Application: Mixed problems

Anouk has a butterfly collection that she puts in %r% red boxes and %y% yellow boxes. She has %s% species of butterflies and %b% butterflies of each species. In total, how many butterflies does she have? 

Lion and mouse b)

Application: Mixed problems

A lion is %l% m tall. A mouse is %m% times smaller than a lion. How tall is the mouse? 

Lion and mouse a)

Application: Mixed problems

A lion is %l% cm tall. A mouse is %m% cm smaller than a lion. How tall is the mouse? 

The bottles b)

Application: Mixed problems

Justin filled %j% bottles of water and his brother filled %b% bottles of water. How many times more bottles did Justin fill than his brother? 

The bottles a)

Application: Mixed problems

Justin filled %j% bottles of water and his brother filled %b% bottles of water. How many more bottles did Justin fill than his brother?

My uncle’s garden

Application: Mixed problems

My grandfather’s garden is %g% square meters. My uncle’s garden is %u%  square meters bigger than my grandfather’s garden. How big is my uncle’s garden? 

My uncle’s garden

Application: Mixed problems

My grandfather’s garden is %g% square meters. My uncle’s garden is %u% times bigger than my grandfather’s garden. How big is my uncle’s garden? 

Harvest season c)

Application: Mixed problems

During the harvest season, the farm, Dagenais and Sons, harvested %w% kg of wheat. The farm harvested %c% more kilograms of corn than wheat. How many kilograms of corn did they harvest? 

Harvest season b)

Application: Mixed problems

During the harvest season, the farm, Dagenais and Sons, harvested %w% kg of wheat. The farm harvested %c% times more wheat than corn. How many kilograms of corn did the farm harvest? 

Harvest season a)

Application: Mixed problems

During the harvest season, the farm, Dagenais and Sons, harvested %w% kg of wheat. The farm harvested %c% times more corn than wheat. How many kilograms of corn did the farm harvest? 

Study time b)

Application: Mixed problems

In one month, Theodore studied for %t% hours. He studied %b% times more hours than Benoit. How many hours did Benoit spend studying?

Study time a)

Application: Mixed problems

In one month, Theodore studied for %t% hours. He studied %b% hours less than Benoit. How many hours did Benoit spend studying?

Squirrel b)

Application: Mixed problems

A squirrel collected some mushrooms and %m% more hazelnuts than mushrooms for the winter. He collected %h% hazelnuts in total. How many mushrooms did the squirrel collect? 

Squirrel a)

Application: Mixed problems

A squirrel collected some mushrooms and %t% times fewer hazelnuts than mushrooms for the winter. He collected %h% hazelnuts in total. How many mushrooms did the squirrel collect? 

Car b)

Application: Mixed problems

A car weighs %c% kg. A plane weighs %p% times more than a car. How much does a plane weigh? 

Car a)

Application: Mixed problems

A car weighs %c% kg. A small tractor weighs %t% kg more than a car. How much does a small tractor weigh?

Winners (d)

Application: Problems involving multiplicative relationships

Last year, %s% students from Winners School participated in competitions and their school won %m% medals. This year, %y% students participated in the competitions and they won %t% times more medals than last year. How many more students competed this year than last year?

Winners (c)

Application: Problems involving multiplicative relationships

This year, %s% students from Winners School participated in the competitions and collected %m% medals in the mathematics category. This year, they won %t% times more medals than was won last year from the %y% participants. How many medals did they win last year? 

Winners (b)

Application: Problems involving multiplicative relationships

Last year, %s% students from Winners School participated in competitions and their school won %m% medals. This year, %y% students from Winners School participated in the same competitions and they won %w% medals. How many times more medals did the school win this year than last year? 

Winners (a)

Application: Problems involving multiplicative relationships

Last year, %s% students from the Winners school participated in competitions and their school won %m% medals. This year, %y% students participated in the same competitions and they won %t% times more medals than last year. How many medals did the school win this year?

Dining Room (c)

Application: Problems involving multiplicative relationships

In a dining room that can accommodate %p% people, %t% tables are occupied and %f% tables are free. How many times fewer tables are free than the number of occupied tables? 

Dining Room (a)

Application: Problems involving multiplicative relationships

In a dining room that can accommodate %v% visitors, %t% tables are occupied, and twice as many tables are empty. In total, how many tables are in the dining room? 

The numbers just in case: %1%, %2%, %3%, %4%, %5%

Apples (d)

Application: Problems involving multiplicative relationships

A group of %c% children went apple picking. Each child collected %b% identical baskets of apples. Each basket contained %k% kilograms of apples. How many kilograms of apples did each child collect? 

Apples (c)

Application: Problems involving multiplicative relationships

Some children went apple picking. Together, they collected %b% baskets of apples with each of them collecting %e% baskets. Each basket contained %k% kilograms of apples. How many children were there? 

Apples (b)

Application: Problems involving multiplicative relationships

A group of %c% children went apple picking. Together, they collected %b% baskets of apples and each of them collected the same number of baskets. Each basket contained %k% kilograms of apples. How many baskets of apples did each child collect? 

Apples (a)

Application: Problems involving multiplicative relationships

A group of %c% children went apple picking. Each of the children collected %b% identical baskets of apples. Each basket contained %k% kilograms of apples. How many baskets of apples did they collect altogether? 

Hazelnuts (d)

Application: Problems involving multiplicative relationships

Dorothy is in 3rd grade and she is in the class choir. She gave %h% hazelnuts to each of the other %f% members of the choir. How many friends does Dorothy have in the choir group? 

Hazelnuts (c)

Application: Problems involving multiplicative relationships

Dorothy is in 3rd grade and she is in the class choir. One day, she brought %h% hazelnuts to school and shared them equally among her %f% friends in the choir. How many hazelnuts did each of her friends receive? 

Hazelnuts (b)

Application: Problems involving multiplicative relationships

Dorothy is in 3rd grade and she is in the class choir. One day she brought %h% hazelnuts to school and gave %f% hazelnuts to each of her friends in the choir. By the end of choir class, she had no hazelnuts left. How many friends does she have in her choir? 

Hazelnuts (a)

Application: Problems involving multiplicative relationships

Dorothy is in 3rd grade and she is in the class choir. She gave %h% hazelnuts to each of her %f% friends in the choir. In total, how many hazelnuts did she share with her friends? 

Measuring the water level (c)

Application: Problems involving multiplicative relationships

When he measured the river’s water level, Paul saw that it was at %p% cm. The normal level for this river is at %w% cm. How many times higher was the water level today than its normal height? 

Measuring the water level (b)

Application: Problems involving multiplicative relationships

When he measured the water level of the river, Paul saw that it was %p% times higher than the normal level. The normal level for this river is %w% cm. How high was the river when Paul measured it?

Measuring the water level (a)

Application: Problems involving multiplicative relationships

When he measured the water level of the river, Jacob saw that it was at %j% cm. This is %w% times less than the normal water level. How high is the normal water level? 

Water Lilies (c)

Application: Problems involving multiplicative relationships

On a lake, the number of water lilies doubles every day. Today I counted %l% water lilies. How many water lilies have appeared since yesterday? 

The numbers just in case: %1%, %2%, %3%, %4%, %5%

Water Lilies (b)

Application: Problems involving multiplicative relationships

On a lake, the number of water lilies doubles every day. Today I counted %l% water lilies. How many water lilies were there yesterday? 

The numbers just in case: %1%, %2%, %3%, %4%, %5% 

Water Lilies (a)

Application: Problems involving multiplicative relationships

On a lake, the number of water lilies doubles every day. Today I counted %l% water lilies. How many will there be tomorrow? 

The numbers just in case: %1%, %2%, %3%, %4%, %5%

Books (d)

Application: Problems involving multiplicative relationships

Amélie counted the books in her library. She found that she has %a% books in total. Her friend, Gilbert, who is %g% years old, also counted his books. Amélie has %b% times more books than Gilbert. How old is Gilbert? 

Books (c)

Application: Problems involving multiplicative relationships

Amélie counted the books in her library. She found that she has %a% books in total. Her friend, Gilbert, who is %g% years old, also counted his books. He found he has %b% books in total. How many times more books does Gilbert have than Amélie? 

Books (b)

Application: Problems involving multiplicative relationships

Amélie counted the books in her library. She found that she has %a% books in total. She knows that this is %b% times more than the number of books in Gilbert’s library. Gilbert is %g% years old. How many books does Gilbert have?

Books (a)

Application: Problems involving multiplicative relationships

Amélie counted the books in her library. She found that she has %a% books in total. She knows that this is %b% times less than the number of books in Gilbert’s library. Gilbert is %g% years old. How many books does Gilbert have? 

Reading (e)

Application: Problems involving multiplicative relationships

Oliver read %p% pages of his new book and he counted %d% drawings on these pages. The book contains %b% times more pages than those he already read. If these drawings are the only ones in the book, how many drawings are there in total? 

Reading (d)

Application: Problems involving multiplicative relationships

Oliver read %p% pages of his new book and he counted %d% drawings on these pages. The book contains %b% pages. How many times more pages are there in the entire book than the number of pages Oliver read on the first day? 

Reading (c)

Application: Problems involving multiplicative relationships

Oliver found that his new book contains %p% pages, which is %f% times more than what he read on the first day. He also counted the number of drawings. There are %d% drawings in all. How many pages did Oliver read on the first day? 

Reading (b)

Application: Problems involving multiplicative relationships

Oliver counted %d% drawings in the first %b% pages of the book he was reading. The number of pages he read is %p% times less than the total number of pages in the book. How many pages does the book contain? 

Reading (a)

Application: Problems involving multiplicative relationships

Oliver read %b% pages of his new book and he counted %d% drawings on these pages. The book contains a total of %p% times more pages than the number of pages he has already read. How many pages does the book contain in total? 

Library Book (d)

Application: Problems involving multiplicative relationships

Gregory borrowed a book from the library for %l% days. He decides that he will read %d% pages each day. The book contains %p% pages. For how many days did he borrow the book? 

Library Book (c)

Application: Problems involving multiplicative relationships

Gregory borrowed a book from the library for %l% days. He decides that he will read the same number of pages every day. The book is %p% pages and he wants to finish it in %d% days. How many pages should he read each day? 

Library Book (b)

Application: Problems involving multiplicative relationships

Gregory borrowed a book from the library for %l% days. He decides that he will read %d% pages each day. If the book is %p% pages, how many days will it take him to finish the book? 

Library Book (a)

Application: Problems involving multiplicative relationships

Gregory borrowed a book from the library for %l% days. He decides that he will read %p% pages each day. This way he will be able to finish the book in %d% days. How many pages does the book contain? 

Notebooks (d)

Application: Problems involving multiplicative relationships

At the end of the school year, a teacher brought %n% notebooks to give to his students. Each of the notebooks contains %p% pages. The teacher gave %s% notebooks to each of his students and there were none left. In total, how many notebook pages did each student receive?

Notebooks (c)

Application: Problems involving multiplicative relationships

At the end of the school year, a teacher brought %n% notebooks to give to his students. The teacher wanted to share them equally among his %s% students. Each of the notebooks contains %p% pages. How many notebooks did each student receive? 

Notebooks (b)

Application: Problems involving multiplicative relationships

At the end of the school year, a teacher brought %n% notebooks to give to his students. He gave %s% notebooks to each of his students and there were none left. Each of the notebooks contains %p% pages. How many students were there in his class? 

Notebooks (a)

Application: Problems involving multiplicative relationships

At the end of the school year, a teacher brought notebooks to give to his students. He gave %n% notebooks to each of his %s% students and there were none left. Each of the notebooks contains %p% pages. How many notebooks did he bring to school? 

Irene (c)

Application: Problems involving multiplicative relationships

Jacob bought %j% identical boxes of coloured pencils for $ %d% and he now has %c% pencils. He has twice as many pencils as Irene. How many pencils does Irene have? 

The numbers just in case: %1%, %2%, %3%, %4%, %5%