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A FREE RESOURCE PACK FROM EDUCATIONCITY

Practical Problem Solving

Free school resources by EducationCity®. This may be reproduced for class use.

Age 7-11

Mathematics School Worksheets Suitability

Practical Problem Solving WorksheetsWhat Does This Pack Include? This pack has been created by teachers, for teachers. In it, you’ll find high quality Activity Sheets, along with their answer sheets to support your students to develop their problem solving skills.

To go directly to the content, simply click on the title in the index below:

CONE WITH THE WIND

Learning Objective:Addition, Subtraction, Multiplication and DivisionSolve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why.

• Activity Sheet• Activity Sheet with Answers

INTO THE UNKNOWN

Learning Objective:AlgebraFind pairs of unknowns that satisfy an equation with two unknowns.


COMBINED HARVESTERS

Learning Objective:AlgebraExpress missing number problems algebraically.


RATIO RATIONS

Learning Objective:Ratio and ProportionSolve problems involving the relative sizes of two quantities where missing values can be found by using integer multiplication and division facts.


BUMPER CARS

Learning Objective:AlgebraUse simple formulae.


MOON MISSION

Learning Objective:MeasurementSolve problems involving the calculation and conversion of units of measure, using decimal notation to three decimal places where appropriate.


JUICE BAR



STRICTLY TALENTED

Learning Objective:Fractions (including decimals and percentages)Recall and use equivalences between simple fractions, decimals and percentages, including in different contexts.


FLUFFY CLOUDS

Learning Objective:Ratio and ProportionSolve problems involving the relative sizes of two quantities where missing values can be found by using integer multiplication and division facts.


Other Resources Linking to the Theme

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Learn Screens:Introduce or Reinforce a New Concept

Activities:Educational Content

ThinkIts:Inspire Creative Ways of Thinking

Cone with the Wind Content ID: 34320 Juice Bar Content ID: 14765 Ratios and Rates Content ID: 14100

Identify the addition or subtraction calculations required to solve the problem and then complete the calculations to find the answer in this interactive Activity.

Explore and practise solving word problems that have unknown values in them with your students using our step-by-step tutorial.

Get your students using ratios to solve word problems successfully.

HOT SEAT

Learning Objective:Number - Multiplication and DivisionSolve problems involving multiplying and adding, including using the distributive law to multiply two digit numbers by one digit, integer scaling problems and harder correspondence problems such as n objects are connected to m objects.


CHEQUERED FLAG

Learning Objective:Ratio and ProportionSolve problems involving unequal sharing and grouping using knowledge of fractions and multiples.


EXPRESSIONS AND EQUATIONS


• ThinkIt Question• ThinkIt Answer

DIVIDING APPLES


• ThinkIt Question• ThinkIt Answer

UNIT CONVERSIONS

Learning Objective:MeasurementUse, read, write and convert between standard units, converting measurements of length, mass, volume and time from a smaller unit of measure to a larger unit, and vice versa, using decimal notation to three decimal places.


Cone with the Wind

Read and complete the question. Use the space provided to show any working out.

Granny travelled a total of 167.34km in three days. She travelled a distance of 56,870m on day one and 12,650m on day two. How many kilometers did she travel on day three?

Sten has spent a total of £467.36 on supplies for the ice cream van. He spent £125.87 on drinks and £97.57 on toppings.How much did he spend on ice lollies?

The fuel tank capacity is 59.38l. Sten uses 24.26l on the first journey and 13,760ml on the second journey. How much fuel is remaining after both journeys? Write your answer in litres.

Sten orders 437.56g of bubble gum. Customers use 243.21g but Granny delivers another 0.2758kg of extra stock. How much bubble gum does Sten have in grams?

Stig buys a tub of ice cream. The tub costs 45p. Vanilla ice cream costs £1.36 per scoop, Sten has 2 scoops. Strawberry ice cream costs £1.89 per scoop, Sten has 1 scoop.How much change does he get from a £10 note?

The ice cream van needs a new machine. It costs £3,624.47. Sten has £342.12 and Granny has £1,523.61. How much more money do they need to buy the machine?

Cone with the Wind

Read and complete the question. Use the space provided to show any working out.

Granny travelled a total of 167.34km in three days. She travelled a distance of 56,870m on day one and 12,650m on day two. How many kilometers did she travel on day three?

Sten has spent a total of £467.36 on supplies for the ice cream van. He spent £125.87 on drinks and £97.57 on toppings.How much did he spend on ice lollies?

The fuel tank capacity is 59.38l. Sten uses 24.26l on the first journey and 13,760ml on the second journey. How much fuel is remaining after both journeys? Write your answer in litres.

Sten orders 437.56g of bubble gum. Customers use 243.21g but Granny delivers another 0.2758kg of extra stock. How much bubble gum does Sten have in grams?

Stig buys a tub of ice cream. The tub costs 45p. Vanilla ice cream costs £1.36 per scoop, Sten has 2 scoops. Strawberry ice cream costs £1.89 per scoop, Sten has 1 scoop.How much change does he get from a £10 note?

The ice cream van needs a new machine. It costs £3,624.47. Sten has £342.12 and Granny has £1,523.61. How much more money do they need to buy the machine?

£243.92

97.82km

21.36l

470.15g

£1,758.74

£4.94

Into the Unknown

If A and B are whole numbers, find suitable values that make each equation true.

A + B = 130

A = B =

A – B = 250

A = B =

2A + B = 60

A = B =

2A + 2B = 500

A = B =

3A + B = 250

A = B =

A ÷ B = 15

A = B =

2A ÷ B = 4

A = B =

3A x B = 105

A = B =

2A x B = 72

A = B =

3A x 2B = 108

A = B =

A + B = 240

A = B =

B – A = 170

A = B =

A – B = 65

A = B =

A x B = 128

A = B =

2A x B = 98

A = B =

A + B = 540

A = B =

A + B = 102

A = B =

2A – B = 90

A = B =

A ÷ B = 2

A = B =

2A ÷ B = 4

A = B =

Where A is twice B Where B is twice A

Where A is twice B Where A is half of B

Where A is the same as B Where A is 150 more than B

Where B is 22 less than A Where B is half of A

Where A is twice B Where B is half of A

Into the Unknown

Use algebraic thinking to help you find the missing values.

In the shop there are 900 cakes. If there are twice as many chocolatecakes as vanilla cakes, how many chocolate cakes are there?

Chocolate cakes =

Klara and Manu each have a bag of seashells. If they have 40seashells altogether, and Manu has 6 seashells less than Klara,how many seashells do they each have?

Klara =

Stig and Sten have some pocket money to spend. Altogether, theyhave £12.40. If Sten has £3.20 less than Stig, how much do theyeach have?

Manu =

Stig =

Sten =

seashells

seashells

Into the Unknown

Granny is paying for theatre tickets. She buys one adult ticket andfour child tickets. If the total cost of the theatre trip is £480, and thecost of each child ticket is half that of an adult ticket, how muchdoes each type of ticket cost?

The farmer is adding some new fencing, some of which is electric,and some is post and rail. Altogether the fencing is 1200cm long.If the length of the electric fencing is 340cm shorter than the postand rail fencing, how long is each type of the fencing?

Adult =

Child =

Electric fencing =

Post and rail fencing =

Into the Unknown

If A and B are whole numbers, find suitable values that make each equation true.

A + B = 130

A = B =

A – B = 250

A = B =

2A + B = 60

A = B =

2A + 2B = 500

A = B =

3A + B = 250

A = B =

A ÷ B = 15

A = B =

2A ÷ B = 4

A = B =

3A x B = 105

A = B =

2A x B = 72

A = B =

3A x 2B = 108

A = B =

A + B = 240

A = B =

B – A = 170

A = B =

A – B = 65

A = B =

A x B = 128

A = B =

2A x B = 98

A = B =

A + B = 540

A = B =

A + B = 102

A = B =

2A – B = 90

A = B =

A ÷ B = 2

A = B =

2A ÷ B = 4

A = B =

Where A is twice B Where B is twice A

Where A is twice B Where A is half of B

Where A is the same as B Where A is 150 more than B

Where B is 22 less than A Where B is half of A

Where A is twice B Where B is half of A

answers will vary

Into the Unknown

Use algebraic thinking to help you find the missing values.

In the shop there are 900 cakes. If there are twice as many chocolatecakes as vanilla cakes, how many chocolate cakes are there?

Chocolate cakes =

Klara and Manu each have a bag of seashells. If they have 40seashells altogether, and Manu has 6 seashells less than Klara,how many seashells do they each have?

Klara =

Stig and Sten have some pocket money to spend. Altogether, theyhave £12.40. If Sten has £3.20 less than Stig, how much do theyeach have?

Manu =

Stig =

Sten =

seashells

seashells

600

2317

£7.80£4.80

Into the Unknown

Granny is paying for theatre tickets. She buys one adult ticket andfour child tickets. If the total cost of the theatre trip is £480, and thecost of each child ticket is half that of an adult ticket, how muchdoes each type of ticket cost?

The farmer is adding some new fencing, some of which is electric,and some is post and rail. Altogether the fencing is 1200cm long.If the length of the electric fencing is 340cm shorter than the postand rail fencing, how long is each type of the fencing?

Adult =

Child =

Electric fencing =

Post and rail fencing =

£160£80

430cm770cm

Combined Harvesters

Read the word problems, and select the equation that could be used to solve them.

Sten divided some apples evenly into 7 boxes. He put 4 apples in each box.How many apples did Sten have altogether?

Sten, Manu, and Klara each had 12 pencils. Which equation could be usedto find how many pencils they had altogether?

Sten picked 31 peaches. Stig ate some of them. They had 15 peaches left.Which equation could be used to find how many peaches Stig ate?

Manu picked some oranges. Sten picked 9 more. They had 34 oranges altogether. Which equation could be used to find how many oranges Manu picked?

In a week, Sten washed 28 cars, the following week he washed 20 more. Which equation could be used to find how many cars Sten had washed altogether?

34 + 9 = P

P + 9 = 34

9P = 34

34 ÷ P = 9

28 - 20 = A

28 ÷ 20 = A

28 + 20 = A

20 – 28 = A

31 + P = 15

P – 15 = 31

15P = 31

31 – P = 15

12 + 12 + 12 = A

12 – A = 12

4A = 12

12 + 12 = A

7 + 4 = A

7 ÷ 4 = A

7 – 4 = A

7 x 4 = A

Combined Harvesters


£4.25 ÷ W = £42.5

Sten bought 3 books for £2.40 and 1 magazine. They cost £3.90 altogether. Which equation could be used to find how much a book cost?

Sten bought 5 footballs at a total cost of £35. Which equation could be usedto find how much each football cost?

Sten sold 20 mugs at the gift stall and made £30 in total. Which equationcould be used to find how much Sten sold each mug for?

Sten sold £4.25 worth of fruit each week. Which equation could be usedto find out how long it would take Sten to make £42.50 in total?

Sten bought a pineapple for £1.55 and 2 coconuts. It cost £4.15 altogether. Which equation could be used to find how much one coconut cost?

£4.25 + W = £42.50

£4.25W = £42.50

£4.250 – W = £42.50

£1.55 = £4.15 ÷ 2C

£1.55 + 2C = £4.15

2C - £1.55 = £4.15

£4.15 + 2C = £1.55

20A = £30

£30 + A = 20

£30 – 20 = A

A ÷ £30 = 20

5P = £35

£35 – 5 = P

£35P = 5

P = £35 x 5

£2.40P = £3.90

£2.40 + £3.90 = P

£3.90 x £ 2.40 = P

£2.40 + P = £3.90

Combined Harvesters


Sten divided some apples evenly into 7 boxes. He put 4 apples in each box.How many apples did Sten have altogether?

Sten, Manu, and Klara each had 12 pencils. Which equation could be usedto find how many pencils they had altogether?

Sten picked 31 peaches. Stig ate some of them. They had 15 peaches left.Which equation could be used to find how many peaches Stig ate?

Manu picked some oranges. Sten picked 9 more. They had 34 oranges altogether. Which equation could be used to find how many oranges Manu picked?

In a week, Sten washed 28 cars, the following week he washed 20 more. Which equation could be used to find how many cars Sten had washed altogether?

34 + 9 = P

P + 9 = 34

9P = 34

34 ÷ P = 9

28 - 20 = A

28 ÷ 20 = A

28 + 20 = A

20 – 28 = A

31 + P = 15

P – 15 = 31

15P = 31

31 – P = 15

12 + 12 + 12 = A

12 – A = 12

4A = 12

12 + 12 = A

7 + 4 = A

7 ÷ 4 = A

7 – 4 = A

7 x 4 = A

28 + 20 = A

P + 9 = 34

31 – P = 15

12 + 12 + 12 = A

7 x 4 = A

Combined Harvesters


£4.25 ÷ W = £42.5

Sten bought 3 books for £2.40 and 1 magazine. They cost £3.90 altogether. Which equation could be used to find how much a book cost?

Sten bought 5 footballs at a total cost of £35. Which equation could be usedto find how much each football cost?

Sten sold 20 mugs at the gift stall and made £30 in total. Which equationcould be used to find how much Sten sold each mug for?

Sten sold £4.25 worth of fruit each week. Which equation could be usedto find out how long it would take Sten to make £42.50 in total?

Sten bought a pineapple for £1.55 and 2 coconuts. It cost £4.15 altogether. Which equation could be used to find how much one coconut cost?

£4.25 + W = £42.50

£4.25W = £42.50

£4.250 – W = £42.50

£1.55 = £4.15 ÷ 2C

£1.55 + 2C = £4.15

2C - £1.55 = £4.15

£4.15 + 2C = £1.55

20A = £30

£30 + A = 20

£30 – 20 = A

A ÷ £30 = 20

5P = £35

£35 – 5 = P

£35P = 5

P = £35 x 5

£2.40P = £3.90

£2.40 + £3.90 = P

£3.90 x £ 2.40 = P

£2.40 + P = £3.90

£1.55 + 2C = £4.15

£4.25W = £42.50

20A = £30

5P = £35

£2.40 + P = £3.90

Ratio Rations

Answer the following ratio questions.


If 12 bananas cost £2.76, how much will 36 bananas cost?

If a bag of flour weighs 1.5kg, how much will 6 bags weigh?

If 4 litres of milk costs £3.80, how much will 12 litres cost?

If 5 jars of honey cost £8.75, how much will 20 jars cost?

If a bag of onions weighs 530g, how much will 3 bags weighin grams?

If a bottle contains 750ml of fruit juice, how much fruit juiceis in 4 bottles? (Give your answer in millilitres)

Klara has 27 sheets of lined paper, to 9 sheets of plain paper, in abox of 180 sheets of paper. How many sheets of plain paper doesshe have?

There are 2 lemon cupcakes, to every 4 chocolate cupcakes, in a boxof 54 cupcakes. How many chocolate cupcakes are there in the box?

There are 6 iced doughnuts, to every ring doughnut, in a box of 35doughnuts. How many ring doughnuts are there in the box?

Manu has a bag containing 72 grapes. The grapes are shared 7red, for every 5 green. How many green grapes are in the bag?

Klara needs 24 beads to fill 3 bags. How many beads would sheneed to fill 6 bags?

Klara shares out 12 playing cards. She gives Manu 1 card for every 3 cards she takes. How many playing cards does Klara get?

Ratio Rations



If 12 bananas cost £2.76, how much will 36 bananas cost?

If a bag of flour weighs 1.5kg, how much will 6 bags weigh?

If 4 litres of milk costs £3.80, how much will 12 litres cost?

If 5 jars of honey cost £8.75, how much will 20 jars cost?

If a bag of onions weighs 530g, how much will 3 bags weighin grams?

If a bottle contains 750ml of fruit juice, how much fruit juiceis in 4 bottles? (Give your answer in millilitres)

Klara has 27 sheets of lined paper, to 9 sheets of plain paper, in abox of 180 sheets of paper. How many sheets of plain paper doesshe have?

There are 2 lemon cupcakes, to every 4 chocolate cupcakes, in a boxof 54 cupcakes. How many chocolate cupcakes are there in the box?

There are 6 iced doughnuts, to every ring doughnut, in a box of 35doughnuts. How many ring doughnuts are there in the box?

Manu has a bag containing 72 grapes. The grapes are shared 7red, for every 5 green. How many green grapes are in the bag?

Klara needs 24 beads to fill 3 bags. How many beads would sheneed to fill 6 bags?

Klara shares out 12 playing cards. She gives Manu 1 card for every 3 cards she takes. How many playing cards does Klara get?

£8.28

3,000ml

1,590g

9kg

£11.40

£35

45

36

5

30

48

9

Bumper Cars

Moon Mission

Juice Bar

d solution.

Strictly Talented

Fluffy Clouds

Hot Seat

Chequered Flag

Answer the unequal sharing and grouping questions below.

Tickets for race day cost £40 for adults and £10 for children. On Saturday, the organisers sold £500 worth of tickets.

of the money made came from adult tickets, how many children’stickets were sold?If 2

5

In one year, Sten and Stig have won 81 races altogether.

If Sten has won49 of those races, how many races have they each won?

The length of the race track is 3km. Sten’s car breaks down after he has

How much further did Sten need to travel to complete a lap in km?

512 of the track. driven around

Sten’s car is 40cm longer than Stig’s car and Stig’s car is 40cm longer than Klara’s car. If the length of all the cars together is 7.2m metres, how long are each of the cars in metres?

There are 24 cars with Sten’s car, lined up for the race.If there are five times as many cars in front of Sten’s car as there are behind his car, how many cars are in front of Sten’s car?

38

are in Stig’s team. of the cars are in Sten’s team andThere are 3 different teams taking part in the race.

how many cars are in Klara’s team?If there are 24 cars in the race altogether,

14

125of the lights in metres?

If the lights are evenly spaced with the distance between them measuring Lights are situated around the side of the race track which is 6km long.

of the length of the race track, what is the distance between each

There are 24 trophies to be won over a one year period. Only Stig, Sten and Klara have ever won trophies. If Klara won twice as many as Sten and Stig won three times as many as Sten, how many trophies did they each win?

Chequered Flag

Answer the unequal sharing and grouping questions below.

Tickets for race day cost £40 for adults and £10 for children. On Saturday, the organisers sold £500 worth of tickets.

of the money made came from adult tickets, how many children’stickets were sold?If 2

5

In one year, Sten and Stig have won 81 races altogether.

If Sten has won49 of those races, how many races have they each won?

The length of the race track is 3km. Sten’s car breaks down after he has

How much further did Sten need to travel to complete a lap in km?

512 of the track. driven around

Sten’s car is 40cm longer than Stig’s car and Stig’s car is 40cm longer than Klara’s car. If the length of all the cars together is 7.2m metres, how long are each of the cars in metres?

There are 24 cars with Sten’s car, lined up for the race.If there are five times as many cars in front of Sten’s car as there are behind his car, how many cars are in front of Sten’s car?

38

are in Stig’s team. of the cars are in Sten’s team andThere are 3 different teams taking part in the race.

how many cars are in Klara’s team?If there are 24 cars in the race altogether,

14

125of the lights in metres?

If the lights are evenly spaced with the distance between them measuring Lights are situated around the side of the race track which is 6km long.

of the length of the race track, what is the distance between each

There are 24 trophies to be won over a one year period. Only Stig, Sten and Klara have ever won trophies. If Klara won twice as many as Sten and Stig won three times as many as Sten, how many trophies did they each win?

30

Sten = 36 Stig = 45

1.75 km

Stig = 2.4m, Sten = 2.8m, Klara = 2m

20

9

240m

Stig = 12, Sten = 4, Klara = 8

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A FREE RESOURCE PACK FROM EDUCATIONCITY Practical … · A FREE RESOURCE PACK FROM EDUCATIONCITY...

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