# Understand and Apply Problem Solving Skills 3

In this worksheet, students will be asked to solve a range of worded problems, using all four operations. These types of problems appear in the two reasoning papers and the pupil is expected to have efficient written methods to support each method required.

Key stage:  KS 2

Curriculum topic:   Exam-style Questions: SATs Maths

Curriculum subtopic:   Exam-Style Questions: Worded Problems

Difficulty level:

### QUESTION 1 of 10

You are going to spend some valuable time revising worded problems.

Worded problems will appear in both of the SATs reasoning papers.

The problems will ask you to use all four number operations (addition, subtraction, division and multiplication).

It's very important that you show your working out for these questions because you may get a mark for it, even if your answer is wrong!

For each of the reasoning tests, you will have 40 minutes to complete it.

There are usually around 20 problem-solving questions in the reasoning tests.

Here is an example of the type of question you may find in a reasoning paper:

Sam buys 7 apples at a cost of 33p each and 8 bananas at a cost of 19p each.

What is the total cost of the fruit purchased?

Step 1: Find the total cost of apples: 7 x 33p = £2.31

Step 2: Find the total cost of bananas: 8 x 19p = £1.52

Step 3: Add the two amounts together = £2.31 + £1.52 = £3.83

With a question like this one, make sure you show your working out and carefully check each step.

Over to you now!

Hamzah scores 60/120 in a test.

Karen scores 40% in the same test.

Who has the higher score?

Hamzah

Karen

Three children swim a race.

Lucy finishes in 15 seconds.

Jack finishes 5 seconds before Lucy.

Bilal finishes 3 seconds after Jack.

How many seconds does it Bilal to finish the race?

Hamzah

Karen

Katie buys a remote-controlled car that costs £7.85.

She also buys 2 batteries to power it.

In total, she spends £9.05.

How much does 1 battery cost?

Hamzah

Karen

A bag of birdseed is £1.35.

How many bags of birdseed can be bought for £10?

A bag of birdseed is £1.35.

How many bags of birdseed can be bought for £20?

There are 80 g of pasta in one portion.

How many portions are there in a 4 kg bag of pasta?

2534 people pay to enter a funfair.

Each person pays £2.40.

What is the total amount of entry money collected?

The distance from Edinburgh to London is 534 km.

5 miles is approximately 8 kilometres.

Use these facts to calculate the approximate distance in miles from Edinburgh to London.

Pancake recipe for 4 people:

- 100 g plain flour

- 2 large eggs

- 300 ml milk

- 1 tbsp of vegetable oil

- lemon wedges to serve (optional)

- caster sugar to serve (optional)

Jodie uses this recipe but needs to make pancakes for 8 people.

How much milk will she need?

450,000 people visited Spain on holiday in one year.

15% visited in April.

45% visited in August.

How many people visited Spain for the rest of the year?

180,000

185,000

160,000

175,000

• Question 1

Hamzah scores 60/120 in a test.

Karen scores 40% in the same test.

Who has the higher score?

Hamzah
EDDIE SAYS
Strong start if you chose Hamzah. Hamzah scored 60/120, which is equivalent to 50%. So, he scored 10% more in the test than Karen who scored 40%. You may be asked to explain how you know the answer, make sure you use numbers and working out to prove it.
• Question 2

Three children swim a race.

Lucy finishes in 15 seconds.

Jack finishes 5 seconds before Lucy.

Bilal finishes 3 seconds after Jack.

How many seconds does it Bilal to finish the race?

EDDIE SAYS
How did you do? You had to read the information carefully to solve this one. Jack finishes 5 seconds before Lucy, so 15- 5 = 10 seconds. Bilal finishes 3 seconds after Jack, so 10 + 3 = 13 seconds. Bilal takes 13 seconds to swim the race.
• Question 3

Katie buys a remote-controlled car that costs £7.85.

She also buys 2 batteries to power it.

In total, she spends £9.05.

How much does 1 battery cost?

EDDIE SAYS
Did you get the hang of it? Step 1: Subtract the cost of the car from the total paid £9.05 - £7.85 = £1.20. Step 2: Divide the answer by 2 to find the cost of 1 battery £1.20 ÷ 2= 60p.
• Question 4

A bag of birdseed is £1.35.

How many bags of birdseed can be bought for £10?

7
EDDIE SAYS
The answer is 7. Take your time with a question like this to work through the options. You may wish to start simply by multiplying the cost by 2 and working up until you find the amount closest to £10. 2 x £1.35 = £2.70 4 x £1.35 = £ 5.40 6 x £1.35 = £8.10 7 x £1.35 = £9.45 7 is the maximum number of bags that can be purchased with £10.
• Question 5

A bag of birdseed is £1.35.

How many bags of birdseed can be bought for £20?

14
EDDIE SAYS
Did you spot that if you are able to buy 7 bags with £10, you will be able to buy 14 bags with £20, which is double the amount? Again, show your working out with these questions, you may well be able to get a mark for it even if your answer is incorrect.
• Question 6

There are 80 g of pasta in one portion.

How many portions are there in a 4 kg bag of pasta?

50
EDDIE SAYS
Did you work out that there are 50 portions in a 4 kg bag of pasta? Convert 4 kg into grams = 4000 g (there are 1000g in 1 kg). 4000g ÷ 80 = 50 portions.
• Question 7

2534 people pay to enter a funfair.

Each person pays £2.40.

What is the total amount of entry money collected?

EDDIE SAYS
Don't worry if you found this tricky, it's definitely a challenge! When completing a question like this, choose whichever method of multiplication you prefer. This may be a grid or column method of multiplication. Having great knowledge of the times tables really helps when using these written methods. Again, remember to show your working out as you may get a mark for it. 2534 x £2.40 = £6081.60
• Question 8

The distance from Edinburgh to London is 534 km.

5 miles is approximately 8 kilometres.

Use these facts to calculate the approximate distance in miles from Edinburgh to London.

EDDIE SAYS
This is a tough one! To solve it we have to divide by 8 and multiply by 5. 534 ÷ 8 = 66.75 66.75 x 5 = 333.75 Round to the nearest whole number = 334 miles.
• Question 9

Pancake recipe for 4 people:

- 100 g plain flour

- 2 large eggs

- 300 ml milk

- 1 tbsp of vegetable oil

- lemon wedges to serve (optional)

- caster sugar to serve (optional)

Jodie uses this recipe but needs to make pancakes for 8 people.

How much milk will she need?

EDDIE SAYS
If 300 ml of milk is needed to make pancakes for 4 people, 600 ml is needed to make pancakes for 8 people. There are 1000 ml in 1 litre, so 600 ml in litres = 0.6 litres.
• Question 10

450,000 people visited Spain on holiday in one year.

15% visited in April.

45% visited in August.

How many people visited Spain for the rest of the year?

180,000
EDDIE SAYS
Did you read this question carefully? This was definitely a tough one! There were a few steps needed to find the answer. Step 1: Find 15% of 450,000 Find 10% = 45,000 Find 5% = 22,500 Find 15% = 67,500 Step 2: Find 45% of 450,000 10% = 45,000 40% = 45,000 x 4 = 180,000 5% = 22,500 45% = 180,000+ 22,500 = 202,500 Step 3: Add 15% and 45% = 60% = 67,500 + 202,500 = 270,000 Step 4: Subtract 60% from 450,000 = 450,000 - 270,000 = 180,000 Answer = 180,000 visited Spain during the rest of the year. Great focus, that’s another activity completed!