Creating and Manipulating Algebraic Expressions - Short Problems


This is part of our collection of Short Problems.

You may also be interested in our longer problems on Creating and Manipulating Algebraic Expressions.

Printable worksheets containing selections of these problems are available here:

Stage 3 ★ Sheet 1 Solutions

Adding and Multiplying

KS 3 Short Challenge Level:

Challenge Level:1

Amy misread a question and got an incorrect answer. What should the answer have be?

The Square of My Age

KS 3 Short Challenge Level:

Challenge Level:1

Weekly Problem 34 - 2011
Lauren and Thomas tell their ages in terms of sums of squares. Can you work out how old they really are?

Forming Groups

KS 3 Short Challenge Level:

Challenge Level:1

Weekly Problem 34 - 2006
Seventy pupils are divided into two groups. Can you work out the differnece between the number of boys in group 1 and the number of girls in group 2?

Cube Pile

KS 3 Short Challenge Level:

Challenge Level:1

Weekly Problem 29 - 2017
Rick has five cubes. Each one is 2cm taller than the previous one. The largest cube is the same height as a tower built of the two smallest cubes. How high would a tower of all five cubes be?

Building Up

KS 3 Short Challenge Level:

Challenge Level:1

Weekly Problem 16 - 2015
In the diagram, the number in each box is obtained by adding the two immediately below. What is the number in the top box?

Stamp Collecting

KS 3 Short Challenge Level:

Challenge Level:1

Weekly Problem 28 - 2016
Last week, Tom and Sophie bought some stamps for their collections. Each stamp Tom bought cost him £1.10, whilst Sophie paid 70p for each of her stamps. Between them they spent exactly £10. How many stamps did they buy in total?

Punky Fish

KS 3 Short Challenge Level:

Challenge Level:1

Weekly Problem 12 - 2008
A male punky fish has 9 stripes and a female punky fish has 8 stripes. I count 86 stripes on the fish in my tank. What is the ratio of male fish to female fish?

Inspector Remorse

KS 3 Short Challenge Level:

Challenge Level:1

Weekly Problem 49 - 2011
How long will it take Inspector Remorse to crack this crime spree?

Paul's Children

KS 3 Short Challenge Level:

Challenge Level:1

Weekly Problem 29 - 2016
Paul is 32 years old. In ten years time, Paul's age will be the sum of the ages of his three sons. What do the ages of his sons add up to at present?

Multiple Magic

KS 3 Short Challenge Level:

Challenge Level:1

Weekly Problem 31 - 2009
Think of any whole number. Each time you perform a sequence of operations on it, what do you notice about the divisors of your answer?

No Matter

KS 3 Short Challenge Level:

Challenge Level:1

Weekly Problem 2 - 2013
After performing some operations, what number is your answer always a multiple of?

Kangaroo Subtraction

KS 3 Short Challenge Level:

Challenge Level:2 Challenge Level:2

Weekly Problem 2 - 2010
Can you solve this 'KANGAROO' alphanumeric subtraction?

Square Total

KS 3 Short Challenge Level:

Challenge Level:2 Challenge Level:2

Weekly Problem 13 - 2017
Anastasia thinks of a number. Each of her friends performs an operation on it. The total of these is a square number. What is the smallest number Anastasia could have thought of?

Standing on the Table

KS 3 Short Challenge Level:

Challenge Level:2 Challenge Level:2

Weekly Problem 39 - 2017
Clement and Dmitri both measure how much taller they are standing on a table compared to the other standing on the floor. Can you work out how tall the table is?

Brothers and Sisters

KS 3 Short Challenge Level:

Challenge Level:2 Challenge Level:2

Can you work out how many brothers and sisters are in the family?

Cuboid Perimeters

KS 3 Short Challenge Level:

Challenge Level:2 Challenge Level:2

Can you find the volume of a cuboid, given its perimeters?

How Many Rectangles?

KS 3 Short Challenge Level:

Challenge Level:2 Challenge Level:2

Weekly Problem 37 - 2016
By drawing 5 horizontal and four vertical lines, one can form 12 rectangles. What is the greatest number of rectangles that can be formed by drawing 15 lines?

Black and Gold Storeys

KS 3 Short Challenge Level:

Challenge Level:3 Challenge Level:3 Challenge Level:3

25 of the storeys of a 50 storey building are painted gold, and the rest are painted black...

Square and Cube

KS 3 & 4 Short Challenge Level:

Challenge Level:1

Weekly Problem 24 - 2014
The square of a positive number is twice as big as the cube of that number. What is the number?

Beans Eating Beans

KS 3 & 4 Short Challenge Level:

Challenge Level:1

Weekly Problem 13 - 2007
The Bean family are very particular about beans. At every meal all Beans eat some beans... At their last meal they ate 23 beans altogether. How many beans did Pa Bean eat?

Nine in a Line

KS 3 & 4 Short Challenge Level:

Challenge Level:1

Weekly Problem 9 - 2008
The sum of 9 consecutive positive whole numbers is 2007. What is the largest of these numbers?

Largest Expression

KS 4 Short Challenge Level:

Challenge Level:2 Challenge Level:2

Weekly Problem 36 - 2006
Which of these five algebraic expressions is largest, given $x$ is between 0 and 1?