Creating and Manipulating Algebraic Expressions - Short Problems

A collection of short Stage 3 and 4 problems on creating algebraic expressions



Gender Balance

Stage: 3 Short Challenge Level: Challenge Level:1

Weekly Problem 36 - 2012
Can you work out how many more boys are in group 1 than girls are in group 2?

Integer and Integer

Stage: 3 Short Challenge Level: Challenge Level:1

Weekly Problem 39 - 2012
For how many values of $n$ are both $n$ and $\frac{n+3}{n−1}$ integers?

Inspector Remorse

Stage: 3 Short Challenge Level: Challenge Level:1

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

Four or Five

Stage: 3 Short Challenge Level: Challenge Level:1

Weekly Problem 19 - 2012
The diagram shows a large rectangle composed of 9 smaller rectangles. If each of these rectangles has integer sides, what could the area of the large rectangle be?

Siblings

Stage: 2 and 3 Short Challenge Level: Challenge Level:1

Weekly Problem 17 - 2013
Anna has 3 brothers and 5 sisters. What is the product of the number of brothers and number of sisters that her brother Tom has?

No Matter

Stage: 3 Short Challenge Level: Challenge Level:1

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

The Mad Hatter's Watch

Stage: 3 Short Challenge Level: Challenge Level:1

Weekly Problem 35 - 2013
The hour hand on the Mad Hatter's watch moves normally, but the minute hand moves too fast! When will it next show the correct time?

Painting the Forth Bridge

Stage: 3 Short Challenge Level: Challenge Level:2 Challenge Level:2

Weekly Problem 14 - 2006
Given the rates at which men can paint, how long will it take them to paint the Forth Bridge?

Largest Expression

Stage: 3 and 4 Short Challenge Level: Challenge Level:1

Weekly Problem 36 - 2006

Forming Groups

Stage: 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?

Beans Eating Beans

Stage: 3 and 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?

Crime Figures

Stage: 3 and 4 Short Challenge Level: Challenge Level:1

Weekly Problem 34 - 2007
Inspector Remorse had a difficult year in 2004. Find the percentage change in the number of cases solved in 2004 compared with 2003.

Nine in a Line

Stage: 3 and 4 Short Challenge Level: Challenge Level:1

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

Punky Fish

Stage: 3 and 4 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?

Knitting Scarves

Stage: 3 Short Challenge Level: Challenge Level:1

Weekly Problem 43 - 2008
A knitted scarf uses three balls of wool. How many balls of wool do I have at the end of the day?

Refuelling

Stage: 3 Short Challenge Level: Challenge Level:1

Weekly Problem 12 - 2009
A car can go r miles on s gallons of petrol. How many gallons of petrol would it need for a journey of t miles?

Petrol Prices

Stage: 3 Short Challenge Level: Challenge Level:1

Weekly Problem 28 - 2009
How much does $u$ litres of unleaded cost in terms of the cost per litre of 4 star petrol?

Multiple Magic

Stage: 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?

Rectangle Cutting

Stage: 3 Short Challenge Level: Challenge Level:1

Weekly Problem 50 - 2009
Tom and Jerry start with identical sheets of paper. Each one cuts his sheet in a different way. Can you find the perimeter of the original sheet?

Kangaroo Subtraction

Stage: 2 and 3 Short Challenge Level: Challenge Level:1

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

Reciprocal Values

Stage: 3 and 4 Short Challenge Level: Challenge Level:1

Weekly Problem 28 - 2010
Manipulate one algebraic fraction to solve another.

The Square of My Age

Stage: 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?

Repeat Product

Stage: 3 and 4 Short Challenge Level: Challenge Level:2 Challenge Level:2

Weekly Problem 3 - 2014
Can you work out the value of P+Q+R in the multiplication shown?

Square and Cube

Stage: 3 and 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?

Relative Time

Stage: 3 and 4 Short Challenge Level: Challenge Level:1

Weekly Problem 25 - 2014
Albert Einstein is experimenting with two unusual clocks. At what time do they next agree?

Pyramidal N-gon

Stage: 3 and 4 Short Challenge Level: Challenge Level:1

Weekly Problem 43 - 2014
The base of a pyramid has n edges. What is the difference between the number of edges the pyramid has and the number of faces the pyramid has?

Building Up

Stage: 3 and 4 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?

Divide and Conquer

Stage: 3 and 4 Short Challenge Level: Challenge Level:1

Weekly Problem 23 - 2015
Can you simplify this algebraic expression with many divisions?