Question 30
How would you explain why a half times a half gives an answer less than a half?
Question taken from Questions and Prompts for Mathematical Thinking

Question 29
In Speedway races, there are heats of 4 riders; each rides against each other rider exactly once.
Device systems for arranging different totals of riders into heats.
Question taken from Points of Departure 2

Question 28
Agree or disagree: I always get an answer bigger than 7 if I add a number to 7.
Question taken from Thinking for Ourselves

Question 27
If I multiply the three digits on car number plates together what number am I most likely to get
(e.g. 377, 737 and 773 are the only plates to give 147 but 234, 243, 324, 423, 432, 146, 138 etc all give 24)
Question taken from Eight Days a Week

Question 26
What solids can you make which have square faces, but which are not cubes?
Question taken from Points of Departure 4

Question 25
A rectangle has a perimeter of 24.
What could its area be?
Question taken from Assessment from the New National Curriculum

Question 24
Two numbers add up to 24. Find the greatest possible value when they are multiplied together (their product).
Try the same with other numbers to see if you can spot patterns.
Question taken from The long and the Short

Question 23
If you had a 3 Litre jug and a 5 Litre jug how could you use them to measure 4 Litres? Investigate other problems like this.
Question taken from Points of Departure 1

Question 22
Agree or disagree: the mean of 5 numbers is always larger than the median.
Question taken from Thinking for Ourselves

Question 21
Explain or refute why it is appropriate to use a linegraph to display specified data.
Question taken from Eight Days a Week

Question 20
Take a cornflake box. If you wanted 20% more cornflakes in the box, how would you change the box?
What if you wanted to put in twice as many cornflakes?
Consider other boxes, packs, tins etc.
Question taken from Points of Departure 3

Question 19
Order these numbers according to how many factors they have: 5,8,12,22,36
Question taken from Thinking for Ourselves

Question 18
Make up a word problem to which the answer is 2.7
Question taken from Questions and Prompts for Mathematical Thinking

Question 17
Which is the greater: the number of metres in a kilometre or the number of Sundays in the next 20 years?
Question taken from Eight Days a Week

Question 16
A stick is broken into three pieces.
When can the pieces make a triangle?
What is the probability this will happen?
If the stick is broken into four pieces, what is the probability that they could make a quadrilateral?
Question taken from Points of Departure 2

Question 15
Find five pairs of numbers that give the answer 0.4 when you divide one number in each pair by the other.
What happens if you use the same five pairs of numbers but this time divide them the other way around
Question taken from Everyone is Special

Question 14
Write down, in order, four consecutive integers.
Choose either addition or subtraction to put between each number and the next to make a calculation.
Work out the result
Repeat for a different arrangement of subtraction and addition, and for different sets of consecutive numbers
Question taken from Assessment from the New National Curriculum

Question 13
What is the same and what is different about the median and the mode?
Quesion taken from Thinking for Ourselves

Question 12
Use the digits 1,2,3,4,5 exactly once each to make two or more numbers.
E.g. 4 21 53
Multiply these numbers together.
4 x 21 x 53 = 4452
Try other arrangements of the digits 1 to 5. What is the greatest product that can be made?
Question taken from Points of Departure 3

Question 11
Elsa noticed that the square of an even number is always even, and is an exact multiple of 4.
And that the square of an odd number is always odd and always seems to be one more than a multiple of 4.
Is she right, and can you explain why?
Question taken from The long and the short

Question 10
A cage contained monkeys, giraffes and llamas.
All but two of the animals were monkeys, all but two were giraffes and all but two were llamas.
How many animals of each kind were in the cage?
Question taken from Eight Days a Week

Question 9
In a set of three consecutive numbers which is larger  the product of the first and last number or the square of the middle number?
Question taken from Bigger Ideas

Question 8
A jar contains 20, 19, 13 and 10 marbles.
You are allowed to take 1 marble from each of 3 jars and put all 3 in the fourth jar.
If you continue in this way, can you ever get all the marbles in one jar?
Question taken from The Long and the Short

Question 7
Show that 30% of 200 is the same as 200% of 30
Question taken from Thinking for Ourselves

Question 6
A woman was born in a year that was a square number, lived a square number of years and died in a year that was also a square number.
What is the latest date on which she could have been born?
When is the next time this could happen?
Make up some similar puzzles of your own?
Question taken from Points of Departure 3

Question 5
Tell me something that must be true if these three numbers are the sides of a rightangled triangle
Question taken from Questions and prompts for Mathematical Thinking

Question 4
Find a pair of numbers which sum to 10.
What is their product?
What pair of numbers gives the greatest product?
Question taken from Assessment in the new National Curriculum an ATM perspective

Question 3
You have got 5p and 7p stamps only.
It is possible to post a letter costing 39p (5+5+5+5+5+7+7=39) but you can’t put the correct amount on a parcel if it costs 23p.
Make up and investigate problems about stamps and parcels.
What is the biggest parcel that you can’t post?
Question taken from Points of Departure 2

Question 2
This is a game for two. Start by writing zero. The first player adds 1,2, or 10 and writes the answer.
The second player adds 1,2, or 10 to this answer and writes the new number, and so on.
The winner is the first to reach 20.
Question taken from Eight Days a Week

Question 1
Choose any whole number. Multiply by the next whole number. Then the answer is always even. Is this true? If so, can you explain Why?
Question taken from The Long and the Short  Book and Download
