How many squares ?
How many squares can you see in this pattern?
Answer
There are 56 squares in total: 32 at 1 x 1, 16 at 2 x 2, 6 at 3 x 3, 2 at 4 x 4.
Number lines
Can you put the numbers 1 to 7 in each circle so that the total number of every line is 12?
Answer
How did you go? Teachers, if students get stuck on this one, give them the middle number 4 as a hint.
The escaping frog
A frog has fallen into a pit that is 30 metres deep. Each day the frog climbs up 3 metres but falls back 2 metres at night.
How many days does it take for the frog to escape?
Answer
It will take 28 days for the frog to escape. After 27 days and nights the frog only has 3 metres to go. On the 28th day the frog is able to jump to freedom!
Missing matches
Remove just 4 matches to leave 4 equilateral triangles. Equilateral means all the triangles must be exactly the same size.
Try using real matches or toothpicks to help work through the problem.
Answer
Mission matches: Solution
Here is one solution. How many different solutions can you find?
Find the path
Can you find a path adding the numbers as you go to make exactly 53?
Start at the bottom left square (5) and move up, down, left or right until you reach the finish square (4).
Answer
How did you go? Here is one solution:
5 + 7 + 6 + 6 + 9 + 4 + 5 + 7 + 4 = 53
Hidden shapes
What is the total number of triangles and the total number of squares in the diagram? Look carefully, some may be hidden.
