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What pattern can you see in the last digits of the powers of 2?
What about the last digits of the powers of 3?
What patterns can you see in the last digits for the numbers in the picture?
Can you explain why all these numbers are multiples of 5?
What about […]
Investigate the last digits of the numbers in the picture when n = 1, 2, 3 , 4 and 5. What do you notice? Does this pattern continue? Why?
Will the first number be a power of 10 for any value of n?
What can you say about the values of n […]
1. Imagine the first number is written out in full. How many zeros would there be at the end? Why? Can you find the answer without doing the whole calculation?
2. Work out a few values of the second number with n = 1, 2, 3 and 4 . Can you show numbers […]
Is this number divisible by 5?
Hint: Just look at the last digits of powers. What values do they take?
Investigate other big powers?
Make up some similar numerical expressions involving powers that have interesting properties.
What about even bigger powers or
?
Click here for the POWERFUL THINKING 4 Worksheet.
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You will need to download and print out this jigsaw (or draw the pieces on squared paper), and cut up the pieces into squares (don’t cut along the diagonal lines!).
Now try to put the square pieces together without rotating any of them (so that in the finished jigsaw all the […]
Do this as you read…
Think of a number.
Multiply it by 3.
Add 6.
Take away your number.
Divide by 2.
Take away your number.
You have finished with 3.
How does this work?
If an object depreciates in value by 10
Why aren’t these two answers the same?
Is there a rate, used for both gain and depreciation, for which those two answers would actually be the same?
See the notes for teachers and solution
See the DATING MADE […]
The wall painting on the house in this photo shows geometric transformations: reflections, rotations and translations. The symmetries of a design are the transformations that leave the pattern looking exactly the same.
Assume that the parts of the design that look the same are identical and that they only appear different because […]
Everyone in the class must shake hands with everyone else and say hello, or bow to each other in a one-to-one greeting. Everyone must join in. How many handshakes (or bows) will there be altogether?
This will be difficult to count, especially if you have a large class. Try the problem in […]
The letters A, B, C, D, E, F, G and H correspond to the numbers from 0 to 7 with no repetitions.
Use the clues that A+C=A and F×D=F to find the values of two letters.
Use the clues B−G=G and B/H=G to find the value of another three letters.
Use the clues A+H=E […]
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