Investigate how you can work out what day of the week your birthday will be on next year, and the year after...
Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?
Arrange the numbers 1 to 16 into a 4 by 4 array. Choose a number.
Cross out the numbers on the same row and column. Repeat this
process. Add up you four numbers. Why do they always add up to 34?
In a number pyramid, the numbers on the lower levels determine the numbers above them.
Try entering some different numbers in the bottom row.
Can you work out how the numbers in the upper layers are generated?
Here are some questions to consider:
If I tell you the numbers on the bottom layer, can you work out the top number without working out the middle layer?
If you change the order of the numbers on the bottom layer, will the top number change?
Given any three numbers for the bottom, how can you work out the largest possible number that could go at the top?
If I give you a target for the top number, can you quickly find three possible numbers for the bottom?
Can you adapt what you learned about 3-layer pyramids to larger pyramids?
Here is an interactive number pyramid with four layers so you can test out your ideas:
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