### Days and Dates

Investigate how you can work out what day of the week your birthday will be on next year, and the year after...

### Summing Consecutive Numbers

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?

### Always the Same

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?

# Lower Bound

##### Stage: 3 Challenge Level:

Younger learners can work with numbers and find out what happens to the sequence.

As you work out more terms does the value seem to get closer to a particular number? Are the values always greater than that number? Why do you think this happens?

If you want to go on to use algebra, a bit of algebra will help you to explain what happens and to prove that there is a limiting value for this sequence. However you will have to know how to multiply two bracketed terms together to do this so it might be something to come back to when you have learnt a little more algebra.