#### You may also like ### Prompt Cards

These two group activities use mathematical reasoning - one is numerical, one geometric. ### Exploring Wild & Wonderful Number Patterns

EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules. ### Worms

Place this "worm" on the 100 square and find the total of the four squares it covers. Keeping its head in the same place, what other totals can you make?

# Sam's Quick Sum

##### Age 7 to 11 Challenge Level:

Congratulations to Jamie, St Angela's School, Forest Gate, London; Joshua, Amptill, Bedfordshire; Sohail, Predesh, Gurpreet, Jessica and James, Jack Hunt School, Peterborough; Charlotte, Helen, Bella, Charis, Christianne, Peach, Sheila, Cheryl, Pen and Lyndsey, Laura and Emma, The Mount School, York. Here is Jamie's solution:

There are $900$ numbers between $100$ and $999$ so you can halve the number $900$ to see how many pairs you get.
Each pair adds up to $1099$ because if you add $100$ to $999$ the answer is $1099$ and if you add $101$ to $998$, or $102$ to $997$ and so on you get the same answer.
The sum of all the three-digit numbers is $450 \times 1099 = 494550$.