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?

Frogs

How many moves does it take to swap over some red and blue frogs? Do you have a method?

The Best Card Trick?

Time for a little mathemagic! Choose any five cards from a pack and show four of them to your partner. How can they work out the fifth?

Perimeter Possibilities

Stage: 3 Challenge Level:
Watch the video below.

How many other possible perimeters can you find, for a rectangle with an area of $24\text{cm}^2$?

Now watch the video to see what Alison and Charlie did next.

Here are some questions you might like to consider:
• What other odd number perimeters can you make, if the area is $24\text{cm}^2$?
• What is the smallest perimeter you can make, if the area is $24\text{cm}^2$?
• What about the largest perimeter?
• Which perimeters in between is it possible to make?

More generally...
• Is it possible to make a rectangle with a fractional perimeter but a whole number area?
• Is it possible to make a rectangle with a whole number perimeter but a fractional area?

Take a look at Can They Be Equal? to explore rectangles where the area is numerically equal to the perimeter.