The key to solving these problems is to notice patterns or properties. Encouraging students to organise their work in a systematic way will allow them to notice what might not otherwise be obvious.
![Summing Consecutive Numbers](/sites/default/files/styles/medium/public/thumbnails/content-97-05-six4-icon.png?itok=qriTyABd)
problem
Summing Consecutive Numbers
15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?
![1 Step 2 Step](/sites/default/files/styles/medium/public/thumbnails/content-00-10-penta1-icon.png?itok=wey3aDMe)
problem
1 Step 2 Step
Liam's house has a staircase with 12 steps. He can go down the steps one at a time or two at time. In how many different ways can Liam go down the 12 steps?
![Pick's Theorem](/sites/default/files/styles/medium/public/thumbnails/content-03-10-six4-icon.gif?itok=F-QyKCMj)
problem
Pick's Theorem
Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.
![What's Possible?](/sites/default/files/styles/medium/public/thumbnails/content-00-11-six5-icon.png?itok=Y1vBIzcp)
problem
What's Possible?
Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?