This website is a great resource for teachers. Their goal is to " [increase] access to quality standards-based resources for teaching and learning mathematics", and they very effective in working toward this goal. They offer over 600 lesson plans and 100 activities all directly related to math.
The lesson plans offer some interesting and engaging ideas, and are sorted by grade level and strand. They offer some novel ideas to get kids engaged, such as the Skin Weight lesson plan, which helps students work with multiplication, division, charts and patterning at the grades 6-8 level. The Orbiting Satellites lesson plan teaches students to use algebra to look at the way real-world devices rely on math to function.
There is a lot of potential in the activities section of the website as well. The Plotter the Penguin activity helps students learn how to plot points on a graph and work with slope, both are things that I have noticed a lot of students struggle with initially. Pick-a-Path encourages students to work with their various math skills - addition, subtraction, multiplication, division, powers of ten, negative numbers, fractions, and decimals- to help Otka the octopus reach his goal and escape the 'mathematical net'. These types of activities work as great hooks for lessons or an end of the class reward for getting work done ahead of schedule.
The website also has brain teasers, something I know a lot of teachers use to provide an extra daily or weekly challenge to help get students thinking, and in that spirit I leave you with two of Illuminations' brain teasers:
The Wolf, Goat, and Cabbage
This problem can be found in eighth-century writings.
A man has to take a wolf, a goat, and some cabbage across a river. His rowboat has enough room for the man plus either the wolf or the goat or the cabbage. If he takes the cabbage with him, the wolf will eat the goat. If he takes the wolf, the goat will eat the cabbage. Only when the man is present are the goat and the cabbage safe from their enemies. All the same, the man carries wolf, goat, and cabbage across the river. How?
The Fibonacci sequence is shown below, with each term equal to the sum of the previous two terms. If you take the ratios of successive terms, you get 1, 2, 3/2, 5/3, 8/5, 13/8, and so on. But as you proceed through the sequence, these ratios get closer and closer to a fixed number, known as the Golden Ratio.
1, 1, 2, 3, 5, 8, 13, …
Using the rule that defines the Fibonacci sequence, can you determine the value of the Golden Ratio?