Are you looking for a great activity to do with your elementary-aged children? Consider playing with a 1-to-100 chart (often called a 100 chart), or its first cousin, the 0-to-99 chart. These visual organizations of numbers are a staple in primary classrooms, but both bear looking at deeply and often.
One great thing to do is to examine the patterns are created when you colour or highlight various skip counting patterns on the chart. Often we think of skip counting by 2, by 5 and by 10. But if you consider each of the skip counting patterns (by 2, 3, 4, 5, 6, etc) you are also playing with the multiples of those numbers. When students in grades 3-6 practice multiplication facts, they usually do not go beyond x10 or in some cases 12. By looking at the skip counting all the way to 100, you can explore the repeating patterns that show up. Some of the patterns are particularly interesting! (Do you know how a knight moves on the chessboard? Try looking for that pattern in the skip counts.)
As an intermediate classroom teacher, I always had my class do these colouring patterns and we stapled the sheets into a little booklet that they kept in their “math toolkits”. We revisited them throughout the year.
Do some general exploring of patterns, too. Just let kids “notice” some things. If you need a few prompts, consider these:
What patterns happen in vertical columns?
What patterns happen in horizontal rows?
Compare the various diagonal rows?
What do you notice when you colour every number with the digit 4 in it? With 5?
What is the same in each of the above? What is different?