Have you been really focused on number sense in your classroom? Are you using number strings, doing number talks, counting around the circle? If so, then you are thinking about numbers and the relationships between numbers. You are thinking about the patterns made by numbers, and the effect of repeated operations on numbers.

Have you ever considered using dot to dots as another way to play with and explore number?

Maybe not. Typically, they are very simplistic, only a few numbers, rarely going beyond the twenties, and only counting by ones; they are a challenge for only the earliest of learners. However, in the last couple of years, I’ve seen a renaissance in dot to dots, going hand in hand with the colouring book trend. There are a couple of very talented designers/artists out there who have created some brilliant dot puzzles, but they still have their limits as to their use in the classroom.

This past year, I’ve been playing with the puzzle design myself, tweaking the structure and mechanics to make something that teachers can use. My puzzles have several essential differences.

First, They skip count by more than just 1s. My puzzles run the gamut from 1s to 10s. This means they help to learn and practise skip counting and growing patterns, and, by extension, addition and multiplication for almost all the basic facts.

Second, they have different starting points. I have several puzzles that skip by 2s, but some of these start at 1 (1, 3, 5…). Some puzzles skip by 3s, but a few of them start at 1 or 2 (1, 4, 7, 10…; 2, 5, 8, 11…). Solving each number in the sequence in these unfamiliar patterns practices mental addition and number fluency.

Third, there are hard and easy versions of each puzzle, allowing teachers to differentiate for different children’s knowledge and skill levels. The “easy” version is useful for students who are struggling with the concept of skip counting and need some supports to get to each new number. The “hard” version throws distractions and red herrings onto the page in the form of extra numbers. Students doing a “hard” puzzle must really know how to apply the pattern, or risk connecting the wrong dots and creating an incomprehensible scribble.

If you want a more thorough explanation, I detail how these puzzles work and ways to use them in my Teacher Package, available for free here by clicking the link or the images, and on TeachersPayTeachers.com where you can see all the puzzles available. The package explains how to distribute or present the puzzles, tips for differentiating, suggestions for how to tie the puzzles to the number and patterning curriculum, and examples of errors that students might make with the puzzles and what these mistakes might be saying about a child’s skill and knowledge.

Have a look at the Teacher Package or download the free previews for the different Holiday themed collections, also available on this blog. Let me know if you try the puzzles with your students and give me feedback about how it went or suggestions you might have.

You can also get the complete collection of “hard” puzzles in paperback at Indigo, Amazon and Barnes & Noble. Click these links to check it out.