No Algorithm, No Problem

Third grade students are natural innovators at play, quickly repurposing items to find workarounds for problems they encounter. In the classroom, though, the same child who knows a hundred uses for a jump rope believes there is only one way to solve a problem and that the faster they answer, the better. The goal of math instruction during this year is to bring the flexibility of thinking seen during play into the classroom. We do this with puzzles, games, small group work, and lots of challenges. 
Early in the year, students solve a number puzzle, sharing strategies and “noticings” with each other. Then, the tables are turned and they are asked to create a similar puzzle for their parents. Now comes a creative challenge! There is a flurry of figuring, calls for extra scrap paper, and much experimentation as they strive for the trickiest puzzle with as many combinations as possible. They revisit strategies, notice patterns, and discover shortcuts. Why, you can flip the tens or ones places and not change the result! (22 + 18 = 40 and 12 + 28 does too!)  Old ideas suddenly sparkle in a new light as they rediscover them for themselves. 

Throughout the year, creative and exploratory opportunities are always included. After learning the multiplication/division facts 0-10, small groups are asked to solve a multi-digit multiplication problem with numbers larger than they have used before. They’re given a big sheet of paper and markers, and turned loose. It’s glorious to see all the different ways each group finds: skip counting, multiplying by smaller numbers and adding, breaking the bigger number into small parts and multiplying by each part. You hear, “That can’t be true!” and then see them fix the problem they’ve identified. 

After we share solutions as a class, groups break out with renewed enthusiasm. We can do it faster, we can do it without adding so often, we can do it by using problems we know and stringing them together! Over the year, they have learned to listen carefully to the explanations of classmates. They can argue productively, learn from each other, and try different ideas without losing focus.

When they do learn the traditional algorithm, they appreciate the economy of regrouping, recognize the partial products, and the math facts working together. It isn’t a magic formula to them. They know they have the creativity and perseverance to solve challenging problems, with or without an algorithm.