Beginning early in the year, and continuing throughout, third-grade students have learned to solve math problems using a very important tool: bar models. This year, you may have even heard your child wondering out loud, “Do I have to do a bar model for this problem?” At first, it is tempting for children to want to skip this step, but bar models provide so many opportunities for learning and understanding mathematics, and bar models are definitely not a step to be skipped. As one third grader put it, “Once you understand bar models, they can be your best friend.”
Early in the year, the third graders were introduced to this new “friend,” or tool, and the concept of defining a unit to solve for an unknown quantity. The children thought about how to organize these units and create labeled bar models. For third graders, this growing “friendship” with bar models has taken time, but it has been time well spent. The process of creating bar models has helped the children become more efficient at sorting out important information. Bar models have also promoted flexible yet organized thinking and have prepared the children to think about multi-step problems. Bar models enabled many students to solve higher-level problems that developed algebraic reasoning. In the picture, you will notice that three students approached the same multi-step problem three different ways, and you can see how the bar model helps children to visually represent the multiplicative relationship of dragonflies to ladybugs.
Finally, bar models promote an important habit that may not be obvious: slowing down. All children rush from time to time and drawing and labeling bar models is a practical strategy that forces some children to actively slow down. Slowing down allows time for so many important things that are missed when children rush, such as critical thinking, error analysis and generally producing a higher quality of work. At this point in the year, all of these things are happening for the third graders, and their relationship with bar models has certainly come a long way. In a perfect expression of how far third graders have come in their understanding of problem-solving this year, a student recently shared this insight, “It’s like the bar model is the picture that proves our equation makes sense.”