I believe teaching multiple grade levels within the same day has value. Being able to observe how students think about numbers and the strategies that they use over time gives teachers a different perspective. It also shows some of the linear progression of math skills and strategies. I found this especially evident as I read through Kathy Richardson’s book during July. I currently serve as a math teacher for students in grades 2-5. I get to see how students progress over time and what tends to trip them up. I also see the problems that emerge when students start to rely on tricks and formulas before having a deep understanding of a particular concept. One thing that I also continue to observe is that students sometimes struggle to be reasonable with their estimates. Part of that may be due to an over-reliance on algorithms and the other part may relate to exposure. Students aren’t given (or take the) time to reflect and ask themselves whether the answer truly makes sense or not. This tells me that students are relying on a prescribed process or algorithm and reasonableness comes second.
In an effort to move towards reasoning, I’ve been using Estimation 180 on a daily basis. I feel that the class is become better at estimating and their justification has improved. Making sense with number puzzles also seem to be helping students create reasonable estimates and solutions. Basically, students are given a story that has blanks.
Students are then are given a number bank. Sometimes too many numbers are in the bank.
Then students have to justify why they picked each answer. This can be completed in verbal or written form.
Usually I have students explain their reasoning with a partner. The class has completed a number of these types of making sense with numbers puzzles. I can say that students are now looking more closely at the magnitude of the actual numbers before estimating or finalizing an answer. That’s progress and I’m confident that students are more willing to use that strategy along their math journey in the future.