One of the beauties of pushing into our second grade, as a support to our 2/3 combo, is that I witness students inventing, learning, and applying new math strategies every day. A strategy that works for one student might not be the right fit for another. Yet, without a doubt, each and every student has at least one strategy that works for them as a learner!
When students invent strategies it shows that they know what they are doing to manipulate numbers and can fluidly go between mental math and paper and pencil. If you think about a time you needed to estimate a grocery bill, make sure you received the correct change, or calculate a tip, you probably weren’t thinking of the traditional algorithm. Rather, I bet you were using a strategy you invented or someone taught you. Strategies are not traditional algorithms. Yet, both strategies and algorithms are part of our state standards.
One strategy a 2nd grader used when subtracting multi-digit numbers:The work of a single student practicing a multitude of strategies with addition:We give students time to invent and discuss strategies and we teach multiple strategies more explicitly because it:
- helps students become efficient as they become adept at changing problems into easy to solve equivalent problems (For example: 40-12 changes to 40-10-2)
- provides scaffolding so that students can find an entry place and problem solving options such as manipulative, drawings, written words or symbols
- motivates students to solve problems due to autonomy created by choice rather than rote procedure
- develops true number sense and the meaning of operations
- Develops grit and confidence
Here are some more examples of how students gain number sense at Mar Vista:
Third graders did a directed drawing of a panda 🐼 then used them to create a multiplication and division resource: .Work places in first grade:
TK students building and counting: