This week we have been reviewing strategies students can use to add larger numbers. The goal is not to remember the strategy itself, but for students to become more flexible with numbers. Students who are flexible with numbers can build numbers and break numbers apart in many ways. They understand that there are different ways to make the whole. For example, at the foundational level, students understand that you can decompose (break apart) the number 10 into 5 and 5, 7 and 3, 6 and 4, and so on. By the beginning of third grade students should be able to compose and decompose numbers from 1-20 with automaticity. This is the foundation that helps them develop more efficient strategies for adding and subtracting larger numbers, and sets them up for success with multiplication and division.
When solving 23-6, some students start and 23 and count backwards by one until they reach the answer. Other students may use the standard algorithm and stack the numbers and use regrouping to solve the problem. Students who are flexible with numbers will understand that they can decompose 6 into 3 and 3 and then solve 23-3=20. Noticing that 20 is a friendly number (a multiple of 10), they will apply their knowledge of making 10 using 3 and 7 to quickly figure out that 20-3=17 just as 10-3=7.
This understanding of mathematical practice is probably much different than how most of us were taught. You might wonder why we just don't teach kids to stack the numbers and add or subtract. The answer is that teaching a standard algorithm does not help students make sense of numbers nor does it build the mathematical reasoning skills they need in order to understand more difficult mathematical concepts they will encounter later in their schooling. It is important to help students build flexibility with numbers and develop efficient use of strategies.
Students will create teaching videos that they can refer to as they continue to practice the strategies that will help them become more efficient at solving math problems. I will embed the videos on our class webpage. Click on the For Students tab > Math > Addition and Subtraction to watch the strategy videos. You can also click the link button below.