Alternative algorithms that break addition, subtraction, division, and multiplication problems that involve large numbers into more manageable pieces are an excellent way to help students develop strong conceptual understanding before instructing standard algorithms. As a parent this can be a wonderful method to understand in order to help your child with their homework, or go over a test that they get back. In this post we will highlight the partial sums and partial differences methods, and over the next few weeks will continue on to the other operations.
As the name implies, this algorithm works by calculating partial sums, one place value column at a time, and then adding up those sums to get the final answer. Students practice using base-10 blocks and estimates to add multi-digit numbers, and also gain a deeper understanding of how those multidigit numbers are actually constructed. Partial sums can be done moving from left to right or right to left, giving students some degree of flexibility in how they come to their answer.
This video demonstrates a sample problem using this method:
The partial differences method is the same as partial sums, with the only change being the introduction of negative numbers when calculating individual differences. Both of these videos show examples using a sample problem, and demonstrate a couple of different methods for organizing the numbers on the page while solving a problem.
The partial sums and partial differences method is taught in most classrooms today, so the next time your child asks you a question about their math worksheet, you will be able to jump right in! Reach out to the math specialists here at My Learning Springboard to organize individualized tutoring for your child in these and other popular classroom methods.By Brad Hoffman, M.S.Ed.
Board Certified Educational Planner and Learning Specialist
My Learning Springboard, Inc.