Rounding & Estimating are difficult concepts for students to understand and apply. Many students when learning how to estimate or to round a number learn a basic procedure to help them understand the process. For example, we have always heard the saying, “If it is 5, 6, 7, 8, 9 round up” but if it’s 1, 2, 3, 4 round down.”
During a math lesson last week children appeared to get this “procedural concept”; however, I was skeptical that they fully understood the application of the process. The number 77 was presented and students were asked to round the number to the nearest ten. One student underlined the 7 in the ones column and claimed that the number would be rounded up to 80. When I asked the student to explain “WHY” he replied, “Um because it ends in 7 and we round up.” When I asked him to elaborate, he explained that he just knew the rule but really wasn’t sure why that was.
I then put an abacus in front of the class and and asked them to look at the number “77.” Then I posed the same question: “Why would your round 77 to 80 and not to 70?” Students shared with their elbow partner and reasoned with each other. It was fascinating watching lightbulbs go off for those students who didn’t really understand rounding. For the first time they were able to see the concrete representation of the mathematical concept being taught. Many of them had great mathematical explanations for why it would be easier to move just 3 beads to get to or round to 80 versus moving 7 beads to go back or round down to 70. We selected specific “at-risk” students to prove their answer on the abacus while working with the activity in the math workshop that day.
Using an abacus to “round” can help students visualize a concept that is more abstract.
Food for thought: Which of the 8 Mathematical Practice Standards is this using?? Feel free to comment and share whatcha think or more ideas!