Look closely at errors in studentsâ€™ work (formative assessment) to help you reflect and make instructional decisions to suit all studentsâ€™ needs.
When looking at the properties of operations, students often have several misconceptions. Students discover that addition is commutative because they are presented with the idea that 307+576 and 576+307 are related expressions. However, some students do not understand why addition is commutative. Addition is the sum of two or more groups and the order does not change the result. This is important to understanding the addition operation. Without an understanding of why addition is commutative, students overgeneralize and begin thinking that subtraction is also commutative. It’s important for students to understand that subtraction is finding the difference or distance of two quantities. MISCONCEPTION:
WHAT TO DO: Addition is commutative. 576 + 307 = 307 + 576 800 (8 flats) + 70 (7 rods) + 13 (units) = 883
Subtraction is not commutative.
* Remember to not say, “You can’t subtract 500 from 300.” In years to come, students will subtract these values when they begin their work with negative numbers.
Students may form misconceptions about addition and subtraction when the operations are taught in isolation and/or they are not given enough experiences to understand and apply invented strategies. Rather than viewing the operations separately, students’ strategies should demonstrate their abilities to use properties and operations to solve a problem. In this example, the misconception shows that the student thinks that the only available operation to use is subtraction when working to “subtract” numbers. However, invented thinking and strategies would allow the student to use subtraction first, but yet realize that addition is also needed to replace the additional values that were taken away. MISCONCEPTION:
WHAT TO DO:
You have $304, and you are buying the newest iDevice product for $198. Explain and model how much money you would have after you purchase your product.
Mentally finding 10 more, 10 less, 100 more, or 100 less than a number may be difficult for a student who does not fully understand the structure of the base-ten system. If a student has to use counting strategies to complete this mental exercise, then itâ€™s clear that the student needs more attention to base-ten concepts with concrete materials, hundreds charts, and bundling ten ones into a group of ten or ten tens into a group of one hundred before mental calculations can be expected. Additional work with decomposing and representing numbers in different ways can also be effective. For example, given the number 57, students can practice representing that number with an equation such as 57 + 10 = 67. You can also use expanded form to help identify the hundreds place value or tens place value to add to or subtract from. MISCONCEPTION:
WHAT TO DO: Students need bundling experiences prior to working with hundreds charts or any pictorial representations.