Math Misconceptions 1.NBT.2-3
Look closely at errors in students’ work (formative assessment) to help you reflect and make instructional decisions to suit all students’ needs.
When students are asked to represent a set of 32 objects, a misconception is for students to represent the digits rather than the amount. For example, a student may use 3 ants and 2 ants as their representation. For students to understand place value, they need to understand the relationship between the number and the amount it represents. Students need to have multiple experiences with bundling ten ones to create a ten when counting objects. They need to work with composing two digit numbers with special attention to the amount of tens and ones.. Ask students to count objects in a variety of ways, and pose questions such as, “Would you still have 32 if you made bundles of ten?” By counting objects first by ones, then bundling objects in tens and checking to see if the quantity remains the same, students understand the relationship between the number and the amount it represents. Making a transition from viewing a “ten” as simply the accumulation of ten ones to seeing it both as ten ones and as one bundle of ten is an important step in understanding the structure of the base-ten system. MISCONCEPTION:
WHAT TO DO:
A common misconception when comparing two two-digit numbers is for students to not attend to the value of each digit. They may look at the digits involved in the comparison and think of them as isolated numbers, rather than composed numbers representing the base-ten system. Have students compare two two-digit numbers based on the meaning of tens and ones and explain their thinking of why one number is greater than another. Additionally, the use of inequality symbols is new and practice is needed to learn the proper names and meanings of each symbol, just as students have to learn the meaning of the equal sign or an operational symbol. Work repeatedly with inequality symbols by recording oral statements such as, “51 is greater than 39”. MISCONCEPTION:
WHAT TO DO:
“40 is greater than 34.” 40 > 34