Math Misconceptions 2.NBT.1-4
Look closely at errors in studentsâ€™ work (formative assessment) to help you reflect and make instructional decisions to suit all studentsâ€™ needs.
When students are asked to represent a multi-digit number such as 327, a misconception is for students to represent the digit rather than the value of each digit in its position, or place, in a number. For example, a student representing the number 327 shows 3 ants, 2 ants, and 7 ants. For students to understand place value, they need to understand the relationship between the digit and the amount (or value) it represents. Students with this misconception need to have multiple experiences with the concept of “bundling”. Using a place value mat and counters, students count out nine counters, placing them in the ones place. One more one creates ten; therefore, this set of ten should be bundled (placed in a cup, rubberbanded, or connected together) and placed in the tens place to make one ten. Work should continue, bundling ten cups of ten and placing the ten tens into a bowl to create a hundred. Students also need to work with composing three digit numbers with special attention to the amount of hundreds, tens, and ones. Ask students to count objects in a variety of ways, and pose questions such as, “Would you still have 327 if you made bundles of hundreds?” By counting objects first by ones, bundling objects in tens, then bundling those objects in hundreds, and checking to see if the quantity remains the same, students are building the understanding of the relationship between the digit and the amount it represents in its place in the number. Making a transition from viewing a “hundred” as simply the accumulation of ten tens to seeing it both as ten tens and as one bundle of a hundred is an important step in understanding the structure of the base-ten system. MISCONCEPTION:
WHAT TO DO:
When students begin working with expanded form, they may see the digits of a multi-digit number in isolation and independent from their place value. For example, a student may correctly read the number 193 as â€œone hundred ninety-threeâ€? and can even count out 193 objects accurately to represent the number by creating bundles of hundreds, tens, and ones, but when asked to write the number in expanded form, the student may write 1 + 9 + 3. Use written equations to illustrate the decomposition of numbers into their expanded forms. Just as students decomposed 18 into 18 = 10 + 8 when they were in kindergarten, students can record expanded form as decompositions of each place value. MISCONCEPTION:
WHAT TO DO:
A common misconception when comparing two three-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 numbers representing the base-ten system. Have students compare two three-digit numbers based on the value of hundreds, tens, and ones and explain their thinking of why one number is greater than another. Additionally, the use of inequality symbols is still 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, “409 is greater than 349 because 4 hundreds are more than 3 hundreds”. MISCONCEPTION:
WHAT TO DO: The top picture uses an area model to compare values. The bottom pictures use place value mats to compare values. 409 > 349