**Chapter 11**

5th Grade Common errors relative to the standards:

The Strangeness of Ones, Tens, and Hundreds....

The use of the word ones, tens, and hundreds as a singular group name is a common error related to the standards.

"Ten ones makes one ten," This concept normally carries the usual meaning of 10 things, the amount that is 1 more than 9 things. (Ex: seven ones, a student is 7 years old...)

ELLs have a difficult time comprehending this concept.

These misunderstanding are due to the language barrier and the way in which the standard is presented.

Students fail to correctly identify that the numeral 1 in 16 corresponds to a physical representation of ten ones; instead they indicated that the 1 simply corresponds to one unit.

Misconceptions Cont....

The student recognizes simple multi-digit numbers, such as thirty (30) or 400 (four hundred), but she does not understand that the position of a digit determines its value.

Example:

Student mistakes the numeral 306 for thirty-six.

Student writes 4008 when asked to record four hundred eight,

Instructional Ideas

" "What to do?"

Provide a clear acceptance of each student. (Treat eat individual including ELLs as equal members of the class).

Make classroom activities structured and predictable (Give students a clear understanding of how task proceed).

Let students know what is expected of them (explain and demonstrate expectations about classroom rules, behaviors, and activities).

Maximize opportunities for language use (Language is really central, make it clear, express ideas, formulate questions, and explain solutions).

Provide feedback (positive reinforcement).

Use cooperative learning (group work).

Chapter 11: Developing Whole-Number Place-Value Concepts

By: Zurelys Esquijerosa, Jackie Paoli, and Maria Ramirez

Misconceptions

When counting tens and ones (or hundreds, tens, and ones), the student misapplies the procedure for counting on and treats tens and ones (or hundreds, tens, and ones) as separate numbers.

Example:

When asked to count collections of bundled tens and ones, such as

|||••, student counts 10, 20, 30, 1, 2, instead of 10, 20, 30, 31, 32.

When counting tens and ones (or hundreds, tens, and ones), the student misapplies the procedure for counting on and treats tens and ones (or hundreds, tens, and ones) as separate numbers.

The student orders numbers based on the value of the digits, instead of place value.

Example :

698 > 102, because 6 and 8 are bigger than 1 and 2.

Cont...

Student misapplies the rule for “rounding up” and changes the digit in the designated place while leaving digits in smaller places as they are.

Examples:

Student rounds 127,884 to 128,884 (nearest thousand).

Student rounds 62.38 to 62.48 (nearest tenth).

Activities

Activity #1

Cont...

Resources

America's Choice Mathematics Navigator. (n.d.). Retrieved from http://www.meridianschools.org/Staff/DistrictCurriculum/MoreResources/Math/All Grades/Misconceptions_Error 2[1].pdf

Cooper, L. (n.d.). Retrieved from http://www.bvsd.org/curriculum/math/Research Resources Instruction/Understanding Place Value.pdf

Van De Walle, J. (2013). Elementary and middle school mathematics. Upper Saddle River, NJ: Pearson

Activity #2 Place Value

Placing decimal number from lease to greatest...

Ex:

Students will get into groups of four to arrange decimal numbers as place value from least to greatest.

Then they will come to front of the class to explain the activity and demonstrate.

Demonstration of Activity