5.NBT.5-7 Math Misconceptions

Math Misconceptions 5.NBT.5-7

Look closely at errors in students’ work (formative assessment) to help you reflect and make instructional decisions to suit all students’ needs.

By the end of the 5th grade school year, students are expected to be able to fluently multiply multi-digit whole numbers using the standard algorithm. In mathematics, an algorithm is defined by its steps and not by the way those steps are recorded in writing. With this mind, minor variations in the methods of recording the standard algorithm are acceptable. Errors in multi-digit multiplication can range from minor mistakes in computation, to larger misconceptions where students do not fully understand the value of each digit. A common error is the omission of one or more zeros to represent the multiplication of a power of ten. Have students show their thinking in a variety of ways, including concrete models and visual representations. Another common misconception is that multiplication always makes things bigger. This “rule” or “statement” is not always true, as students should conclude as they make connections to what they know about multiplication with whole numbers to multiplication with fractions.

MISCONCEPTION:

WHAT TO DO:

When using place value strategies and properties of operations to solve division problems, students may get confused and develop misconceptions about the “unknowns” in the context of the problem. It’s important for students to first determine the situation of the “unknown” in a problem: group size unknown or number of groups unknown. These different situations are highlighted in the CCSS on page 89 and are included in this BLAST module (page 5 sidebar). Division standards should be worked with in connection with the multiplication standards, as they have a relationship to each other (inverse operations).

Students can work with up to four-digit dividends and two-digit divisors by creating equal groups, using partial quotients, and with all of the same models as multiplication. Students may conclude that dividing numbers always creates smaller quotients, but caution should be taken because that “rule” doesn’t work in all situations as students should determine as they make connections to what they know about division with whole numbers to division with fractions. Students often forget that when numbers are being divided, we are creating equal groups or sharing. As students work with their own division strategies, make sure that they can articulate why they work and how they know their answer makes sense.

MISCONCEPTION:

WHAT TO DO:

When students begin to perform operations with decimals, they may incorrectly apply the generalizations of what they already understand about operations with whole numbers. In order for students to perform operations with decimals, they need to have a firm grasp on the quantities of decimals, which can be modeled and illustrated through concrete materials and drawings. Fifth grade teachers should provide experiences with decimal operations in the same way that primary teachers provide experiences with whole number operations. Keep in mind that students need to attend to the meaning of the operation and perform these operations using their knowledge of place value and properties of operations.

Have students estimate solutions prior to modeling and computing with decimals to reinforce the reasonableness of answers.

MISCONCEPTION: Addition Example

Multiplication Example

WHAT TO DO:

If this represents one whole…

then this represents one tenth…

and this represents one tenth of the tenth… or 0.01

one tenth of one tenth is one hundredth 0.1 x 0.1 = 0.01