Understanding the Division Algorithm

Ø  Understanding the traditional long-division algorithm is very difficult for many students because of its many steps. Often students are likely to focus on the individual digits rather than the whole numeral.  Students are taught to ignore place value as they routinely work through a procedure they don’t necessarily understand.  So, when dividing 3,208 by 8, a student who gets a quotient of 41 is unlikely to realize his/her error.  If a student were to see the digit 3 as 3,000, or the digits 3 and 2 as 3,200 instead of 32, they would have realized that 8 can go into 3,200 four hundred times as opposed to 41 times. 

 

Ideas for Instruction

v Teachers need to encourage students to develop efficient problem solving methods by providing a variety of engaging, realistic story problems.

v Have students write and solve their own story problems then record and justify their findings.

v Provide students with manipulative materials to model the story but have them also record what they have done symbolically.

v Ask students to share the strategies they used to get their answers and then discuss whether these answers make sense. 

4,327 ÷ 5=       800

4,000

   327 ÷ 5 =      60

   300

     27 ÷ 5 =      5 r 2

                                    865 r 2

 

·       Look at ways to adjust numbers to make them easier to use.  For example, when dividing 1430 ÷5, you can double the divisor from 5 to 10 and then double the dividend from 1,430 to 2,860, so the balance within the expression remains the same and the quotient is easy to compute.


Home

Counting wtih Word Numbers

Thinking Addition means "Join Together" and Subtraction means "Take Away"

Renaming and Regrouping when Adding and Subtracting Two - Digit Numbers

Misapplying Addition and Subtraction Strategies to Multiplication and Division

Multiplying Two - Digit Factors by Two - Digit Factor

Understanding Fractions

Adding and Subtracting Fractions

Representing, Ordering and Adding/ Subtracting Decimals