5-N-1-2


5.N.1.2 Divide multi-digit numbers, by one- and two-digit divisors, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms.

In a Nutshell

Students will be familiar with estimating a quotient first for reasonableness.  Then they will use the most efficient strategy to find the quotient and then compare with the estimated quotient.  These strategies can be the standard algorithm, partial quotients, or reverse array.

Student Actions

Teacher Actions

  • Develop a Deep and Flexible Conceptual Understanding by connecting place value (partial quotients) to understand the standard algorithm to efficiently  divide multi-digit numbers and use multiplication to check the quotient..

  • Develop Accurate and Appropriate Procedural Fluency by dividing multi-digit numbers using efficient and generalizable methods, including, but not limited to, the standard algorithm and partial quotients.

  • Develop Strategies for Problem Solving as they discover relationships between single and double digit divisors.

  • Build procedural fluency from conceptual understanding by providing activities utilizing a variety of physical models such as arrays and other manipulatives.

  • Establish mathematics goals to focus learning on both concept (meaning of division) and skill development (division).

  • Use and connect mathematical representations of repeated subtraction, multiplication, and partial quotients to help students better understand the concept of division.

  • Pose purposeful questions to help students choose efficient methods to solve particular division situations.

  • Facilitate meaningful mathematical discourse by allowing students to solve division problems with multiple strategies and encouraging them to look for the most efficient ways in a given situation. 

Key Understandings

Misconceptions

  • Understand place value in division.

  • Have more than one strategy to divide.

  • Fluently multiply in order to help with the division process,

  • Use the correct vocabulary of dividends, divisors, quotients, and remainders.

  • Understand how to use inverse operations to check their answer.

  • Divide a fraction less than one to create a decimal equivalent up to the thousandths place.

 

  • Believe that division makes the answer smaller. For example, when you divide, the answer (quotient) is smaller than the starting amount (dividend). While this is true when dividing a whole number by a smaller whole number, it is not true when the divisor is greater than the dividend.

  • Think the standard algorithm for division is a set of steps to be memorized.

  • Have overspecialized their knowledge of multiplication or division facts and restricted it to “fact tests” or one particular problem format.

  • Think that division is commutative, for example 5 ÷ 3 = 3 ÷ 5.

  • Think that the divisor must be less than the dividend. ⅘ = 4 divided by 5

OKMath Framework Introduction

5th Grade Introduction

5th Grade Math Standards