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5.N.2.2 Represent, read and write decimals using place value to describe decimal numbers including fractional numbers as small as thousandths and whole numbers as large as millions.

In a Nutshell

This objective is a critical one that addresses place value.  The students are coming with a background of whole number place value up to 100,000 and decimal place value to the hundredths.  The overarching goal in fifth grade for this objective is to extend whole numbers to the one millions place and decimals to the thousandths place.  Students will be required to convert between the three different forms of a number - standard, written, and expanded

Student Actions

Teacher Actions

  • Develop the Ability to Make Conjectures, Model, and Generalize by utilizing concrete models to develop conceptual understanding of decimal place value.

  • Develop the Ability to Communicate Mathematically when writing, representing, and speaking about  place value decimal numbers.

  • Develop a Deep and Flexible Conceptual Understanding of decimals by applying knowledge of whole numbers when working with tools (manipulatives, drawings, paper fold, etc.) to extend their understanding of the base ten numeration system.

  • Use and connect mathematical representations by providing concrete models to allow students to explore place value patterns (i.e. base ten unit cubes,)

  • Facilitate meaningful mathematical discourse by allowing opportunities for exploration among students involving problems with decimals, fractional numbers and place value.

  • Pose purposeful questions that promote deeper thinking and reasoning about the base ten system and place value.


Key Understandings


  • Use appropriate mathematical vocabulary

  • Read decimals using fractional language and write decimals in fractional form, as well as in expanded notation

  • Identify the equivalent  forms for a given number; i.e. multiple choice, matching, constructed response

  • Create written, expanded, and standard forms of a number

  • Standard Form:  a number written numerically

    • EX:  976

  • Written Form:  a number written in words

    • EX.  45,976 =  forty-five thousand, nine hundred seventy-six

  • Expanded Form:  a way to write numbers by adding the value of the digits

    • EX.  976 = 900+70+6

  • When writing decimal numbers in expanded form, they can be written as decimals or fractions.

    • EX.  5.732 =  5+0.7+0.03+0.002 or 5+7/10+3/100+2/1000

  • Every movement in a place value is either multiplying or dividing by a group of 10.  

    • A place value to the right is 1/10 of the previous place value and a place value to the left is 10 times the previous value.

    • EX: Possible names for the number 0.037 are: 37 thousandths; 3 hundredths + 7 thousandths and a possible name for the number 1.5 is 15 tenths

  • There is a definite difference between a “digit” and a “value” of a number.

    • EX:  976 - the digit in the tens place is a “7”, but the value of the underlined place is “70” which is seven tens.

  • That there can be more than a value of 9 in one place value.  They must understand that “value” begins with zero, and include digits 0-9.

  • They can say the word “And” in other places of a number in addition to representing the decimal point.  Teachers must encourage procedural fluency in conceptual understanding for students to NOT say or use “And” except when representing the decimal.

  • Student applies the alternate conception “Write the numbers you hear” when writing numbers in standard form given the number in words.

    • When asked to write the number five hundred eleven thousand in standard form, the student writes 500,11,000 with or without commas.

    • When asked to write the number sixty-two hundredths, student writes 62.00 or 6200.





OKMath Framework Introduction

5th Grade Introduction


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