• MA.5.NSO.1 Number Sense and Operations

    Understand the place value of multi-digit numbers with decimals to the thousandths place.


    MA.5.NSO.1.1

    Express how the value of a digit in a multi-digit number with decimals to the thousandths changes if the digit moves one or more places to the left or right.

    Purpose and Instructional Strategies
    This purpose of this benchmark is for students to reason about the magnitude of digits in a number. This benchmark extends the understanding from Grade 4 (MA.4.NSO.1.1), where students expressed their understanding that in multi-digit whole numbers, a digit in one place represents 10 times what it represents in the place to its right and 1/10 of what it represents in the place to its left. All of this work forms the foundation for arithmetic and algorithms with
    decimals which is completed in Grade 6 (MA.6.NSO.2.1).

     To help students understand the meaning of the 10 𝑡𝑖𝑚𝑒𝑠 and 1/10 of relationship, students can use base ten manipulatives or simply bundle classroom objects (e.g., paper clips, pretzel sticks). Students should name numbers and use verbal descriptions to explain the relationship between numbers (e.g., “6 is 10 times greater than 6 tenths, and 6 tenths is 1/10 of 6”). In addition to physical manipulatives, place value charts help students understand the relationship between digits in different places. (MTR.2.1)

     Instruction of this benchmark should connect with student work with whole numbers. For example, students who understand 35 × 2 = 70 can reason that 3.5 × 2 = 7 because 3.5 is 1/10 of 35, therefore its product with 2 will be 1/10 of 70. (MTR.5.1) 

    Common Misconceptions or Errors

     Students can misunderstand what “ 1/10 of” a number represents. Teachers can connect 1/10 of to “ten times less” or “dividing by 10” to help students connect 1/10 of a number to 10 times greater.

     Students who use either rule “move the decimal point” or “shift the digits” without understanding when multiplying by a power of ten can easily make errors. Students need to understand that from either point of view, the position of the decimal point marks the transition between the ones and the tenths place.

    Instructional Tasks
    Instructional Task 1
    At the Sunshine Candy Store, salt water taffy costs $0.18 per piece.
    Part A. How much would 10 pieces of candy cost?
    Part B. How much would 100 pieces of candy cost?
    Part C. How much would 1000 pieces of candy cost?
    Part D. At the same store, you can buy 100 chocolate coins for $89.00. How much does each chocolate coin cost? Explain how you know.

    Instructional Items
    Instructional Item 1
    Which statement correctly compares 0.034 and 34?
    a. 0.034 is 10 times the value of 34.
    b. 0.034 is 1/10 the value of 34.
    c. 0.034 is 1/100 the value of 34.
    d. 0.034 is 1/1000 the value of 34.

    Instructional Item 2
    What number is 100 times the value of 45.03? 
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