• MA.5.NSO.2 Number Sense and Operations

    Add, subtract, multiply and divide multi-digit numbers.


    Add and subtract multi-digit numbers with decimals to the thousandths, including using a standard algorithm with procedural fluency. Related Benchmarks/Horizontal Alignment Terms from the K-1

    Purpose and Instructional Strategies
    The purpose of this benchmark is for students to add and subtract multi-digit numbers with decimals to the thousandths with procedural fluency. In Grade 4 (MA.4.NSO.2.7), students explored the addition and subtraction of multi-digit numbers with decimals to hundredths using money and manipulatives. In Grade 6, students add and subtract positive fractions with procedural fluency.

     To demonstrate procedural fluency, students may choose the standard algorithm that works best for them and demonstrates their procedural fluency. A standard algorithm is a method that is efficient and accurate. (MTR.3.1)

     When students use a standard algorithm, they should be able to justify why it works conceptually. Teachers can expect students to demonstrate how their algorithm works, for example, by comparing it to another method for addition and subtraction. (MTR.6.1)

     Along with using a standard algorithm, students should estimate reasonable solutions before solving. Estimation helps students anticipate possible answers and evaluate whether their solutions make sense after solving.

    Common Misconceptions or Errors

     Students can make computational errors while using standard algorithms when they cannot reason why their algorithms work. In addition, they can struggle to determine where or why that computational mistake occurred because they did not estimate reasonable values for intermediate outcomes as well as for the final outcome. During instruction, teachers should expect students to justify their work while using their chosen algorithms and engage in error analysis activities to connect their understanding to the algorithm.

    Instructional Tasks
    Instructional Task 1
    Use a standard algorithm to find the difference of eight hundred two and forty-six thousandths and three hundred and nine tenths. Explain how you use your algorithm to

    Instructional Items
    Instructional Item 1
    Find the sum and difference of 8.72 and 3.032. 



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