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    • ▾5th grade
      • ▸Decimal place value
        • •Decimal place value
        • •Hashi puzzles
        • •Decimals to thousandths
        • •Rounding decimals
      • ▾Multi-digit multiplication and division
        • •Multiplying whole numbers by 10, 100, and 1000
        • •Multiplying and dividing decimals by 10, 100, and 1000
        • •Convert fractions to decimals, 10, 100, or 1000 in the denominator
        • •Multiplication, partial products method
        • •Long division
      • ▸Decimal arithmetic
        • •Decimal arithmetic
        • •Dividing whole numbers to get a decimal
      • ▸Add and subtract fractions
        • •Add and subtract fractions, abstract
        • •Adding and subtracting mixed numbers with regrouping
        • •Add and subtract fractions, word problems
      • ▸Multiply fractions
        • •Multiplication as scaling
        • •Areas and perimeters, fractional side lengths
        • •Multiply fractions, abstract
        • •Multiply fractions, word problems
      • ▸Divide fractions
        • •Understanding fractions as division, word problems
        • •Dividing whole numbers by unit fractions
        • •Dividing unit fractions by whole numbers
        • •Dividing mixed numbers
      • ▸Volume
        • •Volume by counting unit cubes
        • •Volume of right rectangular prisms by multiplying
        • •Volume of composite right rectangular prisms
        • •Volume, word problems
      • ▸Coordinate plane
        • •Plot coordinates
        • •Plot coordinates from word problems
      • ▸Algebraic thinking
        • •Intro to parentheses
        • •Distributive property without variables
        • •Convert between words and arithmetic expressions
        • •Linear equations, tables
      • ▸Measurement and data
        • •Unit conversion
        • •Represent and reason with line plots
      • ▸Properties of shapes
        • •Geometric definitions
        • •Classifying shapes
        • •Classifying triangles
        • •Classifying polygons
        • •Symmetries of regular polygons
        • •Quantifiers
     › 5th grade › Multi-digit multiplication and division

    Long division

    Students will learn how to divide up to four-digit dividends by two-digit divisors. Start with manipulatives and pictures, then gradually move away from them. Students should also be shown how to divide by connecting dots, as seen here. Before attempting to understand long division, students should know their multiplication facts very well. Conclude by giving your students this challenge:

    The solution can be seen by watching either this video, or this one. However, I recommend watching both, as the first video has a better explanation of the solution, but the second video demonstrates a shortcut. Namely, that performing the entire division, for each case, is unnecessary once a digit reoccurs in the quotient. For example, 222222/6 = 3703... which we stop because 3 has reoccured. We know that no digit can reoccur because ABCDE represent unique digits.

    Watch these Khan Academy videos:

    • Dividing by 2-digits: 9815÷65
    • Dividing by 2-digits: 7182÷42
    • Strategies for dividing multiples of 10, 100, and 1000
    • Introduction to dividing by 2-digits

    Do these Khan Academy exercises:

    • Division by 2-digits
    • Estimate multi-digit division problems
    • Divide by taking out factors of 10
    • Basic multi-digit division

    Next, give your students this challenge:

    2020 Math Kangaroo Levels 1-2 Problem #23 by STEM4all

    Conclude by leading this investigation:

    Half Fraction Snake
    by MathPickle

    5.NBT.B.6: Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

    Lessons and practice problems