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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 › Decimal arithmetic

    Decimal arithmetic

    Students will learn how to add, subtract, multiply and divide decimals to hundredths. They'll start with manipulatives and pictures, then gradually move away from them. Students will solve both geometry problems and mathematical ones. For example, given a rectangle with decimal numbers as side lengths, students can find its perimeter to practice adding decimals, and find the area of the rectangle to practice multiplying decimals. Here's such an example.

    Watch these Khan Academy videos:

    • Subtraction strategies with hundredths
    • More advanced subtraction strategies with hundredths
    • Strategies for subtracting more complex decimals with tenths
    • Strategies for subtracting basic decimals
    • Strategies for dividing by tenths
    • Multi-digit division strategies for decimals
    • Division strategies for decimal quotients
    • Developing strategies for multiplying decimals
    • Intro to multiplying decimals
    • Introduction to adding decimals: tenths
    • Adding decimals with ones and tenths parts
    • Multiplying decimals: place value
    • Adding decimals with ones, tenths and hundredths
    • Adding decimals with hundredths
    • Dividing whole numbers to get a decimal
    • Developing strategies for multiplying 2-digit decimals

    Do these Khan Academy exercises:

    • Subtract decimals like 67.89-6
    • Multiply whole numbers by 0.1 and 0.01
    • Subtract decimals like 1.6-0.3
    • Multiply whole numbers and decimals
    • Estimating with multiplying decimals and whole numbers
    • Subtract decimals like 0.75-0.56
    • Divide whole numbers by 0.1 or 0.01
    • Subtract decimals like 56.8-17.9
    • Multiply decimals tenths
    • Subtract decimals visually
    • Add decimals visually
    • Estimating with adding decimals
    • Divide decimals by whole numbers visually
    • Divide decimals by whole numbers
    • Add decimals like 40.1+7.6
    • Multiply decimals (up to 4-digit factors)
    • Multiply whole numbers and decimals less than 1
    • Subtract decimals like 78.4-3
    • Understand multiplying decimals
    • Subtract decimals like 15-7.45
    • Add decimals like 5.53+6.1
    • Add decimals like 0.76+0.21
    • Subtract decimals like 0.9-0.7
    • Estimating with dividing decimals
    • Estimating with subtracting decimals
    • Divide whole numbers to get a decimal (2-digit divisors)
    • Divide whole numbers to get a decimal (1-digit divisors)
    • Divide whole numbers by decimals visually
    • Multiply decimals (1&2-digit factors)
    • Divide whole numbers by decimals
    • Subtract decimals like 0.6-0.43
    • Represent decimal multiplication with grids and area models
    • Multiply decimals and whole numbers visually
    • Estimating with multiplying decimals
    • Add decimals like 4+5.7
    • Add decimals like 47.75+11.98
    • Add decimals like 0.7+0.5

    Next, give your students these challenges:

    • Domino Number Patterns by NRICH
    • 2017 Math Kangaroo Levels 5-6 Problem #26 by STEM4all

    Conclude by leading this investigation:

    Multiplicative Persistence
    by MathPickle

    5.NBT.B.7: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

    Lessons and practice problems