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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 › Properties of shapes

    Classifying triangles

    Students will learn how to classify triangles, given either their side lengths or their angles. Given side lengths, they'll identify whether a triangle is equilateral, isosceles, or scalene. Given angles, they'll identify whether a triangle is right, obtuse, or acute. Finally, students will consider how classification by side length and classification by angle are related. For example, have students draw a Venn diagram, with the left circle labeled isosceles, and the right circle labeled acute. Have students determine which of the regions are occupied, and which are empty. Do this for other pairs as well, such as obtuse and right.

    Watch these Khan Academy videos:

    • Classifying shapes by line and angles types
    • Classifying shapes by lines and angles
    • Classifying triangles
    • Worked example: Classifying triangles
    • Classifying triangles by angles

    Do these Khan Academy exercises:

    • Classify shapes by line and angle types
    • Classify triangles by both sides and angles
    • Identify triangles by angles
    • Identify triangles by side lengths

    Next, give your students these challenges:

    • 2018 Math Kangaroo Levels 5-6 Problem #26 by STEM4all
    • 2019 Math Kangaroo Levels 5-6 Problem #21 by STEM4all

    Conclude by leading this investigation:

    Square Dance (patterns)
    by MathPickle

    4.G.A.2: Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.

    Lessons and practice problems